Electronic structure of new superconductor La0.5Th0.5OBiS2: DFT study

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Regular article

Electronic structure of new superconductor La _0.5 Th _0.5 OBiS ₂ : DFT study

N. Benayad, M. Djermouni

^*

, A. Zaoui

Modeling and Simulation in Materials Science Laboratory (LMSSM), Djilali Liabes University of Sidi Bel-Abbes, 22000, Algeria

a r t i c l e i n f o

Article history:

Received 6 July 2014 Received in revised form 2 October 2014 Accepted 3 October 2014 Available online 8 November 2014

Keywords:

Electronic structure Hydrostatic pressure Electron doping Fermi surface DFT

a b s t r a c t

We studied fromﬁrst-principles the recently discovered BiS2-layered superconductor La0.5Th0.5OBiS2and compared with LaO0.5F0.5BiS2. Firstly, we have performed a global geometry optimization in order to predict an accurate ground state. In contract to the parent semiconductor LaOBiS2and according to other recent works, the band structure of both materials presents superconducting behavior, four bands of Bi- 6porbitals that cross a Fermi-level. Additionally, the systematic study of the electronic properties as a function of pressure shows the same behavior in both materials“Enhancement of superconductivityTC”, where the Fermi-level is shifted upward and the Fermi surface presents a similar dispersion. These similarities between tetravalent cation electron-doped via Th^þ4substitution for La^þ3(La0.5Th0.5OBiS2), and monovalent anion electron-doped via Fsubstitution for O²(LaO0.5F0.5BiS2) may predict the same electronic properties.

1. Introduction

Since the discovery of high-transition-temperature (high-T

_C

) superconductivity in layered copper oxides [1

e

3], many re- searchers have searched for similar behavior in other layered compounds. In these exotic superconductors, tetragonal or ortho- rhombic structures lead to the high-T

C

superconductivity (HTSC) originated within these common layers, similar in nature to the recently discovered iron-pnictides/chalcogenides high-

T_C

super- conductors [4

e

6].

After the discovery of the cuprate family, some layered super- conductors were discovered. Layered magnesium diboride MgB

2

exhibits a comparably high

T_C

of 39 K, although it is a simple binary compound [7

e

9]. Layered nitride HfNCl and ZrNCl are band in- sulators. However, when electrons are doped by intercalation of ions into the interlayer site, an insulator-metal transition occurs and a superconductivity of

TC>

25 K is achieved [10

e

13]. As in the Hf-nitride superconductor, superconductivity in layered Co-oxide Na

_x

CoO

₂

is achieved by intercalation of H

₃

O

^þ

ions into the inter- layer site [14

e

17].

In context of HTSC, cuprates and iron-pnictides/chalcogenides are best examples. In February 2008,

Hideo Hosono

and co- workers reported the discovery of 26 K superconductivity in F-

doped LaFeAsO [18], marking the beginning of worldwide efforts to investigate this new family of superconductors [4

e

6], and since then,

T_C

has been pushed to over 55 K in related FeAs-based ma- terials [19]. Like the copper oxides, the iron pnictides have well- de

ﬁ

ned parent systems, such as LaFeAsO and BaFe

2

As

2

. Typically, superconductivity arises when charge carriers (either electrons or holes) are introduced into the parent compound, for example by substituting

ﬂ

uorine for oxygen in LaFeAsO. Fluorine donates its extra electron to the FeAs layer, thereby changing the layers carrier concentration. In the cuprates system, the parent phase is a Mott insulator; however, the iron pnictides/chalcogenides is a bad metal.

Nevertheless, a new family of layered superconductors has recently been discovered, where the materials possess BiS

₂

layers, with a square lattice of alternative alignment of Bi and S atoms.

Many materials found so far, the

ﬁ

rst one is Bi

4

O

4

S

3

with

TC¼

8.6 K [20,21]; following this report,

LnO_1x

F

_x

BiS

₂

(Ln

¼

La, Ce, Pr and Nd) with

TC

as high as 10 K, have been synthesized and studied [22

e

34].

Soon after, electron doping via substitution of tetravalent Th

^þ4

, Hf

^þ⁴

, Zr

^þ⁴

, Ti

^þ⁴

for trivalent La

^þ³

in LaOBiS

₂

parent, induces su- perconductivity while hole doping via substitution of divalent Sr

^þ²

for La

^þ3

does not [34].

Application of external pressure is a unique method to get a deep insight into physical properties of materials, e.g., heavy- fermion systems, manganese perovskites, and so forth [35,36], because the electronic states, e.g., density of state, Fermi surface, and bandwidth, etc. can be continuously varied under pressure as well as the volume of the materials.

*Corresponding author.

E-mail address:dr.m.djermouni@gmail.com(M. Djermouni).

Contents lists available atScienceDirect

Computational Condensed Matter

j o u r n a l h o m e p a g e :h t t p : / / e e s . e l s e v i e r . c o m / c o c o m / d e f a u l t . a s p

http://dx.doi.org/10.1016/j.cocom.2014.10.002

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Pressure tuning is less well understood. In some cases this powerful control parameter is aligned with its chemical- substitution counterpart. For instance, in LnO

1x

F

x

BiS

2

a good overlap exists between lattice-parameter variations by applied pressure or F substitution [26]; it should be noted that the effect of pressure (P) on superconductivity of electron-doped LaOBiS

2

with F-ion substitution was the subject of a number of investigations [22,27

e

29,31,37

e

41]. However, investigation of the effect of pres- sure on superconductivity of Ln

1x

M

x

OBiS

2

electron-doped regime with tetravalent ion (M) substitution in La site is quite scarce. There is only study of electron-doped La

_1x

M

_x

OBiS

₂

(M

¼

Th

^þ⁴

, Hf

^þ⁴

, Zr

^þ⁴

, and Ti

^þ⁴

) compared by hole-doped system with Sr

^þ²

substi- tution where the superconductivity is absent [34]. Among BiS

2

layered compounds discovered thus far, the maximum

T_C

is ~10 K for La(O,F)BiS

2

. The Fermi-level region is not so sensitive to the doping level, but it is sensitive to structural compression. At ambient pressure, LaO

0.5

F

0.5

BiS

2

shows

TC

~3.3 K; moreover,

TC

of LaO

_0.5

F

_0.5

BiS

₂

reaches a maximum value of ~10.5 K at 1 GPa [37].

In this article, we have examined the pressure effects up to 10 GPa on the electronic structure of electron-doped LaO

0.5

F

0.5

BiS

2

and La

_0.5

Th

_0.5

OBiS

₂

, The

ﬁ

rst-principles band-structure calculation indicated that the superconductivity was derived from the Bi 6p

x

and 6p

y

orbitals [32], using density functional theory (DFT) calcu- lation [42,43], we have investigated in different chemical- substitutions, the behavior of

px

,

py

-Bi and

px

,

py

-S under pres- sure, than their relationship with Fermi surface.

2. Structure

LaOBiS

2

has a layered crystal structure with a space group of tetragonal P4/nmm. As shown in Fig. 1, the structure is composed of a stacking of LaO layer and BiS

2

layer in the unit cell. The crystal structure has previously been designated as having the ZrCuSiAs type structure [22,25,26,29], however, the CeOBiS

₂

type structure may be a more appropriate structure assignment [32]. While the crystal structure of LaOBiS

2

and ThOBiS

2

has a different Wyckoff sequence than that of ZrCuSiAs [34], it has the same Wyckoff sequence and positions, and similar unit cell parameter ratios (c/a) as the crystal structure for CeOBiS

2

.

To dope electrons into the BiS

₂

conduction layers, we have substituted O

²

by F

and to dope electrons into the LaO layers, we have substituted La

^þ3

by Th

^þ4

(see Fig. 1).

We use structural coordinates for LaO

_1-x

F

_x

BiS

₂

and La

_1-x

Th

_x

O- BiS

₂

from powder x-ray diffraction measurements reported by

Mizuguchi

et al. [31] and

Yazici

et al. [34], respectively. In our calculation, the LaO

0.5

F

0.5

BiS

2

presents a space group of P-4m2 (No.

115) and La

_0.5

Th

_0.5

OBiS

₂

presents a space group of P4mm (No. 99), both space groups are reduced symmetry of tetragonal-P4/nmm.

The Wyckoff atomic coordinates for (La,Th) (O,F)BiS

2

are summa- rized in Table 1.

3. Computational detail and materials

Density functional theory has become the

de facto

standard for electronic-structure theory in the solid state and has been widely utilized throughout physics, chemistry, and biology [44]. It has also been employed very successfully in the past to accurately describe the bulk, surface and electronic properties of numerous minerals [45

e

47]. Layered superconductors have received much attention from computational methods, including DFT [5,6,13,16,48

e

51].

The structural optimization and electronic structure calculations were performed within the density functional formalism imple- mented in Wien2K code [52]. To date, the most commonly used exchange-correlation (XC) functional type remains the generalized gradient approximation (GGA), such as the

Perdew

e

Burke

e

Ernzerhof (PBE) functional [53,54], in this letter, the PBE functional introduced by

J. P. Perdew, K. Burke, and M. Ernzerhof

were used [55]. The FP-LAPW method is among the most precise DFT-based methods for performing electronic- structure calculations for crystal structures [56]. The FP-LAPW method divides space into an interstitial region and non- overlapping muf

ﬁ

n-tin (MT) spheres centered at the atomic sites.

In the interstitial region, the basis set is described by plane waves whereas in the MT spheres, the basis set is described by radial so- lutions of the one-particle Schr€ odinger equation and their energy derivatives multiplied by spherical harmonics. The self-consistent calculation is considered to be converged when the maximum value of the absolute difference between the new and the old charge density is put to be less than 10

²e

and the relative dif- ference of the new and the old energy eigenvalues of each state is less than 10

³

Ry. A plane-wave cutoff in the interstitial region is limited by

kmax¼

8.0/R

min

(where

Rmin

is the smallest muf

ﬁ

n-tin radius in the unit cell). The expansion of the partial wave

Fig. 1.(La/Th) (O/F)BiS2crystalline structure in P4/nmm-tetragonal.

Table 1

The Wyckoff positions of (La/Th) (O/F)BiS2.

Atom Site x y z Occupancy

La/Th 2c 1/2 0 zLa/Th 0.5/0.5

Bi 2c 1/2 0 zBi 1

S1 2c 1/2 0 zS1 1

S2 2c 1/2 0 zS2 1

O/F 2c 0 0 0 0.5/0.5

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Table 2

Calculated lattice parameters, bulk modulus and Wyckoff positions of LaOBiS2, LaO0.5F0.5BiS2and La0.5Th0.5OBiS2. Experimental results are also listed for comparison.

LaOBiS2 LaO0.5F0.5BiS2 La0.5Th0.5OBiS2 ThOBiS2

Calc. Expt.[23,29] Calc. Expt.[23,29] Calc. Expt.[34]

a(Ǻ) 4.0602 4.066, 4.0574 4.0896 4.069, 4.0651 4.0552 3.9623

c(Ǻ) 14.1910 13.862, 13.84 13.399 13.366, 13.29 13.6178 13.5062

B(GPa) 82.16 81.46 93.12

zLa 0.089 0.09, 0.0907 0.1067 0.103, 0.1007 0.0969 0.1017

zBi 0.6305 0.632, 0.6312 0.6146 0.622, 0.6207 0.6031 0.6013

zS1 0.3932 0.371, 0.3836 0.3834 0.362, 0.362 0.387 0.308

zS2 0.8089 0.819, 0.8101 0.8132 0.825, 0.815 0.8051 0.8382

Fig. 2.Band structure of LaOBiS2, (blue) Bi-porbitals, (red) S-porbitals, (green) O-porbitals. (For interpretation of the references to colour in thisﬁgure legend, the reader is referred to the web version of this article.)

Fig. 3.Band structure around Fermi level of LaO0.5F0.5BiS2and La0.5Th0.5OBiS2.

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functions was set to

l ¼

10 inside MT atomic spheres while the charge density was Fourier expanded up to

G ¼

12. In the self- consistent calculations a grid of 3000 k-points was employed in the irreducible Brillouin zone that results in 21 21 6 mesh with 264 points. The energy threshold between the core and the valance states was set at 6.0eV. The MT radii were chosen to ensure nearly touching spheres and to minimize the interstitial space. These MT radii were found to be 2.5, 2.5, 2.0 and 1.7

Å

for La/Th, Bi, S and O/F, respectively.

4. Results and discussion

Before calculating the electronic structure, a full structural relaxation is performed for the parent compound LaOBiS

2

using the FP-L/APW

þloþ

LO method and the results are compared with the available experimental and theoretical data. The atomic positions of the tetragonal-P4/nmm structure are described by the

z

parameters for La, Bi, S1 and S2 [31]; the calculated values are presented in Table 2.

The volume dependence of the energy was

ﬁ

tted with Murna- ghan equation of state [57]; the equilibrium lattice constants, the Wyckoff positions and bulk modulus are illustrated in Table 2, which are in good agreement with the experimental values. The band structure of parent compound LaOBiS

2

is shown in Fig. 2. The

circles characters in Fig. 2 represent the importance of the contri- bution of in-plane

p

states for Bi, S and O. the valence band top is dominated by the hybridization between 3p-S and 2p-O orbitals, while, the conduction band bottom consists mainly of in-plane Bi 6p orbital character. In this calculation, we have focused our attention to the BiS

₂

-layers contribution around Fermi level, since the BiS

2

layers are without doubt the origin of the superconducti- vity. The superconductivity doesn't appear in parent compound and it is clear that LaOBiS

₂

is a semiconductor with a large gap of

~0.87eV, and it is well known that DFT-PBE underestimates the gap, even by 100% or more. Recent works show that both the lattice structure and the electron doping affects the band gap, but in a different manner [23]. The discovery of superconductivity in LaO- BiS

2

system occurred when electrons have doped into BiS

2

-layers.

For better understanding of superconductivity in this system, we have chosen two different kinds of electrons doping, substitution of O

²

by F

and La

³^þ

by Th

⁴^þ

. For LaO

1x

F

x

BiS

2

, the optimal super- conducting properties were obtained for

x ¼

0.5 with the

TC

exceeding 10 K, this result is con

ﬁ

rmed by past reports. However, for La

1x

Th

x

OBiS

2

, there is only the work of

D. Yazici

et al., in which

x

is between 0 and 0.45 [34], in this latter, superconductivity were induced with

T_C

around 1.5

e

3 K. In our work and for comparison, we have studied both electron-doped LaO

0.5

F

0.5

BiS

2

and La

0.5

Th

0.5

OBiS

2

.

Fig. 4.Band structure around Fermi level of LaO0.5F0.5BiS2and La0.5Th0.5OBiS2under pressure (from 0 GPa to 9 GPa).

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Fig. 3 shows the band structure of LaO

0.5

F

0.5

BiS

2

and La

0.5

Th

0.5-

OBiS

2

around Fermi-level, as shown in this

ﬁ

gure, there are four bands of 6p-Bi orbitals that cross Fermi level and it is remarkable that the bands are in same dispersion for both compounds, this latter remark may con

ﬁ

rms the superconductivity of La

0.5

Th

0.5-

OBiS

2

. The partial density of states (PDOS) in Fig. 4 presents more details about the orbital contribution of these compounds; we notice that doped ion orbitals don't contribute in transport prop- erties of these materials and there is no states in valence band top or conduction band bottom for F

or Th

^þ⁴

ions. As LaOBiS

₂

, the same distribution of states is appear for both compounds, the

p-O/

p-S hybridization appear between

7 and 2 eV in each cases.

Comparing Figs. 2 and 3, it is clear that the main in

ﬂ

uence of F/Th substitution is a carrier doping characterized by shifting of the Fermi level towards the Bi 6

p

band, and the system becomes metallic.

Right after the discovery of the superconductivity in LaO

_1x

F

_x-

BiS

2

, it was reported that

TC

of LaO

0.5

F

0.5

BiS

2

shows sensitive pressure effect and increases to a maximum of 10.5 K at 1 GPa, suggesting that the lattice contraction is effective in the enhance- ment of the

TC

of BiS

2

-layers compounds. Recently,

Wolowiec

et al.

[37], have observed that the superconducting critical temperature

initially increases, reaches a maximum value of 10.1 K for LaO

0.5

F

0.5

BiS

2

at critical pressures of ~1.1 GPa, beyond this pressure, the compound changes his crystallographic structure from tetrag- onal phase (P4/nmm) to a monoclinic phase (P21/m) [38].

In order to understand the effect of external pressure on

TC

in

LaO

0.5

F

0.5

BiS

2

and La

0.5

Th

0.5

OBiS

2

and clarify similarities and dif-

ferences between the external pressure effect and the F/Th sub-

stitution effect, we have performed an electronic structure

calculation of this compounds under pressure up to 10 GPa, we

hope in this range of pressure that we have examined both mate-

rials in tetragonal structure. Fig. 5 shows the evolution of band

structure in LaO

0.5

F

0.5

BiS

2

and La

0.5

Th

0.5

OBiS

2

under pressure, we

have interested by Fermi-level region ( 2 eV

e

1 eV). For both

compounds, the topology of bands doesn't change; the main

changing is located in the gradual up-shift of the Fermi level

depending on pressure increasing, which apparently related to

T_C

increase. We suggest that the effect of chemical substitution and

hydrostatic pressure is the same. However, these effects are

different in nature, namely, the pressure mainly affects the band

structure, and the chemical doping affects the Fermi level. In fact,

the Fermi level has taken at 0eV which make the both effects

apparently the same. Furthermore, the calculation of PDOS of

p Fig. 5.Calculated partial density of states of LaO0.5F0.5BiS2and La0.5Th0.5OBiS2.

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Fig. 6.Calculated partial density of states of LaO0.5F0.5BiS2and La0.5Th0.5OBiS2under pressure (from 0 GPa to 9 GPa).

Fig. 7.Calculated Fermi surface of LaO0.5F0.5BiS2: (a) cross section forkz¼0 at 0 GPa, (b) 3D view at 0 GPa, (c) cross section forkz¼0 at 10 GPa, (d) 3D view at 10 GPa, (e) Theﬁrst Brillouin zone of P4/nmm space group.

Fig. 8.Calculated Fermi surface of La0.5Th0.5OBiS2: (a) cross section forkz¼0 at 0 GPa, (b) 3D view at 0 GPa, (c) cross section forkz¼0 at 10 GPa, (d) 3D view at 10 GPa, (e) Theﬁrst Brillouin zone of P4/nmm space group.

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orbitals of Bi and S ions, con

ﬁ

rm the past remarks. As shown in Fig. 6, only Bi-p

_x

and Bi-p

_y

states are responsible of superconduc- tivity in this system, in other hand, the similarity plot between both compounds is very clear; the behavior of

px

/p

y

orbitals upon increasing pressure is the same in LaO

_0.5

F

_0.5

BiS

₂

as well as in La

0.5

Th

0.5

OBiS

2

, this notice, con

ﬁ

rm the superconductivity of La

0.5

Th

0.5

OBiS

2.

In both cases, the dominant contribution to the electronic density of states at

E_F

derives from metallic bonding of the Bi 6p-electron orbitals in the BiS

2

layer. These orbitals form fours bands that cross

EF

, resulting in a large two-dimensional-like Fermi surface that is shown in Figs. 7 and 8 for LaO

_0.5

F

_0.5

BiS

₂

and La

0.5

Th

0.5

OBiS

2

respectively. Consistent

ﬁ

nding in other ab-initio works [22

e

24,33,39], our band structure, should give good nest- ing at the Fermi surface, and this electronic feature may cooperate with the bosonic modes that mediate the pairing to enhance the pairing interaction. The enhanced density of states at the Fermi level (N(E

F

)) may also play a role in the Cooper pairing. Comparing N(E

_F

) in both compounds in atmospheric pressure and under pressures, the same values were observed, there is only difference, in the evolution of N(E

F

) with pressure application, there is N(E

F

) decreasing after ~3 GPa in La

_0.5

Th

_0.5

OBiS

₂

, differently to LaO

0.5

F

0.5

BiS

2

, where N(E

F

) keeps her value until ~6 GPa. Figs. 7 and 8 show the comparison of the Fermi surface of LaO

0.5

F

0.5

BiS

2

and La

_0.5

Th

_0.5

OBiS

₂

, without pressure application ((a)-2D and (b)-3D) and with application of 10 GPa hydrostatic pressure ((c)-2D and (d)- 3D). The good nesting of the Fermi surface is shown in red band. As seen, the topology of this band in 0 GPa was almost unchanged in 10 GPa. The same remarks were observed in La

0.5

Th

0.5

OBiS

2

, sug- gesting the same superconducting properties for both compounds.

5. Conclusions

In summary, we studied from

ﬁ

rst-principles the recently discovered BiS

2

-layered superconductors LaO

0.5

F

0.5

BiS

2

and La

0.5

Th

0.5

OBiS

2

. Furthermore, we have performed a global geome- try optimization in order to predict accurately the electronic properties of the ground state of both compounds. The suppression of semiconducting behavior by electron-doped substitution of parent LaOBiS

2

induces the superconductivity in LaO

0.5

F

0.5

BiS

2

and there is markedly similar behavior in La

_0.5

Th

_0.5

OBiS

₂

. Comparing with LaOBiS

2

, one can conclude that F

/Th

^þ⁴

substitutions have only a small effect on the lattice parameters and the BiS

2

-layers bands.

This work based on comparison between past experimental reports about these materials and our electronic structure calcu- lation of each case. Additionally, the systematic observation of the electronic properties as a function of pressure shows that the enhancement of

TC

is predicted in both materials, where the Fermi- level shifted upward by almost the same energies. Moreover, the alterations of Fermi surface with pressure are slightly remarkable, and the principal band (red) keeps her topology under pressure. In DFT calculations, the superconducting

TC

may differ by nearly an order of magnitude. This conclusion is clearly general; i.e., therefore we have studied the pressure effect up to 10 GPa. From the recent works about LaO

0.5

F

0.5

BiS

2

, the

TC

decreasing with increasing pressure, maybe due to structural transition from tetragonal to monoclinic. Finally, we can conclude that electron-doped with tetravalent cations is good way to induce and improve the

TC

, as well as the monovalent anions electron-doped.

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Electronic structure of new superconductor La0.5Th0.5OBiS2: DFT study

Regular article