D-wave quasiparticles in the tilted vortex lattice

Abstract

We investigate the quasiparticle spectrum of a d-wave superconductor in the mixed state, focussing on the effects of varying the in-plane angular alignment (or tilting) of the vortex and crystal lattices. Our approach starts with a linearized Bogoliubov--de Gennes equation cast into a simple form by the Franz-Te\ifmmode \check{s}\else \v{s}\fi{}anovi\ifmmode \acute{c}\else \'{c}\fi{} singular gauge transformation. The zero-magnetic-field spectrum is characterized by the anisotropy ${\ensuremath{\alpha}}_{D}$ near the four Fermi-surface nodes; at large ${\ensuremath{\alpha}}_{D}$ the model simplifies into a one-dimensional form that provides asymptotic results. Numerical and analytical results are presented and compared with previous studies. We find that tilting can be understood in terms of the one-dimensional model at large ${\ensuremath{\alpha}}_{D}.$ We see a striking dependence on the choice of singular gauge, consistent with earlier results, but do not attempt to resolve the issue of which gauge best describes the microscopic physics.