d-wave Quasiparticles in the Tilted Vortex Lattice
  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\v{s}anovi\'{c} singular gauge transformation. The zero magnetic field spectrum is characterized by the anisotropy $\alpha_D$ near the four Fermi-surface nodes; at large $\alpha_D$ 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 $\alpha_D$. 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. 
Michael A. Hermele and Luca Marinelli