Fermionic entropy of the vortex state in d-wave superconductors

TL;DR

This paper investigates the electronic entropy associated with vortices in d-wave superconductors, revealing a potential large entropy jump at vortex transitions and discussing the possibility of a Berezinskii-Kosterlitz-Thouless transition due to fermionic bound states.

Contribution

It introduces the concept of fermionic entropy in vortex states of d-wave superconductors and links entropy jumps to vortex transitions, providing insights into vortex-melting phenomena.

Findings

Entropy per vortex per layer can be much larger than k_B.

A significant entropy jump occurs at vortex transition points.

Discussion of the potential for a BKT transition in 3D d-wave superconductors.

Abstract

In the d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, $S_V$, is much larger than $k_B$ and depends on the distribution of the velocity field $v_s$ around the vortex. If there is a first order transition with the change of the velocity distribution, then there will be a big entropy jump $\Delta S_V \sim 1 k_B$ at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, et. al., Physica C 27, 245 (1997)], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii- Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed.