Quasiparticle spectrum near the gap node directions in the mixed state of d-wave superconductors

TL;DR

This paper analytically investigates the low-energy quasiparticle spectrum in the mixed state of clean d-wave superconductors, revealing how vortex lattice geometry influences the band structure near gap nodes.

Contribution

It provides an approximate analytical solution to the Bogolubov-de Gennes equations for different vortex lattice geometries in d-wave superconductors.

Findings

Eigenfunctions are extended along gap node directions and localized perpendicular to them.

The superfluid velocity field creates a band structure in the quasiparticle spectrum.

Vortex lattice geometry significantly affects the spectrum.

Abstract

We report on a calculation of the quantized energy spectrum and quasiparticle eigenfunctions for low lying excitations in the mixed state of clean d-wave superconductors. Our study is based on an approximate analytical solution of the Bogolubov-de Gennes equations for both rectangular and triangular flux lattices with one of the primitive translations chosen parallel to the gap node direction. For excitations with momenta close to a certain gap node we have obtained a set of eigenfunctions which appear to be extended along the chosen gap node direction and localized along the perpendicular one on a scale determined by the intervortex distance. The periodic superfluid velocity field induces a band structure in the spectrum, which depends essentially on the vortex lattice geometry.