Magnetic flux periodicity in second order topological superconductors

The magnetic flux periodicity of $\frac{hc}{2e}$ is a well-known manifestation of Cooper pairing in typical $s$-wave superconductors. In this paper we theoretically show that the flux periodicity of a two-dimensional second order topological superconductor, which features zero-energy Majorana modes localized at the corners of the sample, is $\frac{hc}{e}$ instead. We further show that the periodicity changes back to $\frac{hc}{2e}$ at the transition to a topologically trivial superconductor, where the Majorana modes hybridize with the bulk states, demonstrating that the doubling of periodicity is a manifestation of the nontrivial topology of the state.