The variation of the transition temperature of high T-c superconductors by electric field effect

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PHYSICA

ELSEVIER Physica C 341-348 (2000) 291-292

www.elsevier.nl/Iocate/physc

The variation of the transition temperature of high Tc superconductors by

electric field effect

Tzong-Jer Yang a* and Wen-Der Lee b

aDept, of Electrophysics, National Chino-Tung University, Hsinchu, Taiwan 300, Rep. of China bDept, of Electrical Engineering, Lee-Ming Institute of Technology, Tai-Shan 24314, Taiwan, R O C

High Tc superconductor is considered as an alternately stacked metal and insulating layers. The electric field effect in this layer superconductor is investigated by the Thomas-Fermi(TF) approximation for the screening of an applied electric field and in the frame of Ginzburg-Landau(GL) theory with the coupling between metallic layers for the transition temperature. The change of the transition temperature related to the coupling constant and applied voltage is derived for two and three C u 0 2 layers. The transition temperature for more than three layers is also briefly discussed.

1. I N T R O D U C T I O N

Electric field induced charge effects to superconductors were studied back to 1960. The changes in conventional superconducting transition temperature Tc were extremely small due to the electric field penetration length of less than 1,~i. T h e discovered high Tc oxide superconductors lightened a new wave to get large electric field effects due to the low carrier density and thus larger penetration length of around ten of ~ and small coherence length. Therefore, the shift of the critical temperature of the high-temperature superconductors(HTSC) is easily observed.

Up to the present time,the mechanism caus- ing the large electric field effects is most ac- cepted to be the charge modulation model.[1] The usual approach is to use BCS weak coupling model, T F model and Poisson equation for a weaker anisotropic HTSC. Sakai[2]used T F model and regarded H T S C as consisting of alternately stacked N superconducting and N insulating layers(thickness d). The present short report uses T F model, g3 interlayer coupling model[3] and plasmon BCS-like mechanism to simulate the field effect of the change of Tc in HTSC. Such an approach is an a t t e m p t to relate the electric field effect to the superconducting mechanism. *This work is supported by NSC of Rep. of China.

Our approach is briefly described in Sec-II. The results and discussion is presented in Sec-III. Fi- nally, a brief conclusion is made.

2. T H E O R Y

Consider a system of a MIS hke structure[2], there is a gate insulator with thickness L between the gate metal and HTSC. Assume, there is also an insulating layer Iowith thickness s between the gate insulator and the topmost C u O 2 layers. The C u 0 2 superconducting layer is considered as a two dimensional.

By application of a gate voltage V, there is the charge density Q induced at the gate electrode

v

isQ = ( - ¢ 1 ) ~ L ~ , s , where ¢1 is the potential of the topmost C u 0 2 layer of HTSC, e~ and eb are the dielectric constant of the gate insulator and the insulator layer Io, respectively.

In the T F model, the induced charge density on the pth C u O 2 layer is 6np = e~F¢(rll , Zp), where CF is density of states at the Fermi energy and zp .= L + S + (p - 1)d. T h e origin of z axis is set at the gate metal and positive z axis is downward perpendicular to the surface of HTSC. The elec- trostatic potential ¢(rLi , z) at the position z may be determined by the Poisson equation[4]

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292 T,-J. Yang, W.-D. Lee/Physica C 341-348 (2000) 291-292

2 N ~gN(ZN ) ,..,,

+~¢~ ~ ¢(z)6(z

-- z p ) + - - - j - - - o t z - Z N + I )

Cs p=2

where es is the dielectric constant of the insulator inside HTSC. Cg is the potential between Nth

Cu02

layer and (N + 1) th

Cu02

layer. While z ¢ 0 and z ~ zp, the Poisson equation becomes Laplace equation. The solution of this equation is Cp(Z)

= gp(Z-Zp)+Bp,

where z~ is a reference coordinate and may be taken to be z~ = zp + d, By using Gauss's law, and the continuity of the potential

Cp(zp+l) = Cp+l(zp+l) = ¢(zp+l)

then we have the recurrence relation among

Ap, Bp,

A1

and B1. To understand the change of T~ of HTSC with the applied electric field, several situations will be discussed separately as follow- ing.

(i)only one

Cu02

layer

The Fermi energy will be modified in the T F approximation as

EF = E ° +

e¢1, where E~ is the Fermi energy of HTSC without applied voltage. Tc of HTSC can be gotten by plasmon mechanism. Tc = 1.134EFexp(-1/A), where A is a coupling constatn depending on the Fermi energy. The essential change of T~ with applied electric field shows a linear behavior.

(ii)only two

Cu02

superconducting layers In this situation, we use th GL theory approach to get Tc of HTSC. The free energy density f of HTSC according to the g3 model[3] is

2

f = a Z ( T - Tcl)[¢i(zi)[ 2 -

g3[¢~(zl)¢2(z2) + c.c.]

i~1

where T~i -- 1.134EFi exp(--1/Ai),

EFi

--- E~ + e ¢ i , i = 1, 2,; ¢ I ( Z l ) and ¢2(2:2) a r e

order parameter on 1st and 2nd

Cu02

layer respectively, g3 is interlayer coupling constant and assumed to be negligible for field effect. The Tc can be obtained by minimizing free energy with respect to ¢~'(zl) and ¢~(z2). Then T~ is

1 [(T~I + T~2) + x/(Tol - T~2) ~ + 4(g~/~)2]

T~=~

According to the result of Sakal[2], the electric field effect is limited within three superconducting

Cu02

layers. The free energy F of more than three

Cu02

layers may be easily expressed. Then minimizing F with respect to ¢~, we may get the linear system equations and finally Tc can be gotten.

3. R E S U L T S a n d D I S C U S S I O N

For one

Cu02

layer, T~ increases linearly as electric field E increases in plasmon mechanism. For two

Cu02

layers, the interlayer coupling strength g3 affects

To,

but the sign of g3 does not change T~. The change of T~ deviates slightly from that in one

Cu02

layer. For more than three

Cu02

layers, the Tc value may be calculated by Ginzbung-Landau theory and taken into account the effect of Debye screening length. The expres- sion of Tc is not shown here. But the qualitative behavior of the change of Tc due to the applied field is essentially limited to two or three

Cu02

layers. Because the Debye screening length is al- most 5-~ in most HTSC. Our present approach may be extended to the other mechanisms. 4. C O N C L U S I O N

Tc of HTSC in an applied electric field is derived on the basis of plasmon mechanism in the framework of T F model and g3 interlayer coupling model. The qualitative behavior of the change of Tc is shown linearly with the electric field E and independent of the sign of 93 for one or two

Cu02

layers. The electric field effect on HTSC is essentially limited within the Debye screening length. Our approach may be easily extended to other mechanism.

R E F E R E N C E S

1. T. Frey, J. Manhart, J.G. bednorz and E.J. Williams, Phys.Rev. B51 (1995) 3257. 2. Shigeki Sakai, Phys. Rev. B47 (1993) 9042. 3. T. Schneider, Z. Gedik, and S. Ciraci, Z.

Phys. B83, (1992) 313.

4. Andre' Fortini, Physica C 257 (1996)31. (iii)More than three

Cu02

layers