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.
Highlights
In a recent paper[1], hereafter referred to as I, two of the present authors considered influence of the vortex zeropoint motion on the energy dependence of local density of electronic states (LDOS) in a s-wave superconductor
Our focus on the zero-point motion of vortices in the cuprates is motivated by a previous proposal that periodic modulations in the spatial dependence of the LDOS inevitably appear over the region the vortex executes its quantum zero-point motion[2,3]. Such periodic LDOS modulations have been observed in scanning tunneling microscopy (STM) studies of the vortex in the cuprate superconductors[4,5]
The present paper examines an alternative approach to computing the sub-gap energy dependence of the LDOS near the vortex
Summary
In a recent paper[1], hereafter referred to as I, two of the present authors considered influence of the vortex zeropoint motion on the energy dependence of local density of electronic states (LDOS) in a s-wave superconductor. A solution of the Bogoliubov-de Gennes (BdG) equations for a vortex in a d-wave superconductor leads to a large peak, as a function of energy, at zero bias at the vortex center[6,7,8] No such peak is observed in the experiments. Paper I extended the BdG equations to include vortex zero-point motion for s-wave superconductors: it found that zero bias peak was reduced (but not eliminated), with a transfer of spectral weight to energies of order the vortex oscillation frequency. This was done in an approach that performed a gradient expansion in the gap function, which is only valid for a large core size.
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