Quasiparticles ofd-Wave Superconductors in Finite Magnetic Fields

We study quasiparticles in the $d$-wave vortex lattice by self-consistently solving the Bogoliubov–de Gennes equations. It is found for a pure $d_{x^2{-y}^2}$ state that: (i) Low-energy quasiparticle bands in the magnetic Brillouin zone have a rather large dispersion even in small magnetic fields, indicating the absence of bound states for an isolated vortex; (ii) in finite fields with $k_{\mathrm{F}}{\xi }_0$ small, the calculated tunneling conductance at the vortex core acquires a double-peak structure near zero bias as the field is increased from $H_{c1\mathrm{}}$. We also find that mixing of a $d_{\mathrm{xy}}$-wave or an $s$-wave component, if any, develops gradually without transitions as the field grows, having little effect on the tunneling spectra.