Quasiparticles and vortices in unconventional superconductors - art. no. 134509

Quasiparticles in the vortex lattice of strongly type-II superconductors ar e investigated by means of a singular gauge transformation applied to the t ight-binding lattice Bogoliubov-de Gennes Hamiltonian. We present a detaile d derivation of the gauge invariant effective low-energy Hamiltonian for th e quasiparticle-vortex system and show how the physics of the "Doppler shif t" and "Berry phase" can be incorporated at the Hamiltonian level by workin g in the singular gauge. In particular, we show that the "Berry phase" effe ct manifests itself in the effective Hamiltonian through a half-flux Aharon ov-Bohm scattering of quasiparticles off vortices and stress the important role that this effect plays in the quasiparticle dynamics. Full numerical s olutions in the regime of intermediate fields H-c1<<B<<H-c2 are presented f or 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-ener gy bound states in the core, in agreement with the existing results. For th e d-wave case only extended quasiparticle states exist. We investigate in d etail the nature of these extended states and provide comparison to the pre vious 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 sin gular gauge transformation.