Quasiparticle spectra of Abrikosov vortices in a uniform supercurrent flow

Abstract

We calculate the local density of states of a vortex in a two-dimensional s-wave superconductor in the presence of a uniform applied supercurrent. The supercurrent induces changes in the electronic structure for the isolated vortex as well as the vortex lattice, which agree with the recent measurements in 2H -NbSe 2 [Maldonado et al., Phys. Rev. B 88, 064518 (2013)]. We find that the supercurrent polarizes the core states when the vortices are pinned. This shows that the transfer of momentum from the supercurrent to the bound states and the rigidity of the wave functions must be considered for understanding the various forces acting on collectively pinned Abrikosov vortices. The quantum states bound to magnetic vortices in type-II superconductors carry information about the fundamental properties of the superconducting state. The existence of bound states was predicted long ago, 1 but the direct observation in NbSe 2 awaited the invention of the scanning tunneling microscope (STM). 2 The complete mapping of the tunneling conductance in real space as a function of applied bias provided a large data set, in striking agreement with the BCS predictions for the local density of states (LDOS) of a vortex. 3 Since then, several groups have investigated the vortex cores by STM in NbSe 2 , 4-6 in other classical superconductors, 7-11 in high-T c cuprates, 12 and, more recently, in the pnictides. [13][14][15][16] While in classical superconductors, including the pnictides, these studies usually reveal vortex-core spectra in good qualitative agreement with the BCS theory, significant deviations are found in high-T c superconductors, probably due to an anomalous normal state. 12 The interpretation of vortex-core spectra in the cuprates remains an open question.Recently, a measurement of the vortex electronic structure in the presence of an in-plane current flow was performed in NbSe 2 . 17 When a supercurrent is established across a vortex lattice, a "Lorentz force" acts on the vortices in the direction normal to the applied current. 18 In Ref. 17, the current was sufficiently small for the force to remain below the depinning threshold, and the authors could map the LDOS of static vortices with and without the applied current. The main observation of this experiment is that the application of a current transfers low-energy spectral weight from inside the cores, where the zero-bias conductance is reduced, to in between the vortices where it is enhanced, while the converse appears at the gap edges, where the spectral weight is enhanced inside the cores and depleted outside. The measurements also suggest that the current increases the size of the vortex cores. To interpret these trends, the authors assume that the applied current reduces the smallest gap on the two-band Fermi surface of NbSe 2 . This would affect the formation of Andreev bound states in the cores, diminishing their energy separation.This interpretation refers to second-order changes in the modulus of the order parameter but ignores that the leading effect of ...

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