Quasi-Particle States with Topological Quantum Numbers in the Mixed State of d-wave Superconductors

TL;DR

This paper explores the topological classification of quasi-particle states in d-wave superconductors' mixed state, revealing a transition from gapless to gapped states and quantum oscillations at high flux densities.

Contribution

It introduces a new topological quantum number classification for quasi-particle states in d-wave superconductors' mixed state.

Findings

Quasi-particle states are classified by new topological quantum numbers.

Transition from gapless to gapped states with increasing flux density.

Quantum oscillations emerge in high magnetic field regions.

Abstract

We investigate the extended quasi-particle states in the mixed state of d-wave superconductors on the basis of the Bogoliubov-de Gennes equation. We prove that the quasi-particle eigen-states can be classified in terms of new topological quantum numbers which are related to the topological nature of the non-trivial phases of the quasi-particles. Numerical results for the quasi-particle eigen-states reveal the crossover behavior from gapless to gapped states as the flux density $B$ increases. In the strong field region quantum oscillations appear in the excitation energy of the quasi-particles.