Transitions de phase quantiques dans des films minces désordonnés

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Transitions de phase quantiques dans des films minces

désordonnés

C. Marrache-Kikuchi, O. Crauste, L. Berge, S. Collin, A. Juillard, F. Lalu, S.

Marnieros, L. Dumoulin

To cite this version:

Quantum Phase Transitions in disordered thin films

Transitions de phase quantiques dans des films minces désordonnés

C.A. Marrache-Kikuchi, O. Crauste, L. Bergé, S. Collin, A. Juillard, F. Lalu, S. Marnieros, L. Dumoulin.

Collaboration : Laboratoire de Physique Quantique (ESPCI, Paris)

Résumé : Le transport à très basse température dans des matériaux conducteurs désordonnés implique les phénomènes d'interférences quantiques, de répulsions coulombiennes, et le cas échéant de fluctuations supraconductrices. Deux (2D) étant la dimension critique inférieure pour l'existence des états métallique et supraconducteur, nous avons étudié deux transitions de phase quantiques - la Transition Supraconducteur-Isolant (TSI) et la Transition Métal-Isolant (TMI) - lorsque l'on diminue l'épaisseur d'un système désordonné, ici a-NbSi. La question sous-jacente est celle de l'articulation entre les différentes phases et les conditions d'apparition d'un éventuel état métallique à 2D. Nous avons étudié les TSI induites soit par un champ magnétique soit par le désordre. Les principales caractéristiques observées (renormalisation, rôle de l'orientation du champ) s'interprètent bien dans le cadre de la théorie de M.P.A. Fisher communément invoquée pour expliquer les TSI. Cependant nous ne trouvons pas une valeur universelle pour la résistance à la transition et les exposants critiques prévus par cette théorie. Concernant la TMI, nous avons diminué l'épaisseur d'un système métallique jusqu'à tendre vers 2D et l'état isolant. Dans ces deux transitions le passage vers l'isolant montre clairement l'existence d'états dissipatifs à température nulle non prévus par les théories conventionnelles. Nous proposons une interprétation de l'ensemble de nos résultats faisant intervenir une nouvelle phase à 2D entre les états supraconducteur et isolant - un métal de Bose -, prédite par des théories récentes. Nous traçons alors le diagramme de phase du système modèle NbSi en fonction de la concentration et de l'épaisseur des films.

Introduction

Low temperature transport in disordered conducting materials imply taking into account quantum interferences, Coulomb repulsion, and superconducting fluctuations. Since 2D is the lower critical dimension for both metallic and superconducting states, transport in disordered thin films is a study of particular interest.

More specifically, in 1979, the localization theory predicted that low dimensional (2D or 1D) independent electron systems in the presence of disorder are always localized [1] and therefore a finite resistance for these systems at T=0 cannot exist. This dogma has been questioned by Kravchenko’s experiments on Si-MOSFETs [2].

On the superconducting side, the study of disordered thin films has started in the 1960s,

but interest for this subject has been renewed at the end of the 1980s with M.P.A. Fisher’s assessment that Superconductor-to-Insulator Transitions (SIT) could be Quantum Phase Transitions (QPT) [3]. SITs would then have common features with other phenomena or systems such as the Metal-to-Insulator Transition (MIT), Josephson junctions arrays,

4

He in porous media or high-Tc

superconductors [4]. Explaining the underlying mechanism(s) of the SIT might hence bring some very interesting insight into other systems.

We have studied these two quantum phase transitions – the MIT and the SIT – as we reduced the thickness of a disordered system, in our case the amorphous material NbxSi1-x.

Thick NbxSi1-x films (d > 100 nm) undergo a

Transition for a concentration of 12%. This system is hence very convenient to study dimensionality effects starting from an initial 3D state that can either be superconducting or metallic. In both cases, the reduction in thickness at a given concentration leads to an insulating state. The ultimate aim is to draw the phase diagram of NbxSi1-x as a function of

the concentration and of the thickness, which would be a model Insulator-Metal-Superconductor phase diagram for disordered systems in the vicinity of dimension 2. The underlying issue is the continuity between the different states, and this especially addresses the possible existence of a metallic state in 2D.

Figure 1: Field-induced SIT for a 12.5 nm-thick Nb15Si85 sample. When the perpendicular magnetic field is increased, the thin film transits from a superconducting to an insulating state. Insert: the corresponding renormalization procedure is an evidence for the QPT [3].

I – Experimental methods

The NbxSi1-x thin films are being synthesized,

characterized and measured in the laboratory. The films are grown by high-vacuum co-evaporation. An experimental effort is continuously undertaken in order to always improve the homogeneity and the composition control of the films, especially since the measured effects are extremely sensitive to any composition difference. In the past three years, the evaporation sources have been put further away from the substrate in order to improve the sample homogeneity. The films’ composition is systematically controlled in situ by piezoelectric quartz as well as ex situ by Rutherford Backscattering

(RBS) measurements. We have moreover performed some additional structural checks on some samples, thanks to the university’s technological centre MINERVE.

Since QPTs only manifest themselves in the vicinity of T=0, we are dealing with very fine quantum effects and it is important to have a specifically designed low temperature measurement apparatus. Amongst other experimental apparatus, we use a dedicated customized dilution cryostat which is able to measure simultaneously 50 channels at a base temperature of 6.9 mK. Moreover, the group’s expertise on very low noise measurements has here also been extremely valuable. For all measurements using a magnetic field, we have developed a collaboration with the Laboratoire de Physique Quantique (ESPCI, Paris).

II – Superconductor-to-Insulator

Transitions in Nb

Si

thin films

SITs in disordered thin films can be induced by applying a magnetic field or by varying the disorder. An example of such transition is shown on figure 1. These SITs are commonly explained by M.P.A. Fisher’s theory: the “dirty boson model” [3].

Figure 2: Phase diagram for the field-induced SIT as function of the magnetic field H and of the temperature (Nb15Si85, 12.5 nm-thick). When the magnetic field is applied perpendicularly to the sample, the features of the transition (notably the critical magnetic field) are temperature-independent at low temperature, implying a quantum origin; whereas under a parallel magnetic field those features display a temperature dependence characteristic of a classic phase transition driven by thermal fluctuations.

the magnetic field for the nature of the field-induced SIT (fig.2) [5]. Second, under a perpendicular magnetic field, we have observed the signature of a QPT : the measured resistance in the critical region obeys a scaling law of the predicted form as shown in the inset of figure 1.

However, some of our samples’ characteristics cannot be explained by the “dirty boson model”. First, we do not observe a universal value of the resistance at the transition which is one of the cornerstone of the theory. Instead of this, we have shown that the resistance for NbxSi1-x can be

smoothly tuned by varying the composition, the thickness or the applied magnetic field [5,6]. Moreover, the resistance renormalization procedure gives access to the value of the transition’s coherence length and dynamical critical exponents (resp. υ and z): we find υz = 0.7 for the field-induced SIT and υz = 0.4 for the thickness-induced SIT. These values are particularly interesting in the present context since they provide one of the first experimental contradictions of M.P.A. Fisher’s theory on this important point (υzFisher>1). More importantly, this

model does not account for the resistance saturations observed at low temperature in the critical region.

III – Metal-to-Insulator Transition

in Nb

Si

thin films

Regarding the MIT, we have studied the evolution of a 3D metallic system when its thickness was lowered down to the dimension 2. Like all disordered systems close to 2D that have been studied up-to-date, NbxSi1-x does not present a metallic

state of the type observed by S.V. Kravchenko et al. [2] (characterized by δR/δT>0 at low temperature). However we do observe a resistance plateau at very low temperature (T < 100 mK), thus indicating a metallic state at T = 0, even for samples that can be called as 2D according to their resistive behaviour at higher temperature (0.1 < T < 1 K) (fig. 3). This contradicts the localization theory [1]. We have discussed

the credibility of these results [7] regarding possible experimental artefacts, and we have concluded that these saturations are intrinsic.

Figure .3: Resistive behaviour of a series of 12.5 nm-thick samples of various concentrations. Despite the films being 2D, their resistive behaviour is metallic (finite resistance at T→0).

IV – Evidence of a Bose Metal in 2D

Figure 4: Phase diagram for a-NbxSi1-x.

Putting our results together, we have shown that, in 2D, it is likely that in between the superconducting and the insulating states lies a metallic state. As a further argument, we have shown that our results may be the first experimental evidence of the existence of a 2D Bose metal [8], in which the Cooper pairs form a non-coherent metallic phase [9]. We have then established a preliminary phase diagram for NbxSi1-x in the (thickness,

(Bose metal), insulating and superconducting (figure 4).

V – Application to low temperature

detectors for astrophysics

experiments

Throughout conducting these basic research, we have tried to apply them to our other research interest: the research and development of cryogenic detectors for astrophysics experiments. These ultra-thin NbxSi1-x films have proved to be promising

thermal sensors for massive bolometers [5]. Moreover, we have shown that the combined effect of the concentration and of the thickness of these thin films could lead to very innovative detectors in the millimetric domain. These prospects have led the group to present the TERIBOL project (supervisor: S. Marnieros) which has received funding from the ANR in 2006.

Conclusion and future prospects

In the past three years, we have shown that a-NbxSi1-x is a model system for the study of

low-dimensional disordered materials. This compound exists in the superconducting, insulating and metallic states ; at 3D as well as 2D, its transport properties can be modified via the concentration, the magnetic field, the thickness or the local disorder that can be fine-tuned through annealing or irradiation (thanks to the lab’s Aramis facility for instance). We have shown the existence of a metallic phase between the superconducting and insulating states that we have interpreted as a Bose metal, according to Das and Doniach’s theory [8]. In the coming years, we would like to continue these studies following three main axes:

1. Determining the conditions for the existence of a Bose metal. We would like to characterize this new phase, especially via noise and tunnel effect measurements. This will give us some information on the nature of this phase as well as on the importance of Coulomb interactions.

2. Continue the study of the QPT in 2D. This implies determining and understanding the limitation of M.P.A. Fisher’s model. We will pursue the work by undertaking new frequency measurements in the vicinity of the different transitions (in collaboration with A. Benoit (Grenoble) and M. Aprili (Orsay), which will allow us to determine some important parameters of the QPT. In parallel, we intend to install a magnetic field in our cryostat and continue with the measurements under magnetic field. 3. The microscopic nature of the system in

the vicinity of QPTs is extremely important. This is why we would like to deepen the structural understanding of our material through some microscopy measurements (AFM, SEM, eventually near field microscopy).

All these axes will be led in synergy with possible applications in high-precision instrumentation.

References:

[1] E. Abrahams, P. Anderson, D. Licciardello, T. ramakrishnan, “Scaling theory of localization : absence of quantum diffusion in two dimensions”, Phys. Rev. Lett., 42, p. 673, 1979.

[2] S. Kravchenko, M. Sarachik, “Metal-insulator transition in two-dimensional electron systems”, Rep. Prog. Phys., 67, p. 1, 2004.

[3] M.P.A. Fisher, “Quantum phase transitions in disordered two-dimensional superconductors”, Phys. Rev. Lett., 65, p. 923, 1990.

[4] S. Sondhi, S. Girvin, J. Carini, D. Shahar, “Continuous quantum phase transitions”, Rev. Mod. Phys., 69, p. 315, 1997.

[5] H. Aubin, C.A. Marrache-Kikuchi, A. Pourret, K. Behnia, L. Berge, L. Dumoulin, J. Lesueur, “Magnetic field-induced quantum superconductor-insulator transition in Nb0.15Si0.85”, Phys. Rev. B, 73, p. 094521, 2006.

[6] C.A. Marrache-Kikuchi, L. Berge, S. Collin, C. Dobrea, L. Dumoulin, A. Juillard, S. Marnieros, “Properties of thermometric NbSi thin films and application to detection in astrophysics”, Nucl. Instr. Meth. A, 559, p. 579-581, 2006.

[7] C.A. Marrache-Kikuchi, Ph.D. dissertation, Université Paris 11, 2006.

[8] D. Das, S. Doniach, “Existence of a Bose metal at T=0”, Phys. Rev. B, 60, p. 1261, 1999.