Quasiparticles and vortices in unconventional superconductors

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 “Doppler shift” and “Berry phase” can be incorporated at the Hamiltonian level by working in the singular gauge. In particular, we show that the “Berry phase” 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 $H_{c1\mathrm{}}\ll B\ll H_{c2\mathrm{}}$ 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 the 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” model. We also investigate internodal interference effects when vortex and ionic lattices have a high degree of commensurability and discuss various specific choices for the singular gauge transformation.