Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator

TL;DR

This paper studies low-energy quasiparticle states in disordered d-wave superconductors using a quantum map approach, revealing conditions for additional states and the emergence of a linear pseudogap due to quantum diffraction effects.

Contribution

It introduces a quantum map model for quasiparticle dynamics in disordered d-wave superconductors and analyzes how disorder and chaos influence the density of states.

Findings

Additional low-energy quasiparticle states exist under specific conditions.

Quantum diffraction shifts states away from zero energy, creating a pseudogap.

Universal random matrix theory behavior is restored in the chaotic regime.

Abstract

We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is longer than the superconducting coherence length. In the classically chaotic regime, universal random matrix theory behavior is restored by quantum dynamical diffraction which shifts the low energy states away from zero energy, and the quasiparticle density of states exhibits a linear pseudogap below an energy threshold $E^* \ll \Delta_0$.