Numerical study of topological SQUIDs

We conducted numerical calculations to obtain the critical current as a function of the magnetic flux through the topologically trivial and non-trivial superconducting quantum interference devices (SQUIDs), with varying the capacitive and inductive couplings of Josephson junctions (JJs). Our calculation results indicate that a nontrivial SQUID is almost indistinguishable from trivial SQUID, considering the effective capacitance coupling. When the SQUID contains 2 pi- and 4 pi-periodic supercurrents, the periodicity of the current-flux relation can be distinguished from the purely trivial or nontrivial SQUID cases, and its difference is sensitive to the relative ratio between the topologically trivial and nontrivial supercurrents. We believe that our calculation results would provide a practical guide to quantitatively measure the portion of the topologically nontrivial supercurrents in experiments.