Numerical study of topological SQUIDs

Abstract

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