Absence of the zero bias peak in vortex tunneling spectra of high-temperature superconductors

The c-axis tunneling matrix of high-$T_c$ superconductors is shown to depend strongly on the in-plane momentum of electrons and vanish along the four nodal lines of the $d_{x^2-y^2}$-wave energy gap. This anisotropic tunneling matrix suppresses completely the contribution of the most extended quasiparticles in the vortex core to the c-axis tunneling current and leads to a spectrum similar to that of a nodeless superconductor. Our results give a natural explanation of the absence of the zero-bias peak as well as other features observed in the vortex tunneling spectra of high-$T_c$ cuprates.