Dirac-Bogoliubov-deGennes quasiparticles in a vortex lattice

TL;DR

This paper models low-energy quasiparticles in a d-wave superconductor's vortex lattice as Dirac fermions with boundary conditions at vortex cores, revealing gauge invariance and the importance of self-adjoint extensions.

Contribution

It introduces a self-adjoint extension framework for Dirac quasiparticles in vortex lattices, accounting for core physics beyond linearization.

Findings

Density of states is gauge-invariant with proper boundary conditions

Vortex core effects are encapsulated by a single parameter 

Identifies self-adjoint extensions consistent with earlier solutions

Abstract

In the mixed state of an extreme type-II d-wave superconductor and within a broad regime of weak magnetic fields H_c1 << H << H_c2, the low energy Bogoliubov-deGennes quasiparticles can be effectively described as Dirac fermions moving in the field of singular scalar and vector potentials. Although the effective linearized Hamiltonian operator formally does not depend on the structure of vortex cores, a singular nature of the perturbation requires choosing a self-adjoint extension of the Hamiltonian by imposing additional boundary conditions at vortex locations. Each vortex is described by a single parameter \theta that effectively represents all effects arising from the physics beyond linearization. With the value of \theta properly fixed, the resulting density of states of Dirac Hamiltonian exhibits full invariance under arbitrary singular gauge transformations applied at vortex positions. We identify the self-adjoint extensions of the solutions found earlier, within the framework of the linearized Hamiltonian diagonalized by expansion in the plane wave basis, and analyze the relation between fully self-consistent formulation of the problem and the linearized model.