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Physica C 412–414 (2004) 178–181

Study of the tunneling effect on quasi-2Dorganic superconductors j-(ET)2X

Y. Tanuma a,*, K. Kuroki b, Y. Tanaka c, S. Kashiwaya d

a Institute of Physics, Kanagawa University, Yokohama, Chofu, Tokyo 221-8686, Japanb Department of Applied Physics and Chemistry, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan

c Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japand National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8568, Japan

Received 29 October 2003; accepted 15 December 2003

Available online 6 May 2004

Abstract

We study the tunneling spectroscopy via Andreev bound states, which can be used to determine the pairing sym-

metry if one can prepare well-treated surfaces in the superconducting plane. In the present study, we investigate the

tunneling spectrum in systems having multiple Fermi surfaces, where we focus on organic superconductors j-(ET)2X.We show that the multiplicity of the Fermi surfaces can lead to a splitting of the zero-bias conductance peak (ZBCP).

We propose that the presence/absence of the ZBCP splitting is used as a probe to distinguish the pairing symmetry in

j-(ET)2X.� 2004 Elsevier B.V. All rights reserved.

PACS: 74.20.Rp; 74.50.+r; 74.70.)bKeywords: Pairing symmetry; Organic superconductors; Andreev bound states; Splitting zero-energy peak

1. Introduction

Pairing symmetry of quasi-2D organic super-

conductors j-(ET)2X [1] remains to be controver-sial. There are strong experimental evidences

suggesting that this material has a d-wave pair

potential [2–4]. According to earlier theoretical

works [5–7], the pairing symmetry of j-(ET)2X is

accepted as dx2�y2 -wave pairing. On the other

* Corresponding author. Tel.: +81-45-491-1701/481-5661;

fax: +81-45-413-7288.

E-mail address: tanuma@n.kanagawa-u.ac.jp (Y. Tanuma).

0921-4534/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.physc.2003.12.034

hand, a recent thermal conductivity measurement

suggests dxy-wave pairing [8]. In order to solve this

puzzle, two of the present authors have shown that

a dxy-like pairing may slightly dominate over dx2�y2

pairing when the dimerization of the ET molecules

is not so strong [9].

Now, it is known that tunneling spectroscopy

via Andreev bound states (ABS’s) enables us to

detect the sign change in the pair potential as well

as its nodal structure [10–15]. The existence of

ABS’s, which manifests itself as a zero-bias con-

ductance peak (ZBCP), has been actually observedfor high-Tc cuprates, and so on. In this context, it

is of great interest to investigate whether the ZBCP

ed.

x

y

b

c

t'

tx

tx'

txty

ty'

ty'

t'

tx'

Fig. 1. Schematic of the surface of the xy plane on the aniso-

tropic triangular lattice.

Y. Tanuma et al. / Physica C 412–414 (2004) 178–181 179

due to the ABS’s can be observed in organic

superconductors [16].

However, a scanning tunneling microscopy

(STM) experiment for j-(ET)2X showed the ab-

sence of ZBCP for arbitrary angle of the super-

conducting bc-plane [17]. According to thepioneering studies [10,12–15], if the pairing sym-

metry of j-(ET)2X is d-wave, ABS is expected to

be created at well-treated surfaces for arbitrary

injection orientations. This is contradictory to the

case of high-Tc cuprates.Motivated by this point, here we investigate the

tunneling spectrum, where we focus on multiplicity

of Fermi surfaces in j-(ET)2Cu(NCS)2, consistingof two portions separated by small gaps [18]. Re-

cently, we found the atomic-size wave nature of the

ABS’s with zero energy depends on the shape

of the Fermi surface and the geometry of the sur-

face. The results indicate that theABS’s are sensitive

to the shape of the Fermi surface. So far, it has not

been clarified how the multiplicity of the Fermi

surface influences the ZBCP. In this paper, we ex-tend our previous studies [19] on anisotropic trian-

gular lattice by taking into account the multiplicity.

þ y y

2. Formulation

We start from an extended Hubbard model

given by

H ¼ �Xi;j;r

tijcyi;rcj;r

� V2

Xi;j;r;r0

cyi;rcyj;r0cj;r0ci;r;�

Xi;r

lcyi;rci;r; ð1Þ

where cyi;r creates a hole with spin r ¼"; # at site

i ¼ ðix; iyÞ, where each site corresponds to ET

molecule dimmers. Here, we consider five kinds of

hopping integrals, txð¼ tÞ, tx0 , ty , ty0 , and t0 in the xyplane on the anisotropic triangular lattice shown

in Fig. 1. We choose the values of t0 ¼ 0:8t, ty0 ¼ tx,tx0 ¼ ty , in order to reproduce the shape of Fermisurface for j-(ET)2Cu(NCS)2 [18]. The chemical

potential l is determined for the half-filled band.

The effective attraction V is assumed to act on a

pair of electrons.

Next, by solving the mean-field equation for a

unit cell with NLð¼ 500Þ sites in the x direction and

two sites in the y direction, we obtain the eigenen-ergy Em. In terms of the eigenenergy Em and the wave

functions umi , v

mi , the Bogoliubov-de Gennes equa-

tion for the (1 0 0) surface in the xy plane is given by

Xj

Hij FijF ij �H

ij

� �umj

vmj

� �¼ Em

umi

vmi

� �; ð2Þ

HijðkyÞ ¼ �txgþdjx ;ixþ1 � tx0g�djx;ixþ1

� tye�2ikydiy ;2gþdjy ;iyþ1

� ty0e�2ikydiy ;2g�djy ;iyþ1

� t0e�2ikydiy ;2djx;ixþ1djy ;iyþ1

� txg�djx;ix�1 � tx0gþdjx ;ix�1

� tye2ikydiy ;1g�djy ;iy�1

� ty0e2ikydiy ;1gþdjy ;iy�1

� t0e2ikydiy ;1djx;ix�1djy ;iy�1 � ldix;jxdiy ;jy ; ð3Þ

where we define gþ ¼ 12f1þ ð�1Þixþiyg and g� ¼

12f1� ð�1Þixþiyg.As for plausible pairing symmetries in j-

(ET)2Cu(NCS)2, we consider dx2�y2 -wave pairing

given by

FijðkyÞ ¼ Dxgþdjx;ixþ1 þ Dx0g�djx;ixþ1

� Dye�2ikydiy ;2gþdjy ;iyþ1 þ Dxg�djx;ix�1

þ Dx0gþdjx ;ix�1 � Dy0e�2ikydiy ;2g�djy ;iyþ1

� Dye2ikydiy ;1g�djy ;iy�1

� Dy0e2ikydiy ;1g dj ;i �1; ð4Þ

(a)

(b) dxy-like

0

2

4

6tx' /tx=1

0.90.8

-1 0 10

10

20

tx' /tx=10.90.8

E / 2∆0

N(E)

N(E)

d x -y2 2

Fig. 2. Tunneling spectrum for (a) dx2�y2 and (b) dxy -like-waves

fixed in Dx0 ¼ Dx.

180 Y. Tanuma et al. / Physica C 412–414 (2004) 178–181

and dxy-like pairing given by

FijðkyÞ ¼ Dxgþdjx;ixþ1 þ Dx0g�djx;ixþ1

þ Dye�2ikydiy ;2gþdjy ;iyþ1

þ Dy0e�2ikydiy ;2g�djy ;iyþ1

� aDpe�2ikydiy ;2djx;ixþ1djy ;iyþ1

þ Dxg�djx;ix�1 þ Dx0gþdjx;ix�1

þ Dye2ikydiy ;1g�djy ;iy�1

þ Dy0e2ikydiy ;1gþdjy ;iy�1

� aDpe2ikydiy ;1djx;ix�1djy ;iy�1; ð5Þ

with a ¼ 0:8t [9]. Here, we select Dx0 ¼ Dy and

Dx ¼ Dy0 ¼ Dp ¼ D0, where D0 is a bulk value. For

organic superconductors, at the present stage, we

can only assume that the pairing symmetry at the

surface is the same as that in the bulk.

In order to compare our theory with STM

experiments, we assume that the STM tip ismetallic with a constant density of states, and that

tunneling occurs only to the site nearest to the

tip. This has been shown to be valid through the

study of tunneling conductance of unconventional

superconductors [10]. The tunneling conductance

spectrum is then given at low temperatures by the

normalized surface density of states [10],

NðEÞ ¼

R1�1 dxNSðxÞsech2 xþE

2kBT

� �R1�1 dxNNðxÞsech2 x�2D0

2kBT

� � ; ð6Þ

NSðxÞ ¼Xkb;m

½jum1j2dðx � EmÞ þ jvm

1j2dðx þ EmÞ�:

ð7ÞHere NSðxÞ denotes the surface density of states

for the superconducting state while NNðxÞ the bulkdensity of states in the normal state.

3. Results

In this section, we present the calculation results

for the model of j-(ET)2X. Fig. 2(a) and (b) show

the tunneling spectrum for dx2�y2 and dxy-like-wave

pairings, respectively. In the case of tx0 ¼ tx, thereexists a distinct peak at zero energy, which

resembles those obtained in previous theories

assuming round shape Fermi surface. The ZEP

arises because incident and reflected (including

oblique incidence) quasiparticles normal to the

surface feel opposite signs of the pair potential,

which results in a formation of the ABS. If we turn

on the multiband effect by letting tx0 6¼ tx, the ZEP

is found to split into two.Next, let us show the tx0=tx dependence of the

ZEP splitting. In Fig. 3, the width of the ZEP

splitting W is plotted as functions of tx0=tx for dx2�y2

and dxy-like pairings. W for the dxy-like pair po-

tential is almost proportional to tx0=tx, and larger

than that for dx2�y2 . In the regime of tx0=tx > 0:9, inparticular, we see no splitting for the dx2�y2 pairing.

Since t0x=tx is estimated to be �0.9 [20], we may be

Fig. 3. The tx0=tx vs the zero-energy peak splitting width W .

Y. Tanuma et al. / Physica C 412–414 (2004) 178–181 181

able to distinguish between dx2�y2 and dxy-like

pairings through the presence/absence of ZEP

splitting.

4. Summary

To summarize, we have studied the multiband

effect on tunneling spectroscopy of organic

superconductors j-(ET)2X. We find that the mul-

tiplicity of the Fermi surface can lead to a splittingof the ZEP. As regards j-(ET)2Cu(NCS)2, since

t0x=tx is estimated to be �0.9 [20], we can distin-

guish between dx2�y2 and dxy-like pairings through

the presence/absence of ZEP splitting. At this

stage, it is not easy to make a well oriented surface

of organic superconductors due to its fragile

crystal structures. For this reason, it is very diffi-

cult to observe ZBCP. We hope the substantialadvance of microfabrication technique of organic

films in order to observe ZBCP near future.

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