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 a different parity with respect to frequency from that in the bulk if $m$ is an odd number, while it 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 an even (odd-) frequency superconductor. We propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.

Figure 1

(Color online) Results for ESE $s$-wave superconductor. (a) Normalized local DOS around the vortex at $E=0$. The center of the vortex is situated at $x=y=0$. Spatial dependencies of (b) ESE and (c) OSO components at $E=0$. Only OSO component $\text{Re}{f}_1$ can survive inside the core (near $x=0$).

Figure 2

(Color online) Results for OSO $p_x$-wave superconductor. (a) Normalized local DOS around the vortex at $E=0$. The center of the vortex is situated at $x=y=0$. Spatial dependencies of (b) OSO and (c) ESE components at $E=0$. Only ESE components can exist inside the core (near $x=0$).

Figure 3

(Color online) Suggested experimental setup to probe the local Josephson coupling between a superconducting tip and a superconductor with Abrikosov vortex core.