Quasiparticles in the Vortex State

I have been interested for many years in heavy fermion and, more recently, high temperature cuprate superconductivity. The heavy fermion materials are metals involving rare earth or actinide ions in which electrons behave as though they have masses much larger than their bare mass, sometimes as much as a proton mass. Transition temperatures are only about 1K. The cuprate materials, with Tc's of order 100K or above, typically have a layered perovskite structure, and superconductivity seems to be nearly 2D. Here's a recent New York Times assessment of their technological potential. In both classes of systems there is strong evidence that superconductivity is unconventional in the sense that the superconducting order parameter or pair wave function has symmetry less than the underlying crystal lattice. In particular it is now established that the cuprate materials have d-wave symmetry. Here is a recent review explaining why we think so. One of the key differences between conventional superconductors and superconductors with nodes is the nature of the quasiparticle excitations in the Abrikosov vortex state, where the system is threaded by magnetic flux bundles. In the conventional, s-wave state, the magnitude of the order parameter vanishes linearly in the core of the vortex, forming an effective potential for bound quasiparticle excitations. The density of these excitations is roughly that of a normal metal, so the specific heat in a field is C ~ H T, since a normal metal has a T-linear specific heat, the number of vortices scales with H, and no other low-energy excitations exist.

d-wave superconducting gap. Note "+" and "-" means the order parameter has this sign for these directions of k on the Fermi surface. The gap goes to zero in the (110) directions, and low-energy properties are dominated by single particle excitations near these nodes.

  Recent projects

• Thermodynamics and transport: semiclassical theory

  Comparison of experiment of Chiao et. al. on YBCO with semiclassical theory of Kuebert & PH. Angular DOS dependence leads to oscillations in specific heat.

  The usual theory of quasiparticle states in the Abrikosov vortex lattice of a type-II superconductor says that only the localized states near the core are populated at low T, while the extended ones are gapped. The situation is reversed in d-wave materials, where Volovik (1993) showed that the extended states dominate the DOS, giving rise to a sqrt(H) field dependence. Kuebert & I developed a simple semiclassical extension of these ideas to transport, wherein at low T quasiparticles are assumed to scatter off the same entities they do in the H=0 state, i.e. vortex scattering is neglected. This theory provides a remarkably good fit to low-T experiments of Toronto group (Chiao et al. PRL 98), but needs to be extended to high temperatures. This work was described in cond-mat/9801105 (Phys. Rev. Lett. 80, 4963 (1998)). Related work within the same semiclassical model about anisotropy of field dependence for thermodynamic properties with field in the ab plane with Vekhter, Nicol, & Carbotte appears in Phys. Rev. B 59, R9023 (1999), (cond-mat/9809302). A reformulation of the entire theory in terms of superfluid velocity probability distributions, which allows one to calculate for vortex liquid states as well as regular lattices, appears in cond-mat/0011091( Phys. Rev. B 64, 064513 (2001)). With the field in the plane of the "2D" superconductor, different d-wave nodes contribute different Doppler shift energies according to their orientation.

• Structure of vortex in d-wave superconductor

  A vortex in a d-wave superconductor has unusal phase structure. Although the d-wave phase winds once, as in ordinary superconductors, there exist mixed symmetry gradient terms in the free energy, such that the supression of the d-wave order parameter near the vortex core induces subdominant order parameters of s- or dxy- symmetry. This problem has been studied intensively in the GL regime near Tc, but the physics is very different at low temperatures. Li, Woelfle and I studied this problem and gave an analytical solution (cond-mat/0003160, Phys. Rev. B 63, 054504 (2001)). At right is a picture of the relative phase of dx2-y2 (blue) and dxy (red) order parameters. at intermediate and large distances from the vortex core.