Electronic states near a quantum fluctuating point vortex in a d-wave superconductor: Dirac fermion theory

TL;DR

This paper models low-energy electronic states near a quantum fluctuating vortex in a d-wave superconductor, revealing satellite features in the LDOS that align with experimental STM observations.

Contribution

It introduces a simple Dirac fermion model with vortex quantum zero-point motion, explaining LDOS features without a zero bias peak in cuprate superconductors.

Findings

No zero bias peak in LDOS at vortex center

Presence of satellite features in LDOS due to vortex eigenmodes

Qualitative agreement with STM measurements in cuprates

Abstract

We introduce a simple model of the low energy electronic states in the vicinity of a vortex undergoing quantum zero-point motion in a d-wave superconductor. The vortex is treated as a point flux tube, carrying pi-flux of an auxiliary U(1) gauge field, which executes simple harmonic motion in a pinning potential. The nodal Bogoliubov quasiparticles are represented by Dirac fermions with unit U(1) gauge charge. The energy dependence of the local density of electronic states (LDOS) at the vortex center has no zero bias peak; instead, small satellite features appear, driven by transitions between different vortex eigenmodes. These results are qualitatively consistent with scanning tunneling microscopy measurements of the sub-gap LDOS in cuprate superconductors. Furthermore, as argued in L. Balents et al., Phys.Rev.B 71, 144508 (2005), the zero-point vortex motion also leads naturally to the observed periodic modulations in the spatial dependence of the sub-gap LDOS.