Odd-frequency pairing in a superconductor coupled to two parallel nanowires

We study the behavior of Cooper pair amplitudes that emerge when a two-dimensional superconductor is coupled to two parallel nanowires, focusing on the conditions for realizing odd-frequency pair amplitudes in the absence of spin-orbit coupling or magnetism. In general, any finite tunneling between the superconductor and the two nanowires induces odd-frequency spin-singlet pair amplitudes in the substrate as well as a substantial odd-frequency interwire pairing. Since these amplitudes are odd in spatial parity, they do not directly impact the local observables. However, in the regime of strong superconductor-nanowire tunneling, we find that the presence of two nanowires allows for the conversion of non-local odd-frequency pairing to local even-frequency pairing. By studying this higher-order symmetry conversion process, we are able to characterize the effect of the odd-frequency pairing in the superconductor on local quantities accessible by experiments. Specifically, we find that odd-frequency pairing has a direct impact on the local density of states of the superconductor and on the maximum Josephson current, measurable using Josephson scanning tunneling microscopy.