Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy

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Thesis

Reference

Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy

MCKEOWN WALKER, Siobhan

Abstract

In this thesis I have investigated the electronic structure of two-dimensional electron liquids (2DEL) induced at different surfaces of the transition metal oxide band insulators SrTiO3, KTaO3 and anatase TiO2 by angle-resolved photoemission spectroscopy (ARPES). I present high-resolution ARPES data, spin-resolved ARPES data and the results of self-consistent tight binding supercell calculations of 2DEL band structures.

MCKEOWN WALKER, Siobhan. Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy . Thèse de doctorat : Univ.

Genève, 2016, no. Sc. 4939

URN : urn:nbn:ch:unige-882537

DOI : 10.13097/archive-ouverte/unige:88253

Available at:

http://archive-ouverte.unige.ch/unige:88253

Disclaimer: layout of this document may differ from the published version.

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UNIVERSITÉ DE GENÈVE Département de Physique de la Matière Quantique

FACULTÉ DES SCIENCES Professeur Felix Baumberger

Two Dimensional Electron Liquids at Oxide Surfaces Studied by Angle Resolved Photoemission Spectroscopy

THÈSE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de docteur ès Sciences, mention Physique

par

Siobhan McKeown Walker de

Leeds (Royaume-Uni)

Thèse n 4939

GENÈVE

Atelier d’impression ReproMail 2016

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Il faut deux choses: de l’enthousiasme et de la lucidité.

Gaston Rébuﬀat

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Résumé

Les oxydes de métaux de transition SrTiO3, KTaO3et TiO2 anatase sont des isolants de bande induisant des liquides d’électrons à deux dimensions (2DEL: 2D electron liquids) sur diﬀérentes surfaces. Dans cette thèse, j’ai étudié la structure électronique des ces 2DEL en utilisant la photoémission résolue en angle (ARPES: Angle Resolved Photoemission Spectroscopy).

Je présente d’abord la structure détaillée des sous-bandes du 2DEL de la surface SrTiO3(001) en utilisant l’ARPES à haute résolution (HR- ARPES). Celles-ci montrent que les sous-bandes sont polarisées orbitalement et sont bidimensionnelles, ce qui s’explique par le confinement quantique dû à la courbure des bandes à la surface du SrTiO3. La structure trouvée expérimentalement est cohérente avec les résultats du calcul auto-consistant sur une super-maille, obtenu avec la méthode des liaisons fortes, et qui modélise la courbure de la bande à la surface en faisant varier le potentiel avec la couche atomique. Les données ARPES résolues en spin, mesurées avec une résolution de 100 meV, indiquent que la polarisation du photocourant est négligeable. Ceci s’accorde bien avec les calculs de structure de bande : si le couplage de type Rashba est faible sur la plus grande partie de la surface de Fermi, près des points de croisement évités dans les sous-bandes, ce couplage de type Rashba augmente pour atteindre des valeurs atteignant 10 meV, et ce à cause d’un rétablissement partiel du moment cinétique orbital. En exposant la surface alternativement aux rayons ultra-violets et à l’oxygène, on démontre que le 2DEL apparaissant à la surface du SrTiO3 est dû à des lacunes d’oxygène créées par des désexcitations Auger interatomiques induites par des photons. Avec ce lien, on a pu faire varier la densité des porteurs de charge confinés et ainsi analyser l’évolution du couplage électron- phonon avec la densité du 2DEL. Lorsque la densité est faible, des bandes dispersives apparaissent, qui sont les répliques de celles croisant le niveau de Fermi, et que l’on interprète comme des signatures d’un liquide de polarons de Fröhlich stabilisé par un couplage à longue portée à un unique phonon

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optique d’environ 100 meV. En augmentant la largeur de bande jusqu’à ce qu’elle dépasse la fréquence de ce phonon, le système évolue vers un état métallique plus conventionnel, dont la principale signature spectroscopique est un point de rupture de pente dans la relation de dispersion, indiquant un couplage électron-phonon à faible portée modéré.

Les données du 2DEL de la surface (111) du SrTiO3avec l’HR-ARPES montrent les eﬀets de la direction du confinement sur le 2DEL. En eﬀet, en comparant sa structure électronique à celle du bulk dans le plan (111), on montre que ce confinement entraîne une forte augmentation de la masse.

Contrairement au cas de la surface (001), le 2DEL de la surface (111) du SrTiO3 n’est pas polarisé orbitalement car les trois orbitales atomiques t2g

sont équivalentes pour la direction de confinement, (111). Pour le KTaO3, un oxyde de métal de transition 5d, le 2DEL de la surface (111) a une interaction spin-orbite atomique beaucoup plus importante que le composé isostructurel SrTiO3.

L’étude de la structure électronique du 2DEL à la surface reconstruite 4x1 de films minces de TiO2 anatase permet d’analyser les eﬀets de la reconstruction de surface et de la tension dûe à la croissance épitaxiale. Ces eﬀets sont également mis en évidence grâce à des calculs sur une super-maille de TiO2: on retrouve le gap unidirectionnel au niveau de Fermi observé expérimentalement avec succès.

Finalement, je présente des résultats préliminaires annonçant qu’exposer la surface de l’isolant de Mott LaTiO3à de faibles doses d’oxygène n’introduit pas de porteurs de charge itinérants.

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Abstract

In this thesis I have investigated the electronic structure of two-dimensional electron liquids induced at diﬀerent surfaces of the transition metal oxide band insulators SrTiO3, KTaO3and anatase TiO2by angle-resolved photoemission spectroscopy (ARPES). I first present high-resolution ARPES data detailing the subband structure of the SrTiO3 (001) surface 2DEL. These data show an orbitally polarized ladder of subbands with two-dimensional character which is explained in the context of quantum confinement due to band bending at the SrTiO3surface. The experimental subband structure shows good agreement with the results of self-consistent tight binding supercell calculations which model surface band bending through on-site potential terms. I further present spin-resolved ARPES data revealing negligible polarization of the photocurrent measured with an energy resolution of

⇠100meV, typical of such experiments. This is found to be consistent with our band structure calculations which predict an unconventional Rashba coupling that is small for large parts of the Fermi surface but increases near avoided crossings in the subbands ladder up to values of⇠10 meV, due to a partial restoration of the orbital angular momentum. Using alternate exposure of the surface to UV and oxygen, it is demonstrated that the SrTiO3

surface 2DEL originates from oxygen vacancies created by photon-induced inter-atomic Auger processes. Using this understanding to tune the density of confined carriers, the evolution of electron-phonon coupling as a function of the 2DEL density is studied. At low density dispersive replica bands are found and are interpreted as signatures of a liquid of Fröhlich polarons stabilized by long-range coupling to a single optical phonon of⇡100meV.

As the bandwidth is increased to exceed the frequency of this phonon, the system evolves to a more conventional metallic state whose principal spectroscopic signature is a low energy kink in the subband dispersion indicative of moderate short-range electron-phonon coupling.

The eﬀects of confinement direction on the SrTiO3 2DEL electronic

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structure are revealed in this thesis by HR-ARPES data from the 2DEL at the (111) surface of SrTiO3. Compared to the bulk band structure in the (111) plane, a strong mass enhancement is observed. This is shown to originate purely from confinement effects. In strong contrast to the case of the (001) surface, the SrTiO3 (111) 2DEL is not orbitally polarized, which can be traced back to the rotational equivalence of thet2g atomic orbitals along the confinement direction. This study is extended to include results from the 2DEL at the (111) surface of the 5dtransition metal oxide KTaO3 which has far greater atomic spin orbit interaction than the isostructural SrTiO3. The effects of surface reconstruction and epitaxial strain are explored by studying the electronic structure of the 2DEL at the4⇥1reconstructed (001) surface of anatase TiO2 thin films. Supercell calculations simulating the effect of this reconstruction successfully reproduce the unidirectional band gap at the Fermi level observed experimentally. Finally, I present preliminary results showing that exposing the surface of the Mott insulator LaTiO3to low doses of oxygen does not introduce itinerant carriers.

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CHAPTER 1 Introduction

1.1 Oxide Electronics

Two-dimensional electron gases (2DEGs) at semiconductor interfaces form the basis of modern electronics. Band alignment in semiconductor- semiconductor heterostructures such as GaAs/AlxGa1 xAs generally causes band-bending at the interface resulting in a narrow charge accumulation layer. The utility of such 2DEGs lies in their response to externally applied fields. The canonical example of a device using a 2DEG is silicon-based metal-oxide-semiconductor field eﬀet transistors (MOSFET). In a MOSFET a metal "gate" is separated from the conducting channel by a dielectric oxide.

The gate applies an external electric field which modulates the strength of the confining potential in the semiconductor thereby changing the density of charge carriers which can switch the conductivity of a conducting channel.

The response of such 2DEGs to external magnetic fields has lead to fundamental advances in physics such as the discovery of the integer quantum Hall eﬀect [1]. Semiconductor 2DEGs have also been used to achieve purely electrostatic control of the electron spin. The broken inversion symmetry inherent to 2DEGs induced by band bending at interfaces or surfaces leads to a lifting of the spin degeneracy via the Rashba eﬀect [2, 3]. The magnitude of the degeneracy lifting can be controlled by modifying the band bending potential with a gate voltage. This has permitted the electrostatic tuning of the spin precession length and, combined with ferromagnetic source and drain electrodes, has permitted the realization of the first spin FETs [4, 5].

Engineering 2DEGs with more exotic responses to external stimuli could

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Figure 1.1:Sketch from reference [6] showing the degrees of freedom that may be manipulated at transition metal oxide interfaces and surfaces.

result in advanced functionalities beyond those of contemporary devices. In materials where the electrons do not behave as a gas of independent fermions, but rather interact strongly with each other and bosonic degrees of freedom can have multiple ground states as a function of density. Thus combining the tunability of semiconductor heterostructures with the rich properties of correlated electron systems is a central goal in materials science.

Transition metal oxides (TMOs) are particularly promising in this respect [7]. They exhibit many ground states including ferroelectric, (anti- )ferromagnetic and quantum para-electric insulators as well as Fermi liquids and both BCS and high-Tcsuperconducting states. The phase diagram of the cuprates highlights the importance and non-trivial evolution of correlations in TMO systems, for example by showing proximity between superconducting and insulating anti-ferromagnetic ground states.

Advances in epitaxial film growth have enabled atomic scale precision interface engineering in TMOs [8]. The ABO3perovskite TMO materials have received much attention in recent years because their quasi-cubic structures and compatible lattice constants make them well suited to heterostructure growth. In this family of oxides, the formal valence of the transition metal ions and hence the occupancy of the atomic d orbitals which form the conduction band plays a key role in defining the ground state of the system [9]. Thus charge accumulation or charge leakage [10] at interfaces may alter the phase of the interface with respect to the bulk constituents. For example by inducing a superconducting interface between two band insulators [11], or a ferromagnetic interface between two anti-ferromagnets [12]. Additionally,

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1.2 LaAlO3/SrTiO3 interface

Figure 1.2: A sketch of the polar catastrophe scenario proposed to result from an atomicly sharp (001) interface between SrTiO3 and LaAlO3. Considering the oxidation states of the atoms in the unit cell, each layer can be assigned a charge, indicated by black numbers, in units of the elementary charge per unit cell. SrTiO3

has non polar layers (green/yellow) while LaAlO3has layers of alternating±1charge (blue/orange). In the "perfect" heterostructure (left) this leads to a build up of potential V in the LAO layer. The transfer of 0.5eper unit cell from the LAO surface to the interface (right) prevents a diverging potential build up in the LAO.

From [7].

broken inversion symmetry and changes in correlation strengths at interfaces may alter the interplay of charge, spin, orbital and lattice degrees of freedom (as sketched in Fig. 1.1) leading to novel phases that do not exist in the bulk

materials.

1.2 LaAlO

₃

/SrTiO

₃

interface

The two-dimensional electron system observed at the interface between the band insulators LaAlO3 and SrTiO3 [11] has emerged as a particularly promising model system combining high mobility with properties such as gate-tunable superconductivity [13] and its possible coexistence with mag- netism [14] and gate-tunable Rashba spin-orbit coupling [15]. While the expression "2DEG" is applicable to semiconductor interfaces where charge carrier motion is unaﬀected by interactions, in oxide interfaces correlation eﬀects cannot be neglected. Thus a two-dimensional system at an oxide interface, where masses are nominally larger and many body interactions are important is better described as a two-dimensional electron liquid (2DEL).

The origin of the charge carriers in the LAO/STO 2DEL has long been a subject of debate. An intrinsic mechanism for the accumulation of charges at the interface invokes electronic reconstruction necessitated by the diverging electrostatic potential arising from the stacking of polar LAO and non-polar STO crystal structures along the [001] direction. This polar catastrophe mechanism is illustrated in Fig. 1.2 and predicts an interfacial carrier density

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Figure 1.3:(a) Ideal cubic structure of ABO3perovskites. The A atom (for example strontium), B atom (for example titanium) and oxygen atoms are shown as green, grey and red respectively. The unit cell boundary is indicated by solid black lines and an undistorted oxygen octahedral is represented by dashed black lines. (b) The superconducting transition temperature Tc of bulk STO as a function of excess electrons per unit cell x for both reduced and Nb substituted STO. The approximate correspondence with the superconducting phase of LAO/STO interfaces is indicated by the red shaded are. From reference [23].

of3.3⇥10¹⁴ cm ²(or 0.5 electrons per unit cell) and a critical thickness of the LAO layer for a metallic interface of 3-4 unit cells. The critical thickness has been demonstrated experimentally [16], however Hall measurements indicate interfacial carrier densities are an order of magnitude lower than those predicted by the ideal polar catastrophe scenario. Additionally, the potential gradient expected inside the LAO layer within this scenario as well as the corresponding hole band arising from the transfer of half an electron per unit cell from the LAO surface to the interface have not been seen by spectroscopic measurements [17–19]. It is possible that other mechanisms also donate electrons to the interface. Defects such as cation intermixing [20] and oxygen vacancies [21] at the interface have also been suggested as electron sources. In STO/LAO/STO heterostructures is was shown that the charge carriers are distributed predominantly on the STO side of the conducting interface [22] suggesting that, no matter the origin of the carriers the electronic properties of the interface are defined by STO.

Indeed 2DELs have been created in STO (001) single crystals by very diﬀerent means, such as bombardment by Ar⁺ ions [24], electrolyte gating [25], hydrogen adsorption [26] or deposition of amorphous [27] and non- perovskite oxides [28]. The resulting 2DELs all display similar electronic transport phenomena, suggesting a common underlying electronic structure defined by the properties of STO.

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Figure 1.4:Sketch of the three dimensional Fermi surface corresponding to bands arising from thet2gmanifold in a cubic environment in the absence of atomic spin- orbit coupling, which is representative of the bulk Fermi surface of electron doped STO.

1.2 Bulk properties of SrTiO3

The bonding in ABO3 perovskites is predominately ionic with the transition metal selectrons transferred to the oxygen 2porbitals. In stoichiometric form SrTiO3 is a band insulator with a⇠3.2 eV gap and 3d⁰ electronic configuration. STO has a Goldschmidt tolerance factor of⇠1which reflects that in an ideal cubic structure, the atomic radii of the O² , Sr²⁺ and Ti⁴⁺

ions just touch each other. Greater mismatch of atomic radii in other ABO3

perovskites (indicated by a Goldschmidt factor6= 1) is accommodated by distortions of the cubic structure. Thus at room temperature STO is cubic and as shown in Fig. 1.3(a) the transition metal ions sit within undistorted octahedra of oxygen atoms (indicated by dashed lines in Fig. 1.3(a)). The cubic crystal field of SrTiO3lifts the degeneracy of the 3dorbitals, lowering the energy of thet2gmanifold with respect to theegmanifold. For degenerate t2gorbitals the conduction band is formed of three bands of uniquelydxy,dxz

ordyz orbital character each with fully quenched orbital angular momentum.

The strong anisotropy of these orbitals results in two bands with light band mass and one with a comparably heavy band mass along each of the cubic axes such that the Fermi surface would have three intersecting ellipsoids with long axes along the high symmetry directions as shown in Fig. 1.4.

Weak spin-orbit coupling results in orbital mixing which lightly lifts the Gamma point degeneracy of thet2g conduction band minimum by⇠30meV as shown in Fig. 1.5(a). At⇡105K STO undergoes a tetragonal distortion, where neighbouring oxygen octahedra alternately rotate around thec axis.

This raises the energy of dxy orbitals, leading to a further lifting of the degeneracy of the conduction band minimum as shown in Fig. 1.5(b).

STO becomes a Fermi liquid at extremely low carrier densities [29–31]

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50

40

30

20

10

0

Energy (meV)

0.2 0.1

0

k_x (π/a) 50

40

30

20

10

0

Energy (meV)

0.2 0.1

0

k_x (π/a)

Tetragonal (a) (b)

Cubic

Figure 1.5:Low energy conduction band dispersion of bulk STO along the [100]

(orkx) direction from DFT calculations including atomic spin-orbit coupling.(a) A calculation for the cubic structure of STO. (b) A calculation for the tetragonal structure of STO from reference [29]. The conduction band minimum has been set to zero in both cases.

which can be achieved by chemical doping by substitution of Sr²⁺ by La³⁺

or Ti⁴⁺ by Nb⁵⁺ or by the inclusion of oxygen vacancies giving SrTiO3

[32]. Metallic STO is superconducting with a transition temperature Tc that follows a dome-like evolution (Fig. 1.3) as a function of carrier density [23, 33]

with T^maxc ⇠400mK. Within a BCS framework, superconductivity at such low densities is indicative of very strong pairing potential. Other important properties of STO include quantum paraelectric behaviour and field and temperature dependent dielectric constant [34]. With low temperature values on the order of 10000 this plays a central role in defining the spatial extent of 2DELs in STO [35].

1.2 Interface Band Structure

Electronic transport experiments have established the thermodynamic phase diagram of the LAO/STO 2DEL as a function of carrier density and provided evidence for a complex electronic structure with multiple subbands [36, 37].

Direct evidence for orbital polartization was provided by x-ray absorption spectroscopy linear dichroism [38]. These experiments find that the energy

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Figure 1.6:The band structure found by DFT calculations for a supercell of STO and LAO. The orbital character of the bands is indicated. The inset shows the corresponding Fermi surface. From reference [41].

of thedxy orbitals is lowered at the interface which is qualitatively consistent with first-principles electronic structure calculations [39–41]. One such calculation from reference [41] is shown in Fig. 1.6. When the energy scale of confinement is larger than the few meV energy scales of the tetragonal distortion and spin-orbit coupling (shown in Fig. 1.5) the orbital character of the bands is defined by their symmetry with respect to the interface, and multiple orbitally polarized subbands are expected. As shown by Fig. 1.6 the subband with the highest binding energy is expected to havedxyorbital character and light in-plane eﬀective mass while heavy bands ofdxz/yz character are much shallower in energy. Neglecting hybridization eﬀects such as can be seen in the inset of Fig. 1.6, this subband structure corresponds to a two-dimensional Fermi surface formed of concentric circular sheets ofdxy

character intersected by cigar-shaped sheets ofdxz/yz character.

Determining the intricacies of the subband structure for a real interface will help provide constraints for future band structure calculations and is an important step towards understanding the underlying physics of this system.

Both resonant inelastic x-ray scattering (RIXS) [42, 43] and resonant soft x-ray ARPES (SX-ARPES) [19, 44] experiments on the LAO/STO interface have made progress in this direction. As shown in Fig. 1.7 SX-ARPES data reveal orbital symmetries and Fermi surface volumes qualitatively consistent with transport measurements and calculations. However, the details of the subbands at the Fermi level and their bandwidths are not resolved due to the experimental limitations inherent to probing a buried interface with a surface sensitive technique such as photoemission spectroscopy.

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Figure 1.7:Sofy x-ray angle resolved photoemission spectroscopy measurements of LAO/STO interfaces. (a) Energy momentum dispersion along the [100] direction from reference [19] reveals bands ofdxy orbital character. (b) Fermi surface from reference [45] (in four Brillouin zones) reveals Fermi surface sheets elongated along thek_y/xaxes corresponding to band derived fromd_xz/yzorbitals respectively.

1.3 Bare SrTiO

₃

(001) surface

In 2011 it was shown in two papers by Meevasanaet al.[46] and Santander- Syroet al.[47] that the bare surface of SrTiO3 supports a 2DEL. La:STO, Nb:STO and stoichiometric insulating STO cleavedin situ were all shown to exhibit the same universal subband structure at the surface. While the density of the surface 2DEL was estimated to be an order of magnitude higher than the interface 2DELs, the subband structure was consistent with that of calculations for the LAO/STO interface suggesting that this surface system may be able to provide important insights into the physics at the interface. Furthermore subsequent band structure calculations predicted similar electronic structure for both surface and interface systems [40, 48].

The authors of both papers observed that the O2pvalence band on an STO surface that supported a 2DEL was shifted to lower binding energies and that there were non-dispersive in-gap states approximately 1.3 eV below the Fermi level in addition to the spectral weight at the Fermi level associated with the conduction band minimum. These in-gap states were attributed to localized electrons associated with oxygen vacancies, and the valence band shift is consistent with a downward band bending. Meevasana et al.

also observed that, as shown in Fig. 1.8, these two features were influenced by irradiation. These observations caused both Santander-Syro et al.and Meevasanaet al.interpret their data in the context of band bending at the surface induced by surface oxygen vacancies. In particular reference [47]

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1.3 Bare SrTiO3 (001) surface

Figure 1.8: Valence band spectra on the surface of cleaved Nb:STO showing the O2pvalence band at⇠ 6eV. After irradiation (red and purple lines) the spectra show a peak at the Fermi level due to the surface 2DEL and an in-gap state at⇠1.3 eV attributed to localized oxygen vacancy states, shown magnified in the inset. The leading edges of the valence band acquired after irradiation of the surface with light for 10 and 25 minutes (red and purple respectively) are shifted to higher biding energies with respect to the valence band from the pristine surface. This is consistent with downward band bending at the surface. From [46].

invoked a wedge model, as often used to describe semiconductor 2DEGs.

This simple model captured the fundamental aspects of the band structure including the orbital polarization which results directly from the real space anisotropy of thet2g orbitals. However, it did not reproduce the subband binding energies. Reference [46] modelled the surface using coupled Poisson- Schrödinger equations for a single non-parabolic band as often used to describe conventional semiconductors. This calculation predicted a more realistic charge profile however since this calculation did not start from a full description of the STO conduction band it did not find orbital polarization.

Control of the 2DEL density at the LAO/STO interface has been achieved by electrostatic gating and by growing samples at diﬀerent temperatures [36, 49]. High quality ARPES experiments (on fractured) STO were long restricted to measurements of a single carrier density largely because the mechanism by which the 2DEL develops in the bare STO surface under UV- light irradiation remained unclear. Possible mechanisms proposed included light-induced oxygen vacancies [46], ferro-electric surface reconstructions [50, 51] and oxygen vacancies produced as the sample is cleaved. A much earlier publication by Aiuraet al.[52] had already demonstrated that the bandwidth of states at the surface of cleaved STO was sensitive to very low

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does of oxygen. However, the significance of this experiment was not initially recognised possibly because the reduction of spectral weight at the Fermi level was interpreted as the formation of a charge depletion layer rather than neutralization of oxygen vacancies.

1.3 Surface 2DELs in other materials

The discovery of a 2DEL at the surface of STO (001) suggests a route to direct spectroscopic investigation of two-dimensional systems on the surface of other TMOs. Candidate materials must be susceptible to surface doping by either electrons or holes, for example by the creation of oxygen vacancies at the surface or by adsorption of electronegative species respectively. They should also have the same propensity as STO to become metallic at extremely low carrier density which is by no means a universal property of the ABO3

perovskite crystals. One material that does show similar semiconducting, high mobility behaviour at low densities [53] is the isostructural KTaO3(KTO).

KTO has much in common with SrTiO3including a high dielectric constant (⇠4000at 10K), quantum paraelectric behaviour and superconductivity in electrolyte gated transistor devices [54]. The formal valency of the transition metal ion is Ta⁵⁺ resulting in a 5d⁰ electronic configuration. Indeed it was found that the cleaved surface of both Ba:KTO and stoichiometric KTO support a 2DEL [55, 56]. The spin orbit coupling in KTO is nominally thirty times greater than that of STO. The KTO surface 2DEL provides an interesting opportunity to study how changes of the relative strength of atomic spin-orbit coupling and confinement interplay with broken inversion symmetry to aﬀect the subband structure in an oxide 2DEG.

LaTiO3 is the 3d¹ end compound of the solid solution La1 xSrxTiO3

and is a Mott insulator with antiferromagnetic ordering below the Neel temperature of⇠140K [9]. In the bulk, hole doping is achieved either by subsitution of La³⁺ for Sr²⁺ or by inclusion of interstitial oxygen. Thus is conceivable that oxygenating the surface of LTO could induce a two- dimensional conductive state on the surface of a three dimensional Mott insulator. This kind of system has not been demonstrated to date and it is hard to predict the properties it might have.

Another TMO material which is sensitive the creation of oxygen vacancies and which displays metallic conductivity at low density is the anatase phase of TiO2. Anatase TiO2is an insulator with a tetragonal structure and two Ti atoms per lattice site. Due to the crystal field the conduction band minimum is, unlike STO, composed of a single band of dxy orbital character. The dielectric constant of anatase TiO2is⇠40at 10 K, dramatically lower than that of STO. This combined with the unique orbital character of the bands occupied at low density could lead to a rather diﬀerent behaviour of a 2DEL in TiO2 compared to STO.

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1.4 Outline

This thesis is organised as follows. In Chapter 2 I will introduce the theory and practicalities of angle resolved photoemission spectroscopy (ARPES) which I have used to probe the band structure of two-dimensional electron systems at the surface of several transition metal oxides. In Chapter 2 I will also briefly introduce the tight binding formalism which I used to perform band structure calculations. In Chapter 3 Sect. 3.1 I will present the detailed subband structure, many-body physics and origin of the SrTiO3(001) surface 2DEL revealed by ARPES and spin-resolved ARPES studies with reference to tight-binding supercell calculations. This section represents the development of our understanding of this system since the first publication on this subject from our group (Meevasanaet al.Nature Materials10114118 (2011)) and incorporates unpublished results alongside my own first author publications and results from a publication by my colleague Z. Wang, to which I contributed. In Sect. 3.2 I will present published results on the creation and density control of a 2DEL at the (111) surface of SrTiO3 and preliminary results from the (111) surface of KTaO3. In Sect. 3.3 I will present tight-binding supercell calculations which I performed to support the experimental work by my colleague Z. Wang on the surface of anatase TiO2. Finally in Sect. 3.4 I will summarize our experimental attempts to induce an itinerant two-dimensional state on the surface of LaTiO3.

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CHAPTER 2 Methods

2.1 Angle-Resolved Photoemission Spectroscopy

As a direct probe of the energy-momentum dispersion of charge carriers in a crystal, angle resolved photoemission spectroscopy (ARPES) has provided significant insights into both the fundamentals of solid state physics [57, 58] and the emergent physics of strongly correlated materials such as the cuprates high temperature superconductors [59–61]. It has also been pivotal in the discovery of new phases of matter such as topological insulators [62, 63] and more recently is playing a prominent role in the rapidly evolving understanding of Weyl semi-metals such as TaAs and (Mo/W)Te2 [64–66].

2.1 Theoretical description

All photoemission techniques are based on the photoelectric eﬀect, the emission of an electron from a material following absorption of a photon. Angle- resolved photoemission spectroscopy probes the energy and momentum distribution of these photoelectrons. Very generally the photocurrent intensity I(k,!)can be written

I(k,!)/|M|²f(!)A(k,!) (2.1) where!is energy referenced to the Fermi level andkis the crystal momentum.

Direct photoemission probes only the occupied states which is described by the Fermi functionf(!).Mis a matrix element that determines the intensity modulation of the signal andA(k,!)is the one-electron spectral function

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which describes the energy and momentum distribution of the interacting system with bare band dispersion⇠(k).A(k,!)includes many body eﬀects through the electron self-energy⌃(k,!) =⌃⁰(k,!) +i⌃⁰⁰(k,!)and is given by

A(k,!) = 1

⇡

⌃⁰⁰(k,!)

(! ⇠(k) ⌃⁰(k,!))²+⌃⁰⁰(k,!)² (2.2) In the non interacting case ⌃(k,!) = 0 and the spectral function reduces to the delta function (! ⇠(k)at the energies and momenta defined by the bare band. For the case of weakly interacting electrons, it is clear from Eq. (2.2) that for a self-energy that depends only weakly on momentum and energy the spectral function for a linear bare band is approximately Lorentzian. The width of the Lorentzian is defined by the imaginary part of the self-energy ⌃⁰⁰ and the pole of the spectral function position is oﬀset from the bare band dispersion by the real part of the self-energy⌃⁰.

No complete theoretical description of the many-body photoemission process exists and there are diﬀerent approaches for derivingMandA(k,!).

In linear response theory where the photocurrent is described as the steady response of the system to an applied electric field [67, 68] and is a so called one-step model in which the photoemission is treated as a single coherent process. Another example is the Fermi’s Golden rule approach which describes the photocurrent as the transition probability from an N particle initial state to an N particle final state. An advantage of linear response theory over the Fermi’s Goleden rule approach is that it is not necessary to know, or make assumptions about the full many body wave functions of the initial and final states and it naturally incorporates many-body behaviour. However, when combined with the common phenomenological three-step model of the photoemission process, the Fermi’s Golden rule approach is often more useful.

The three-step model artificially separates the single coherent photoemission process into the following three steps:

1. The bulk initial state is excited by a photon to a bulk final state inside the crystal.

2. The excited electron travels to the surface.

3. The photoelectron is transmitted through the surface into a free electron vacuum final state.

In order to associate the raw photocurrent measured by ARPES with the energy-momentum dispersion of electrons in the crystal, we must map the measured quantities of the photoelectron emission angle#(see Fig. 2.1) and kinetic energyEkin to initial state crystal momentum kand binding energyEB respectively. Conservation of energy for a single coherent process requires that the kinetic energy of the final state photoelectron in vacuum is

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2.1 Angle-Resolved Photoemission Spectroscopy

given by

Ekin =h⌫ EB (2.3)

where his the Planck constant,⌫ the frequency of the exciting radiation and the work function of the material. The free electron final state in the vacuum has total momentum ~ ¹p2meEkin (here~is the reduced Planck’s constant andme is the free electron mass). Therefore the wave vector of the free electron final state in the vacuum can be completely determined by measuring the kinetic energyEkin and the angle at which the photoelectron is ejected from the crystal surface. The crystal momentum of the initial state kis given by the sum of the in-plane and out-of-plane componentsk_k and k_?. Neglecting the photon momentum, conservation of momentum between the initial and final states and the translational symmetry of the crystal surface imply that the in-plane component of the crystal momentum of the initial state can be written as

k_k =~ ¹p

2meEkin·sin# (2.4)

where#is the angle at which the photoelectron is emitted measured from the surface normalnˆ as shown in Fig. 2.1. The surface breaks the translational symmetry of the crystal in the direction perpendicular to the surface therefore this component of the initial state crystal momentumk_? is not conserved across the surface. Approximating the bulk final state inside the crystal as free-electron-like we can write

Ekin= ~² 2me

(k_k²+k_?²) +Vin (2.5) where the inner potential Vinis a free parameter that can be determined experimentally and kis expressed in the extended zone scheme. This approximation is better for final states of high kinetic energy, however a large body of experimental work has shown that it is usually applicable down to kinetic energies around 20 eV [69]. Using Eq. (2.4) and Eq. (2.5), within the free electron final state approximation we can now write the perpendicular component of the crystal momentum as

k_?=~ ¹p

2meEkincos²#+Vin (2.6) Eq. (2.4) and Eq. (2.6) define the curved surface in reciprocal space probed at a given photon energy. Therefore, in order to probe the dispersion of states as a function of k? over an entire bulk Brillouin zone for a given k||we must vary the photon energyh⌫ over a large range. From such ak_? dispersion it is possible to determineVin by matching the periodicity of the signal to the periodicity of the Brillouin zone. Photon energy dependent measurements allow us to determine if the initial state disperses alongk_? which provides insight into the dimensionality of the crystals electronic structure.

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The intensity of the energy and momentum resolved photocurrentI(!, k) is governed by the matrix element M of the electron-photon interaction.

Adopting thesudden approximation, which assumes that the photoelectron does not interact with the photohole after excitation, within the three step model we can factorize the N particle final state into a one-particle photoelectron state|fiand anN 1particle state of the system left behind.

Further assuming that the initial state can be similarly factorized into a single particle state |iiand an N-1 particle state, the matrix element takes the form

M/ hf|A·p|ii (2.7)

whereAis the vector potential of the exciting radiation andpis the electron momentum operator. Realistic calculations of the matrix elements for a given material require detailed knowledge of both the initial and final states.

However using Eq. (2.7) simple symmetry considerations (which are discussed more extensively in Sect. 3.1.1) allow the orbital character of the initial state to be deduced from polarization dependent measurements using diﬀerent orientations of the vector potentialA.

The finite width of the pole of the spectral function is indicative of the finite lifetime of the photohole due to interactions described by the imaginary part of the self-energy. However when extracting experimental self-energies from data, the contributions to the total lineshape of the photocurrent from both resolution and matrix element eﬀects must be considered. As the photoelectron travels to the surface it undergoes inelastic scattering processes which lead to a finite kinetic energy dependent photoelectron escape depth [70]. This is responsible for the surface sensitivity of the technique at VUV excitation energies. The finite inelastic mean free path in turn leads to uncertainty ink_? of the final state. ARPES probes the initial state at the k_? of the final state. Therefore the range ofk_?values of the final state leads to a finite k_? resolution through the matrix element M in Eq. (2.7). In materials with three dimensional electronic dispersion this broadens direct- transition peaks in the photocurrent. For a two-dimensional system this does not eﬀect the measured line-width, but similar considerations can explain strong matrix element variations that reflect the spatial extent of the initial state wave function.

2.1 Experimental Principle

Angular and energy resolution of the photoelectrons is achieved with a cylindrical electron lens and hemispherical analyser respectively as sketched in Fig. 2.1. The lens and hemispheres image the photoelectron distribution onto a two-dimensional detector where single photoelectrons are amplified by a multi channel plate (MCP) and the resulting avalanche of electrons is accelerated to a phosphor screen which in-turn is monitored by a CCD camera.

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UV source

Hemispherical Analyzer

2D detector

Sample Lens

Lens axis

ˆn

ϑ,k

ϑ

E_kin

Figure 2.1: Schematic of an angle resolved electron spectrometer.#is defined as the angle between the surface normalnˆand the lens axis and encodes information about the momentumk_kof the intial state.

The electron lens maps the angle at which electrons enter the lens onto positions on the entrance slit of the analyser and accelerates/decelerates the photoelectrons to the working energy of the hemispheres. The two concentric hemispheres are held at a certain voltage diﬀerence and the trajectories of the photoelectrons through the hemispheres is defined by their kinetic energy.

The hemispheres map the entrance slit (and therefore emission angle) on to the tangential coordinate of the MCP and disperses them in energy along the radial coordinate.

Spin- and Angle-Resolved Photoemission Spectroscopy

The spin polarization vector of the photoelectron emitted from a crystal surface can be measured by coupling the electron lens and hemispherical analyser to a Mott Polarimeter. Photoelectrons of the pre-selected energy and emission angle are accelerated to voltages on the order of a few 10 keV before scattering from a thin film target of highZ elements such as Au. The angular distribution of the back-scattered electrons depends on their spin vector due to a strong spin-orbit coupling near the heavy nuclei of the target which is known as Mott scattering. The spin polarization of the incoming electron beam along a given axis results in an asymmetric distribution of the back scattered electrons which is detected as an asymmetry in the photo- currents of symmetrically placed channeltrons. The detected asymmetry of a fully polarized electron beam is given by the eﬀective Sherman function

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of the spin-polarimeter Se↵, which is determined experimentally and for realistic Mott polarimeters takes values of ⇠15%[71]. Within this thesis I used such a setup the the Bessy II synchrotron in Berlin, Germany in order to investigate the spin structure of the STO (001) surface 2DEL.

Geneva Lab

During my doctoral studies I contributed to the set-up and commissioning of the ARPES lab at the University of Geneva. This system has three light sources: a Helium discharge lamp from MBS with a plane grating toroidal mirror monochromator from SPECS, a frequency converted CW diode laser fromLEOS Solutions providing photons of 6.05 eV and aLumeras source generating 113 nm (11 eV) radiation by mixing the fourth harmonic and the fundamental of a pulsed, narrow bandwidth pump laser with 1024 nm wavelength. It uses an MBS analyser with two deflectors in the lens which allows Fermi surface maps to be measured without moving the sample.

Combined with the small focus of the 6.05 eV laser this system is optimised for measuring very small samples or samples with very inhomogeneous surfaces. We have a home-built 6-axis cryo-manipulator with a sample base

Figure 2.2:Left: data from the Geneva lab on Sr3Ru2O7 at 4.5 K. Right: EDC on gold at 2K integrated across the entire detector demonstrating the ultimate resolution of the system with the 6.05 eV CW laser is 0.85 meV.

temperature of ⇡4.5K. The ultimate resolution of our system is ⇡0.85 meV as shown in Fig. 2.2 for a Fermi edge taken on polycrystalline gold at 2 K. This resolution was achieved in part by reducing noise on the sample position originating from poor high frequency electrical contact between the chamber and the cryostat at the rotary seal of thexyz-stage, to below 0.2 meV (see Fig. 2.3). An example of high resolution ARPES data from the Geneva lab is shown in Fig. 2.2(a).

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The data presented in this thesis were all acquired at Synchrotron beam- lines: I05 beamline of the Diamond Light Source, Surface and Interface Spec- troscopy (SIS) beamline of the Swiss Light Source (SLS) and the PHOENEX endstation on the UE112-PGM1 beamline of BESSY II. An advantage of synchrotron-based ARPES is the availability of higher and variable photon energies. Additionally, the small spot size of the synchrotron beam (compared to a He discharge lamp) reduces the detrimental eﬀect of spatial averaging over inhomogeneous sample surfaces. These advantages were particularly important for the samples measured during the course of my thesis for several reasons:

• The cubic structure of the crystals studied in this thesis do not possess a natural cleavage plane. This leads to rather inhomogeneous surfaces being exposed by fracturing.

• The matrix elements of the STO 2DEL are more intense in the second Brillouin zone which is not accessible at laser energies.

• Variable polarization and photon energy were important for demonstrating the orbital nature and dimensionality of the investigated states respectively.

• Creation of 2DELs at the surfaces of STO, KTO and TiO2requires light induced oxygen vacancies. These vacancies are created more eﬃciently at the photon energies and intensities provided by a synchrotron.

1.0 0.8 0.6 0.4 0.2 Normalized Counts 0.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Noise Amplitude (meV)

∆=0.2 meV ∆=0.9 meV

Figure 2.3:Histogram of the potential diﬀerences between sample and UHV chamber with (black) and without (red) good high frequency electrical contact between the system and the manipulator at the rotary seal. Full width half maximum is indicated by .

Surface Preparation

The extreme surface sensitivity of VUV photoemission experiments demands atomically clean sample surfaces, which imposes the need for ultra high

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vacuum (UHV) conditions. To achieve an atomically clean surface the most common approach is to cleave the samplein situ. This is achieved by glueing a post to the sample surface (see figure) and hitting this in vacuum to break the crystal. This works well in samples with natural cleavage planes.

However in the cubic or quasi-cubic crystals studied in this thesis there is no natural mirror plane which makes them diﬃcult to break. In order to facilitate cleavage in a preferred plane, we cut deep notches parallel to the plane using a diamond wire saw (as sketched in Fig. 2.4).

≈ 2 mm

ˆn

(a) (b)

Figure 2.4:(a) A sample mounted with a top-post prior to being loaded into the UHV chamber (upper) and a sketch of a cubic sample that has been notched with a wire saw perpendicular to the surface normalnˆ (lower). (b) CAD assembly (left) and photograph (right) of the UHV resistive heater in the Geneva lab.

Alternatively, clean surfaces can be obtained by sputtering and annealing.

During my studies I designed and built the resistive heater stage shown in Fig. 2.4 which can reach800 C and provides rotation around two axes and which is used forin situ annealing.

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2.2 Tight Binding Band Structure Calculations

Bulk Hamiltonian

The Schrödinger equation in the bulk of any crystalline solid can be written

as H˜bulk kn(r) =Ekn kn(r) (2.8)

where the eigenstate wave functions kn(r)correspond to Bloch states at the wave vector k of the band n defined over all real space spanned by the vector r.Ekn are the corresponding eigenenergies that form the bulk band dispersion. These ground state solutions are usually found byab initio density functional theory (DFT) and they include core levels as well as the conduction band which is of interest for understanding the electronic properties of the material. By down-folding a subset of thesenbands onto a basis of maximally localized Wannier functions (MLWFs)'R↵(r), where Ris a lattice site and↵is a band-like index, it is possible to construct an eﬀective HamiltonianHbulkfor the conduction band, where the corresponding Schrödinger equation is now

Hbulk kn(r) =⇠kn kn(r) (2.9) with eigenstate wave functions kn(r)and eigenvalues⇠kn that should, to a good approximation, reproduce the band structure defined byEkn.

Hbulk is an eﬀective tight binding Hamiltonian that can be written in the form

Hbulk= X

k↵↵⁰

t^↵↵_k ⁰c^†_k↵c_k↵0 (2.10) where the operator c^†_k↵(ck↵) creates (annihilates) a state |⌥k↵i which is related to the MLWFs by a change of basis. Thus the wave functions of the basis used in Eq. (2.10) are related to the maximally localized Wannier functions by

⌥k↵(r) = 1 pN

X

R

e^ik^·^R'R↵(r) (2.11) where N is the number of unit cells in the crystal, which is equal to the number ofkpoints in the sum in Eq. (2.10).

The matrix elements of the eﬀective conduction band Hamiltonian are defined by

t^↵↵_k ⁰ =X

R

t^↵↵_R⁰e ^ik^·^R. (2.12) These are Fourier transforms of the transfer integrals (or colloquially "hopping parameters")t^↵↵_R ⁰ that describe the kinetic energy cost for an electron to tunnel along the lattice vectorRfrom the MLWF state ↵to the state

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↵⁰. In practice, the nature of the MLWF are such thatt^↵↵_R ⁰ quickly becomes negligible for largeR.

Hbulk in the form of Eq. (2.10) is a matrix that is block diagonal ink.

The size of the matrix is determined by the number of MLWF states{↵} at each lattice site. In the case of STO the conduction band is derived from the 3d t2g manifold and the MLWF states can be identified with thedxy, dyz anddxz atomic orbitals. In this case↵becomes an orbital index and the basis can be written as

{↵}={xy^", xy^#, yz^", yz^#, xz^", xz^#} (2.13)

where"#indicates the spin character of the Wannier function andxy,yz or xz indicate thet2g orbital character of the Wannier function. The spin index is necessary if the DFT calculation used as a starting point includes spin- orbit interactions. Therefore in STO the diagonal blocks ofHbulk for eachk are6⇥6matrices with matrix elementst^↵↵_k ⁰. These6⇥6 matrices must be diagonalized at each kpoint in the Brillouin zone to find the eigenenergies

⇠knwhere the band indexnruns from 1 to 6. The corresponding eigenvectors have six components with the coeﬃcients{ kn^↵ }, that describe the relative contribution by each state of orbital character↵to the total wave function.

The wave functions of the eigenstates of Eq. (2.10) have the form

kn(r) =X

↵

kn⌥k↵(r) (2.14)

with the normalization condition X

↵

| kn^↵ |²= 1. (2.15)

The charge density can be calculated from the wave functions using n3D(r) = |e|X

kn

f(⇠kn)| ^kn(r)|² (2.16) wheref(⇠kn)is the Fermi function which ensures that the sum in Eq. (2.16) only counts occupied states.n(r)has the periodicity of the lattice and some structure within the unit cell. The mean bulk densityn¯ is found by averaging over all space which, by utilizing the orthogonality properties of MLWFs, gives the intuitive result

¯ n= 1

V Z

V

d³r n3D(r) (2.17)

= |e| V

X

kn

f(⇠kn)X

↵

| kn^↵ |² (2.18)

= |e| V

X

occupiedk

1 (2.19)

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2.2 Tight Binding Band Structure Calculations

whereV is the volume of the discrete lattice. For a cubic lattice with lattice constanta,V =a³N .

Quasi-2D Supercell Hamiltonian

It is possible to make a simple extension of the above tight-binding formalism, such that the Hamiltonian is quasi-2D rather than 3D. This quasi-2D Hamil- tonian will be useful for modelling the subband structure of two-dimensional systems at oxide surfaces.

The lattice vectorRcan be separated into two contributionsR=R_k+z wherezdenotes the component of the lattice vector perpendicular to the surface and R_k the in-plane lattice vector. If the Fourier transform of Eq. (2.12) is performed only overR_k such that the matrix elements of the Hamiltonian have the form

t^↵↵_k_k_zz⁰ 0 =X

R_k

t^↵↵_R_k⁰_zz0e ^ik^k^·^R^k (2.20) the corresponding quasi-2D supercell Hamiltonian is given by

Hbulk= X

k_k↵↵⁰zz⁰

t^↵↵_k_k_zz⁰ 0c^†_k

k↵zc_k_k_↵0z⁰ . (2.21) By retaining the explicit sums overzandz⁰Eq. (2.21) is block diagonal ink_k such that the resulting band dispersion is only defined in a 2D Brillouin zone.

At each kpoint it is now necessary to diagonalize matrices of dimension 6L⇥6L where L is the number of layers included along the z axis of the crystal. The6⇥6diagonal elements of these blocks are given by the Hamiltonian of a single layer of the crystal and the oﬀ diagonal matrix elements describe the interlayer coupling. There are6Leigenvalues⇠k_kn for everyk_k point in the 2D Brillouin zone. The eigenvectors have length6L whose coeﬃcients{ k^↵z_kn}describe the layer-resolved orbital composition of the wave functions

k_kn(r) =X

↵z

k_kn⌥k_k↵z(r). (2.22) with the normalization condition

X

↵,z

| ^↵,zk_kn|²= 1. (2.23) ForL! 1the supercell Hamiltonian Eq. (3.5) produces6Lsolutions which are degenerate with the solutions of Eq. (2.10) atkz= 0. In practice

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the supercell sizeLis finite and the hopping parameters must be truncated at the limits of the supercell slab such that

t^↵↵_R_k⁰_zz0 =

(t^↵↵_R_k⁰_{z z}0 for z, z’ in the bulk.

0 for z and/or z’ in vacuum. (2.24) This produces artefacts in the band structure due to the eﬀective confinement of the system in an infinite potential well of widthL.

In analogy to Eqs.(2.16 - 2.19), but with a spatial average only over the thexyplane and one unit cell in thez direction, it is possible to determine the layer resolved density resulting from this quasi 2D Hamiltonian using

n3D(z) = |e| A

X

k_kn

f(⇠k_kn)X

↵

| k^↵z_kn|² (2.25)

HereA=a²Nk is the area of the surface of the crystal withNk the number of points in the 2Dkgrid.

The explicit form of the matrix elements of Eq. (2.12) and Eq. (2.20) is discussed for a simplified model Hamiltonian of STO in Appendix B.

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CHAPTER 3 Results

3.1 SrTiO

₃

(001) surface 2DEL

Fig. 3.1(a) and (b) show the energy-momentum dispersion of the SrTiO3(001) surface 2DEL, measured by high-resolution angle-resolved photoemission spectroscopy (HR-ARPES) at the I05 beamline of the Diamond lightsource at 10 K with an excitation energy of 47 eV and usings and p polarized light respectively. The data are measured in the second Brillouin zone parallel to the ky axis which is perpendicular to the scattering plane of the light.

Four bands dispersing along the ky axis are clearly visible, three with a light band mass of⇠0.6me and one with a heavy band mass of⇠8.5me. Throughout this thesis these subbands will be referred to as the L1, L2, L3 and H1 subband respectively, as is sketched in Fig. 3.2. The bandwidth of the individual subbands areE₀^L1 ⇡260meV, E₀^L2 ⇡120 meV,E₀^L3 ⇡70 meV andE₀^H1⇡45meV. The Fermi surface of this state, shown in Fig. 3.3, reveals three circular Fermi surface sheets which correspond to the light subbands in Fig. 3.1 and two low intensity elongated "cigar-like" Fermi surface sheets. The long axis of one of these Fermi surface sheets corresponds to the heavy band shown in Fig. 3.1. The second non-isotropic Fermi surface sheet is expected from the symmetry of thet2g orbitals, and corresponds to a subband with a heavy mass along thekx axis. Note that the "cigar- like" Fermi surface sheets corresponding to heavy bands are observed more clearly in the data of Fig. 3.8 which was taken under diﬀerent experimental conditions.

The high quality of the data in Fig. 3.1 reveals details of the subband

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-0.3 -0.2 -0.1 0.0

-0.5 0 0.5

pi/a -0.3

-0.2 -0.1 0.0

-0.5 0 0.5

k_y (π/a)pi/a k_y (π/a)

E - EF (eV)

(a) (b)

Figure 3.1:Subband structure of the STO (001) surface 2DEL measured with (a) s-polarized and (b)p-polarized light at 47 eV in the second Brillouin zone. Three light and two heavy subbands are visible. The light bands show an abrupt change of dispersion at⇡30meV indicative of coupling to a bosonic mode. Angular resolution was<0.3 and energy resolution<15meV. Measurements were performed at 10 K and at pressures<1⇥10 ¹⁰mbar.

Figure 3.2:Schematic of the STO (001) surface 2DEL subbands that are observed by ARPES. L(H) indicates that the nominal band mass of the subband is light(heavy) and the number in the naming scheme indicates the order of the subbands.

structure which were not resolved in the earliest ARPES measurements of the 2DEL at the (001) surface of STO [46, 47]. In particular the confinement energy of the H1 subband and the existence of both a third light subband and a second heavy subband (H2) with a shallower occupied width of⇡10 meV, which is most evident in Fig. 3.1(b). A weak kink is visible in the dispersions of the light subbands at ⇡30meV which is indicative of a peak in the real part of the quasi-particle self-energy due to coupling to a bosonic mode. This discussed in more detail in Sect. 3.1.5.

The data in Fig. 3.1 and Fig. 3.3 is obtained from the surface of single

Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy

Thesis

Reference

Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy

MCKEOWN WALKER, Siobhan

MCKEOWN WALKER, Siobhan. Two dimensional electron liquids at oxide surfaces studied by angle resolved photoemission spectroscopy . Thèse de doctorat : Univ.

Genève, 2016, no. Sc. 4939

URN : urn:nbn:ch:unige-882537

DOI : 10.13097/archive-ouverte/unige:88253

Two Dimensional Electron Liquids at Oxide Surfaces Studied by Angle Resolved Photoemission Spectroscopy

Résumé

Abstract

Contents

CHAPTER 1

Introduction

1.1 Oxide Electronics

1.2 LaAlO

/SrTiO

interface

1.3 Bare SrTiO

(001) surface

1.4 Outline

CHAPTER 2

Methods

2.1 Angle-Resolved Photoemission Spectroscopy

ˆn

ˆn

2.2 Tight Binding Band Structure Calculations

CHAPTER 3

Results

3.1 SrTiO

(001) surface 2DEL