$h/2e$ Flux Trapping without Superconductivity

Abstract

Recently, it was shown by Komargodski and Popov [arXiv:2601.09847] that ordinary metals threaded with an Aharonov-Bohm solenoid exclusively trap either 0 or h/2e flux. The latter value is familiar in the superconducting setting, yet we find that it holds in ordinary metals as well, with no condensate or pairing necessary. We provide an analytic explanation for the flux trapping, and extend the results to the cases of finite temperature, time-reversal invariant potentials, and lattice regularization, where we find that the flux remains trapped at 0 and h/2e.