Nonequilibrium superconductivity

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. In conventional superconductors, the study of non-equilibrium QP relaxation was used successfully to extract information on residual particle--particle interactions, as well as to pin down QP and phonon lifetimes. The typical time-resolved experiment is a measurement of the change in the system's dielectric constant as a function of time following a pump pulse which creates a non-equilibrium QP distribution. The excited QPs decay to equilibrium over a series of timescales involving several steps, including at least: (i) a cascade of pair production until a quasi-equilibrium is reached between ``hot" QPs of roughly the gap energy and phonons of energy twice the gap, and (ii) slow recombination of QPs into Cooper pairs. The timescales involved in step (i) are O(ps), but can be much longer in step (ii) O(ns--mus)] since energy is continually exchanged between the electron and phonon systems until heat is removed at the sample surfaces; this long decay is sometimes referred to as the ``phonon bottleneck".

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.

  Current project

• Relaxation of hot d-wave quasiparticles

  A priori, several differences are to be expected in the cuprate superconductors. The very strong interactions in the normal state and the larger gap scale suggest that electron--electron rather than electron--phonon scattering is the dominant relaxation mechanism. Furthermore, the gap anisotropy and the equilibration with thermal QPs at the nodes leads to a new type of slow decay, which we call the ``antinodal bottleneck". This is the inability of antinodal QPs to decay rapidly by pair-breaking while simultaneously satisfying energy and momentum conservation, due to the large difference in velocities at the nodal and antinodal points of the Fermi surface. In recent pump-probe measurements on YBCO crystals relaxation rates are found to be orders of magnitude slower than ordinary superconductors and strongly T dependent; it is likely that different relaxation mechanism must be at work. Together with P. Howell and A. Rosch, I have presented a theory (cond-mat/0307168) of the single aspect of the complicated non-equilibrium physics of pump--probe experiments most peculiar to the d-wave superconductor, namely the mechanism intermediate between steps (i) and (ii) whereby hot QPs scatter through the antinodal bottleneck before recombination. Within a model where QPs are scattered by a simple local interaction, we show that at high T there is a fast relaxation due to Umklapp scattering, but below some crossover temperature relaxation is dominated by diffusion in momentum space along the Fermi surface from the antinode to the nodes. This idea is a momentum-space analog of real-space ``QP traps" in conventional superconductors, in the sense that there is an intermediate stage of relaxation in which QPs diffuse to a region of lower gap. New directions to be explored include: 1) direct calculation of the reflectivity change in a pump-probe experiment; 2) numerical solutions to quantum kinetic equation including realistic collision models; 3) analysis of spatially inhomogeneous situations including pumped "optical lattice" experiments of Orenstein group.

  Data from Segre et al 2001