Low-lying excitations around a single vortex in a d-wave superconductor

TL;DR

This paper provides a quantum-mechanical analysis of low-energy excitations around a vortex in a d-wave superconductor, revealing unique extended states and bound state formations not present in s-wave superconductors.

Contribution

It presents a full quantum treatment of vortex excitations in d-wave superconductors, highlighting novel extended states and bound state phenomena.

Findings

Extended low-energy states in four diagonal directions

Four-fold symmetry due to quantum effects

Presence of a large energy gap peak in the density of states

Abstract

A full quantum-mechanical treatment of the Bogoliubov-de Gennes equation for a single vortex in a d-wave superconductor is presented. First, we find low-energy states extended in four diagonal directions, which have no counterpart in a vortex of s-wave superconductors. The four-fold symmetry is due to 'quantum effect', which is enhanced when $p_{F}\xi $ is small. Second, for $p_{F}\xi \sim 1$, a peak with a large energy gap $E_{0}\sim \Delta $ is found in the density of states, which is due to the formation of the lowest bound states.