The Vortex Nernst effect in Cuprates Return to NPO Homepage
Are there vortices or vortex-like excitations above the zero-field superconducting transition temperature Tc0 in the cuprate superconductors?
If one regards the aggregate of electrons participating in Cooper pairing as a uniform superfluid, vortices are tiny 'pin-holes' in the superfluid in which the superfluid density ns is zero. In low-Tc superconductors such as Nb and V the vortex core is a cylinder. An extremely strong supercurrent wraps around the vortex, trapping a definite amount of magnetic flux called the flux quantum (or fluxoid). The existence of a vortex presupposes that the superfluid density is non-zero: in order to define a vortex, we must have substantial superfluid density in the vicinity.
When vortices flow, they produce an electric field perpendicular to their velocity. In principle, this Josephson ‘phase-slip’ voltage can be exploited as a highly sensitive probe of vortex motion.
In the cuprate superconductors, vortices exist in the vortex liquid state over most of the field-temperature (H-T) plane (see extended phase diagram). In the liquid state, the vortices flow easily in an applied temperature gradient. The motion engenders an electric field Ey parallel to the y-axis if the gradient -dT is applied along the x-axis and the the magnetic field H along the z-axis. In transport experiments, the existence of an electric field transverse to an applied temperature gradient that changes sign with H is known as the Nernst effect. The Josephson electric field produced by vortex motion is called the vortex-Nernst signal.
To address the question whether vortices exist at temperatures T above Tc0 we have used the Nernst effect extensively to search for the Josephson phase-slip signal.
We have obtained the unexpected result that the vortex Nernst signal persists to temperatures high above Tc0. Initially, the experiments were carried out in the single-layer cuprate LaSrCuO (Figure 2, Xu et al. Nature 2000)1. Subsequently, similar results were found in the double-layer cuprate YBaCuO (Wang et al., preprint), single-layer Bi 2201 (Wang et al. Phys. Rev. B 2001)2, single-layer Tl 2201, and double-layer Bi 2212 (unpublished).
Figure 2 Traces of the Nernst signal Ey/|dT| versus magnetic field H at fixed T in LaSrCuO (x = 0.12). Below Tc0 (29 K), the signal appears only when H exceeds the melting field Hm. Above Tc0, the signal is initially linear in weak fields but shows curvature at larger H. Note that it persists to above 60 K. From Wang et al. [Ref. 2].
In the underdoped regime of LaSrCuO (0.05 < x < 0.12), the signal persists as a long fluctuation tail up to 100 K above Tc0. These observations are rather outrageous when regarded within the purview of low-Tc superconductivity (the condensate amplitude vanishes above Tc0, so vortices should not exist at all except as a rapidly diminishing fluctuation signal). The persistence of the vortex signal implies that, in the cuprates, the pairing amplitude remains observable to temperatures high above Tc0. This implies that the loss of the Meissner effect (flux-expulsion) at Tc0 corresponds to a loss of long-range phase coherence rather than the vanishing of the pairing amplitude. This scenario was proposed theoretically for the cuprates by Kivelson and Emery (Nature, 1995) and others. Although there were early hints that this is indeed the case, the high sensitivity of the Nernst experiment has provided the clearest and most compelling evidence for this scenario. The broad range of temperatures above Tc0 in which the vortex signal is observed presents a direct challenge to the conventional BCS scenario (for this reason it has encountered stiff resistance from a large segment of the high-Tc community).
These observations are directly relevant to the central issue of the pseudogap state in the cuprates. The pseudogap state is a state that exists above the superconducting phase in a broad region of the T-x phase diagram. The pseudogap gradually becomes observable at a temperature T* as high as 300-400 K at small doping x (T* approaches Tc0 near x = 0.20) [Fig. 3].
While there is broad consensus that a large, partial gap exists in the pseudogap state, the physical nature of this state is strongly debated. Is it (1) an essential precursor to high-Tc superconductivity, (2) a competitive state that is hostile to superconductivity or (3) a mere 'spectator' state that is neither related nor detrimental to superconductivity?
Figure 3 The contours of the Nernst coefficient v = ey/H in the phase diagram of LaSrCuO. The numbers indicate the magnitude in microvolts per Kelvin-Tesla. As x decreases, the onset temperature rises to a maximum of 130 K at x = 0.10. All the contours display a maximum at 0.10 as well. The broken line indicates the pseudogap temperature T*. The steep decrease below 0.10 is caused by loss of hole carriers. From Wang et al.(Ref. 2).
The present results show that vortices exist up to an onset temperature Tonset that is approximately half way to T* (see Fig. 3). Moreover, Tonset varies with x in virtually the same way as T*. The trend strongly suggests that the pseudogap state is intimately related to the occurence of high-Tc superconductivity. There exists fluctuations between the pseudogap state and d-wave superconductivity which become stronger as Tc0 is approached from above. As shown in the Fig. 3, the fluctuation regime (light blue) penetrates deep into the pseudogap state. The trend in Fig. 3 implies that, as x decreases, the pairing energy scale becomes stronger, despite the steep decrease in hole density. The Nernst results strongly imply that the pseudogap state must be a precursor to the superconducting state (case 1). [See extended phase diagram for further discussion].
1. Z. Xu, N.P. Ong, Y. Wang, T. Kakeshita and S. Uchida, `Vortex-like excitations and the Onset of Superconducting Fluctuation in underdoped La2-xSrxCuO4.', Nature 406, 486 (2000).
2. Yayu Wang, Z. A. Xu, T. Kakeshita, S. Uchida, S. Ono, Yoichi Ando, and N. P. Ong, "The onset of the vortex-like Nernst signal above Tc in La2-xSrxCuO4 and Bi2Sr2-yLayCuO6.", cond-mat/0108242; Phys. Rev. B 64, 224519 (2001).