Quasiparticles and Vortices in Unconventional Superconductors

Abstract

Quasiparticles in the vortex lattice of strongly type-II superconductors are investigated by means of a singular gauge transformation applied to the tight binding lattice Bogoliubov-de Gennes Hamiltonian. We present a detailed derivation of the gauge invariant effective low energy Hamiltonian for the quasiparticle-vortex system and show how the physics of the &#34;Doppler shift&#34; and &#34;Berry phase&#34; can be incorporated at the Hamiltonian level by working in the singular gauge. In particular, we show that the &#34;Berry phase&#34; effect manifests itself in the effective Hamiltonian through a half-flux Aharonov-Bohm scattering of quasiparticles off vortices and stress the important role that this effect plays in the quasiparticle dynamics. Full numerical solutions in the regime of intermediate fields H_c1<<B<<H_c2 are presented for model superconductors with s-, p- and d-wave symmetries and with square and triangular vortex lattices. For s- and p-wave cases we obtain low energy bound states in the core, in agreement with the existing results. For d-wave case only extended quasiparticle states exist. We investigate in detail the nature of these extended states and provide comparison to the previous results within linearized ``Dirac fermion&#39;&#39; model. We also investigate internodal interference effects when vortex and ionic lattices have high degree of commensurability and discuss various specific choices for the singular gauge transformation.