Mixed-state quasiparticle transport in high-T_c cuprates

Discovery by Krishana, Ong and co-workers [Science 277, 83 (1997)] of the mysterious high-field plateau in the longitudinal thermal conductivity $\kappa_{xx}(H)$ of Bi2212 superconductor set theorists scrambling for possible explanations of this phenomenon.  Such a plateau behavior stands in a stark contrast to the strong field-dependences in \kappa_{xx}(H) found in conventional superconductors over the entire range of fields. More significantly, it has long been recognized that measurements of thermal conductivity contain considerable information pertinent to the pairing mechanism in cuprates (such as the inelastic scattering rates), which can however only be extracted if a detailed understanding of the quasiparticle dynamics in magnetic field is established. The initial interpretation of the plateau involved a field-induced transition to a fully gapped state, such as the d+id' state proposed by Laughlin, which would effectively freeze out the quasiparticle transport at low energies. However, experimentally there appears to be little additional evidence for such a transition, except perhaps for the apparent bound states found by scanning tunneling microscopy (STM) in the vortex cores of YBCO which should not exist in a pure d-wave state (see below).

I have developed a theory which accounts for the plateau effect in a very natural way, invoking only the fundamental properties of Dirac fermions which are the relevant low-energy excitations in a d-wave superconductor. In particular I have demonstrated that, if the vortex array is disordered, a field-independent longitudinal thermal conductivity arises quite naturally in a pure d-wave state above a crossover field H*. This occurs as a result of exact compensation between the enhancement of the quasiparticle density of states due to vortices (the ``Volovik effect'') and the reduction in the quasiparticle mean free path by scattering from vortices. The limiting high-field value of \kappa_{xx}(H) is universal just like the impurity induced universal microwave conductivity predicted by Patrick Lee. The approach to this limiting value depends on the distribution of vortices in the sample and will therefore be material and sample dependent, in agreement with experimental data. At present I am generalizing this theory to include Hall thermal conductivity \kappa_{xy}(H) which is also a measurable quantity and is of even greater potential interest since it is strictly electronic with no phonon contribution. [For more details see Phys. Rev. Lett. 82, 1760 (1999). ]
 

Electronic structure of d-wave vortices

Although the notion of unconventional d-wave superconductivity in high-T_c cuprate superconductors has been generally accepted for a relatively long period of time, the modeling of the vortex dynamics and transport in the mixed state of these materials has been based almost exclusively on conventional s-wave concepts. This is largely because until very recently the understanding of various aspects of the structure of individual vortices in a d-wave superconductor was either incomplete or lacking altogether. In collaboration with Z. Tesanovic (Johns Hopkins) I have performed the first detailed analysis of this problem focusing primarily on the properties of the order parameter and of the electronic states near the core. Using a combination of numerical and analytical techniques we came to a surprising conclusion that, in a pure $d_{x^2-y^2}$ superconductor, the vortex core states are delocalized with wave functions extended along the gap node directions (see figure), and exhibit continuous energy spectrum. This finding is in a sharp contrast to the well known result of Caroli, de Gennes and Matricon, who showed (more than 30 years ago) that vortex core in an s-wave superconductor contains a discrete set of quasiparticle states, localized on the length scale set by the superconducting coherence length. I am presently exploring the consequences of these findings and investigating in detail the relation of our results to the experimental data recently obtained using the cutting edge technique of scanning tunneling spectroscopy. [For more details see Phys. Rev. Lett. 80, 4763 (1998) and Phys. Rev. Lett. 79, 4513 (1997).]
 
 

Spectral properties of underdoped high-T_c cuprates

A large amount of data exists on underdoped cuprates showing a ``pseudogap'' behavior above the superconducting transition temperature T_c which persists up to a much higher temperature T^*. One school of thought, put forward by Emery and Kivelson, explains this behavior by postulating a state above T_c with a finite magnitude of a local superconducting order parameter which, however, has lost its global phase coherence due to fluctuations. T^* is then interpreted as the temperature at which the amplitude vanishes and the pseudogap is lost. Within such a picture the transition to a superconducting state is of a 3D XY type and the physics above T_c is dominated by fluctuating unbound vortex-antivortex pairs. A detailed understanding of such a phase is lacking at present. With A. J. Millis (Johns Hopkins) we are currently performing the very first in-depth analysis of the effect of such a fluctuating medium on various physical properties in the psudogap regime. We find that photoemission and tunneling spectroscopy data are well accounted for by a simple model in which mean field d-wave quasiparticles are semiclasically coupled to supercurrents induced by fluctuating unbound vortex-antivortex pairs. We also conclude that while transverse phase fluctuations are important at temperatures above T_c, longitudinal fluctuations are suppressed at all temperatures. This is in contrast to some theories which suggest that longitudinal fluctuations are responsible for the experimentally observed suppression of the superfluid density at low temperatures. More recently I became interested in dynamical and transport properties of this pseudogap regime and I am presently investigating the consequences of the above scenario for these quantities. [For more details see Phys. Rev. B 58, 14572 (1998) ]


Flux lattices in unconventional superconductors

In collaboration with C. Kallin, A. J. Berlinsky, P. I. Soininen (McMaster) and A. L. Fetter (Stanford) we solved the problem of the vortex state in a d-wave superconductor in the limiting cases of an isolated vortex (near H_{c1}) and of the Abrikosov lattice (near H_{c2}). In view of the fact that in high-T_c cuprates H_{c2} typically exceeds 100T, most experiments are done in the regime of intermediate field H such that H_{c1}<< H << H_{c2}. Here, strictly speaking, our results do not apply. In collaboration with I. Affleck and M. H. S. Amin (UBC) I have formulated a generalized London model for a d-wave superconductor, which is valid precisely in this experimentally important regime. For a vortex lattice this model reproduces very well results obtained from the Ginzburg-Landau (G-L) theory, however the physics becomes much more transparent and the calculations are considerably easier. More recently we have extended this model to low temperatures, where the G-L theory does not apply. In this regime the microscopic effects of d-wave pairing become important and lead to a non-local relationship between supercurrent and superfluid velocity which becomes singular at T=0. We have shown that this singular behavior has profound implications for the structure of the vortex lattice which, as a function of decreasing temperature, undergoes a series of sharp structural transitions and attains a universal limit at T=0. Such behavior should be readily observable in experiment and several groups now actively search for these effects in the cuprates. [For more details see Phys. Rev. B 58, 5848 (1998), Phys. Rev. Lett. 79, 1555 (1997), and Phys. Rev. B 55, R704 (1997). ]


back home...