Kirtley and Tsuei - Physics

998 C. C. Tsuei and J. R. Kirtley: Pairing symmetry in cuprate superconductors
dominantly d-wave pair state in several cuprate superconductors;
but is it universal? There exists considerable
theoretical work suggesting that the stability of the
d-wave pair state depends on the details of the electronic
band structure as well as the pairing potential
(Wheatley and Xiang, 1993; Dagotto, 1994; O’Donovan
and Carbotte, 1995a, 1995b; Koltenbah and Joynt, 1997;
T. Sakai et al., 1997; Wysokinski, 1997; Varelogiannis,
1998a, 1998b). Given both s-wave and d-wave pairing
channels, the general conclusion of these studies is that
pairing symmetry is a function of band filling and certain
band parameters. Based on the t-t-J model, with t/t
0.4, the d-wave pair state prevails in a doping range
centered around half-filling of the band, and s-wave-like
pairing is more stable in the under- and over-doped regimes
(Wheatley and Xiang, 1993; O’Donovan and Carbotte,
1995a; Koltenbah and Joyut, 1997). There are
some Raman data on Bi-2212 and Tl-2201 as a function
of oxygen content suggesting that the gap is d wave near
optimal doping and isotropic in the overdoped range
(Kendziora et al., 1996). Like many other indirect symmetry
experiments, such an interpretation of the results
is controversial. For an alternative point of view, see
Hewitt et al. (1997).
It has been suggested that as the temperature decreases
below a certain characteristic value, a pure
d-wave pair state is not stable against the formation of
mixed pair states such as d x 2 y 2is or d x 2 y 2id xy
(Kotliar, 1988; Laughlin, 1994, 1998; Liu et al., 1997;
Ghosh and Adhikari, 1998a, 1998b; Zhu et al., 1998; Zhu
and Ting, 1998). Due to the coupling between the two
subcomponents of the order parameter, the mixed pair
state is fully gapped, much like that in an s-wave superconductor
(Ghosh and Adhikari, 1998a, 1998b). The
power-law temperature dependence of observables such
as specific heat, thermal conductivity, and penetration
depth characteristic of d-wave superconductors reverts
to the exponential behavior typical of s-wave superconductors.
Measurements of the penetration depth of Znsubstituted
LSCO (Karpińska et al., 2000) shows that it
retains a T 2 dependence, indicative of d-wave pairing in
the presence of scattering, until T c is suppressed to zero.
This argues against an admixture of s-wave pairing at
any T c . There has been a report of a temperaturedependent
pair state with broken time-reversal symmetry
(i.e., d x 2 y 2is state) in YBCO near T c (Koren
et al., 1998). The gap anisotropy in Bi-2212 measured by
ARPES also suggests a temperature-dependent twocomponent
order parameter with only a d x 2 y 2 symmetry
component near T c and both s- and d-wave components
at lower temperatures (Ma et al., 1995).
Furthermore, there is thermal transport evidence suggesting
that a phase transition from a pure d x 2 y 2-wave
state into states of broken time-reversal symmetry such
as dis or d x 2 y 2id xy can be induced in Bi-2212 at
low temperatures by magnetic field (Krishana et al.,
1997) or by magnetic impurities (Movshovich et al.,
1998). However, there are new experiments (Aubin
et al., 1998, 1999; Krishana et al., 1998) and calculations
(Anderson, 1998) indicating that the interpretation of
the original experiments is much more involved.
In view of these interesting but controversial results, it
is worthwhile to examine the universality issue by performing
phase-sensitive symmetry experiments with different
superconducting cuprate systems, and as a function
of composition (doping) and temperature for a
given cuprate system.
1. Hole-doped cuprates
As shown in Table IV, evidence for predominantly
d-wave pairing has been found in all the hole-doped cuprate
superconductors tested using phase-sensitive
methods. This is generally consistent with the numerical
studies of band structure which address the form of pairing
symmetry. As mentioned above, the d-wave channel
is favored near half-filling. More phase-sensitive symmetry
experiments are needed in the under- and overdoped
regimes to fully test the universality issue. The interpretation
of symmetry experiments with twinned YBCO
single crystals or films depends on the exact nature of
the twin boundaries (Annett et al., 1996; Walker, 1996).
However, phase-sensitive experiments with a tetragonal
cuprate superconductor such as Tl-2201 (Tsuei et al.,
1996, 1997) and untwinned YBCO samples (Wollman
et al., 1993; Brawner and Ott, 1994) make such complications
irrelevant. The fact that a d-wave signature has
been consistently and reproducibly observed in both
orthorhombic and tetragonal cuprates argues strongly
that the twin boundaries in YBCO have odd reflection
symmetry (Walker, 1996). The d-wave component of
the order parameter continues across the twin boundary,
whereas the s-wave counterpart changes its sign. An
even-reflection twin boundary corresponds to a predominantly
s-wave pair state, which is not observed in
any of the YBCO experiments listed in Table IV.
2. Electron-doped cuprates
Non-phase-sensitive symmetry tests have been contradictory
in the electron-doped cuprate superconductors
Nd 1.85 Ce 0.15 CuO 4 (NCCO) and Pr 1.85 Ce 0.15 CuO 4
(PCCO). For example, the in-plane penetration depth
ab (T) in NCCO has been fit both with an exponential
temperature dependence (Wu et al., 1993; Andreone
et al., 1994; Anlage et al., 1994; Alff et al., 1999), indicating
s-wave symmetry, and a power-law dependence
(Kokales et al., 2000; Prozorov et al., 2000), indicating a
symmetry with a line of nodes. The penetration depth
measurements in these materials are complicated by the
fact that they likely have large impurity scattering, which
tends to change ab (T) from a T to a T 2 temperature
dependence in a superconductor with a line of nodes
(Annett et al., 1991; Hirschfeld and Goldenfeld, 1993),
and by the paramagnetism of Nd 3 ions in NCCO (Cooper,
1996). Similarly, penetration depth measurements
of PCCO have been interpreted as indicating either an
s-wave (Alff et al., 1999) or non-s-wave (Kokales et al.,
2000; Prozorov et al., 2000) pairing symmetry. Quasiparticle
tunneling measurements in NCCO (Huang et al.,
Rev. Mod. Phys., Vol. 72, No. 4, October 2000