Theory of pairing symmetry inside the Abrikosov vortex core

We show that the Cooper pair wave function at the center of an Abrikosov vortex with vorticity m has different parity with respect to frequency from that in the bulk if m is an odd number and has the same parity if m is an even number. As a result, in a conventional vortex with m=1, the local density of states at the Fermi energy has a maximum (minimum) at the center of the vortex core in even(odd)-frequency superconductor. We propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.