Quasiparticle spectra in the vicinity of a d-wave vortex

We discuss the evolution of the local quasiparticle spectral density and the related tunneling conductance measurable by the scanning tunneling microscope, as a function of distance r and angle theta from the vortex core in a d(x2-y2) superconductor. We consider the effects of electronic disorder and of a strongly anisotropic tunneling matrix element, and show that in real materials they will likely obscure the similar to 1/r asymptotic tail in the zero-bias tunneling conductance expected from the straightforward semiclassical analysis. We also give a prediction for the tunneling conductance anisotropy around the vortex core and establish a connection to the structure of the tunneling matrix element. [S0163-1829(99)11329-8].