Anomalous scaling and gapless fermions of d-wave superconductors in magnetic field

TL;DR

This paper investigates the behavior of d-wave quasiparticles in disordered vortex lattices of superconductors, revealing topological properties, violations of scaling laws, and specific dependencies of electronic properties on vortex disorder.

Contribution

It provides a topological analysis of gapless fermions in d-wave superconductors and demonstrates how disorder affects their scaling and physical properties.

Findings

Topological structure of magnetic crystal momenta identified

Quantum anomaly causes violation of Simon and Lee scaling

Electronic density of states scales with vortex displacement, thermal conductivity remains H-independent

Abstract

The problem of d-wave quasiparticles in a weakly disordered Abrikosov vortex lattice is studied. Starting with a periodic lattice, the topological structure of the magnetic crystal momenta of gapless fermions is found for the particle-hole symmetric case. If in addition the site centered inversion symmetry is present, both the location and the number of the gapless fermions can be determined using an index theorem. In the case of spatially aperiodic vortex array, Simon and Lee scaling is found to be violated due to a quantum anomaly. The electronic density of states is found to scale with the root-mean-square vortex displacement as $\sqrt{H}f(\bu_{rms}^2/\xi^2)$, while thermal conductivity is H-independent, but {\it different} from the H=0 case.