Quasiparticle scattering from vortices in d-wave superconductors: Superflow and Berry phase contributions

Anatoli Polkovnikov, Subir Sachdev A, Matthias Vojta C

Xu-Cheng Wang, Xiao Yan Xu, Yang Qi

Steven H. Simon, Patrick A. Lee

Manas Kulkarni, Sriram Ganeshan, Adam C. Durst

In the vortex state of a $d$-wave superconductor, massless Dirac quasiparticles are scattered from magnetic vortices via a combination of two basic mechanisms: effective potential scattering due to the superflow swirling about the vortices, and Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex. In this paper, we study the superflow contribution by calculating the differential cross section for a quasiparticle scattering from the effective noncentral potential of a single vortex. We solve the massless Dirac equation in polar coordinates and obtain the cross section via a partial wave analysis. We also present a more transparent Born-limit calculation, and in this approximation we provide an analytic expression for the differential cross section. The Berry phase contribution to the quasiparticle scattering is considered in a separate paper.

Frank Gaitan

A microscopic analysis of the nondissipative force ${\mathbf{F}}_{\mathrm{nd}}$ acting on a line vortex in a type-II superconductor at T=0 is given. All work presented assumes a charged BCS superconductor. We first examine the Berry phase induced in the BCS superconducting ground state by movement of the vortex and show how this phase enters into the hydrodynamic action ${\mathit{S}}_{\mathrm{hyd}}$ of the superconducting condensate. Appropriate variation of ${\mathit{S}}_{\mathrm{hyd}}$ give ${\mathbf{F}}_{\mathrm{nd}}$ and variation of the Berry phase term is seen to contribute the Magnus or lift force of classical hydrodynamics to ${\mathbf{F}}_{\mathrm{nd}}$. This analysis, based on the BCS ground state of a charged superconductor, confirms in detail the arguments of Ao and Thouless within the context of the BCS model. Our Berry phase, in the limit e\ensuremath{\rightarrow}0, is seen to reproduce the Berry phase determined by these authors for a neutral superfluid. We also provide a second, independent, determination of ${\mathbf{F}}_{\mathrm{nd}}$ through a microscopic derivation of the continuity equation for the condensate linear momentum. This equation yields the acceleration equation for the superflow and shows that the vortex acts as a sink for the condensate linear momentum. The rate at which momentum is lost to the vortex determines ${\mathbf{F}}_{\mathrm{nd}}$ in this second approach and the result obtained agrees identically with the previous Berry phase calculation. The Magnus force contribution to ${\mathbf{F}}_{\mathrm{nd}}$ is seen in both calculations to be a consequence of the vortex topology and motion. A preliminary discussion is given regarding finite temperature extensions of the Berry phase calculation, with emphasis on its relevance for the sign anomaly occurring in Hall-effect experiments on type-II superconductors in the flux flow regime.

P. J. Hirschfeld, P. C. Howell