Electron correlation effects and induced superconductivity in LaxSr1−xTiO3

Physica C 235-240 (1994) 2267-2268 North-Holland

PHYSICA

Electron correlation effects and induced superconductivity in LaxSrl.xTiO 3 R.Ramakumar a, K.P.Jain a and C.C.Chancey b aphysics Department, Indian Institute of Technology, New Delhi-J6, India bPhysics Department, Purdue University Calumet, Hammond, IN 46323-2094, USA A study of electron correlation effects on the properties of LaxSrt.xTiO3 is presented using a single band repulsive Hubbard. model and employing Gutzwiller approximation. A possibility of inducing superconductivity in this material is suggested.

1

INTRODUCTION

Recently a new material, Srl.xLax..TiO3, has been studied 1"2 extensively by the group of Tokura et al., with a view to understanding the doping dependence of the electronic properties of correlated electron systems. The ground state of LaTiO 3 with integer filling of the Ti-3d band is Mott insulator with gap of 0.1 eV. Sr substitution removes electrons from this band and the material undergoes a insulator to metal transition. As the integer filling situation is approached, Tokura et al., have found that spin-susceptibility, effective mass and specific heat shows a strong enhancement and the plasma frequency is anomalously suppressed. So, this material goes from an ionic insulator (SrTiO3) to a metal with negligible correlation effects to metal with strong correlations and finally to a Mort insulator (LaTiO3). The Wilson ratio of .-- 2 implies that the enhancement in the properties as LaTiO 3 is approached is not due to Stoner factor. The main aim of this paper is to interpret the experimental results on LaxSq.xTiO 3 on the basis of a single band repulsive Hubbard model taking cognisance of the localization effects of on-site electron correlation (U). Applied to this material the Hubbard model describes electrons in the Ti 3d -band. The Gutzwiller approximation is utilized here to incorporate the effects of electron correlation.

2

ELECTRON CORRELATION EFFECTS IN THE NARROW BAND METAL

The Hubbard model imployed here is (1)

H = ~. Tij Ci~ Cio + U Y, nit nil ija

i

which in the Gut~viiler3proximation is written as

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+

H = y. q, T(i C~a Cia

(2)

ijo where q,, is the band-width renormalization factor given by .........

{ qo

o-d)a}

--"

n,,(1 - n o) (3)

Minimising the energy (wih respect to d) Eg= q:e! (where c o=

+ q!e~ ~

~-Ud ek<0)

lkl
the condition to determine 4 double occupancy ,d, is obtained. Wc will use these results, in the paramagnetic limit, to calculate the effective mass and the plasma frequcncy as function of doping (,5) in LaxSrt.xTiO 3 (for details sec Rcf.4)

R. Ramalatmar et aL IPhysica C 235-240 (1994) 2267-2268

2268

•:.1

Effective m a s s

Starting from the closed shell insulator SrTiO 3, substituting Sr sites with La, electrons are introduced into the Ti-3d-band. As the electron concentration increases in this band, correlation effects should start becoming dominant resulting in an increase of m* of the charge carriers. In the Gutz'willer approximation m* is given by m*/m = I/q, where m is the electron mass in the uncorrelated band. The results are shown in Fig. 1. The enhancement of m*/m is clearly seen in the experiments of Tokura et al.

reduction of the As at the interface would considerably reduced since m/m* is decreased in the correlated phase of LaxSq.xTiO3. So, if the film of the titanate is such that the Ti 3d -band is close to integer filling, correlation incuced localization effects would lead to an enhancement of the induced superconducting gap in this material. We have shown that localization effects of the electrons due to electron correlations in the Ti-3d -band in LaxSrt.xTiO3 is the predominant factor which determines the doping dependence of the properties of this material.

2.2 P l a s m a f r e q u e n c y The plasma frequency of a correlated narrow band metal can be written as 2 Up

4rtNse2 )

¢.m

nq

o, I,o

,

o,'/

•

(5)

-o, V

where N, is number of lattice sites per unit volume and q is given in Eq.3. The factor which determines plasma frequency, nq, is shown in the inset of Fig. 1. This is consistent with the suppression of plasma frequency found in Ref.1.

O.0 0.0 0 - 2 0 . t . =0.95

\ 0.6 0.8 6"~

,... 1.00

3

INDUCED SUPERCONDUCTIVITY

It should bc possible to induce superconductivity, through proximity effect, in LaxSq.xTiO3 by making NS system by depositing a thin film of this material on a known superconductor, Cu-O based high-Tc materials for example. The proximity induced superconducting gap is determined by the conditions

Ed ]=D d 1

(NV)s - (NV)N ; D s ~

s

N[ ' ~ x

Ol

0.0

,

I 0.2

~ n 0.~. 0.6 6 .---~

i 0.8

i 1.0

Figure 1. Effective mass and nq verses deviation from half-filling. REFERENCES I.

(6)

2,

where V~ is the pairing field associated with the induced gap in the N layer, D's are the diffusion cocffccicnts and NN,s are the density of states. Since D N is givcn by 1/3(m/m*)(lFv~. ) , the

3. 4.

Y. Tokura et al. Phys. Rcv. Letters 14, 2126(1993) Y. Fujish]ma ct al., Physica C165-189, 1001(1989) M.C. Gutzwillcr, Phys. Rcv. 173, A923(1964); 137, A1726(1965) R. Ramakumar ct al., Phys. Rev. B48, 6509 (1993) and Phys. Rev.B, 1994, submitted