Dirac quasiparticles in vortex lattice

In the mixed state of extreme type-II superconductors the low energy d-wave quasiparticles can be effectively described as Dirac fermions experiencing combined effects of singular scalar and vector potentials. Although the effective linearized Hamiltonian operator formally does not depend on the structure of vortex cores, the singular nature of the perturbation requires choosing a self-adjoint extension of the Hamiltonian by imposing additional boundary conditions at vorte Xlocations. Every vortex is described by a single parameter that represents all effects associated with physics beyond linearization. Alternatively, the singularities at the vorte Xcore can be regularized by demanding that quasiparticles acquire position-dependent mass which grows rapidly very near vortices, but vanishes everywhere else. Such mass terms generally break the time-reversal symmetry and lead to small gap in the excitation spectrum. We analyze and establish equivalence of the two approaches theoretically and numerically. We discuss the tunneling conductance experiments in YBCO and suggest a description of the peaks at 5.5 meV in the local density of states near vortices observed in STM/STS measurements.