Distinguishing Majorana from Andreev bound states with a Cooper pair transistor

Abstract

We study a Cooper pair transistor realized by a mesoscopic superconductor island that couples to a pair of s-wave superconducting leads. For a trivial island, the critical supercurrent between the leads exhibits a well-known 2e periodicity in the island-gate charge. Here, we show that for an island with spatially separated zero-energy Majorana or Andreev bound states, the periodicity of the magnitude of the critical supercurrent transitions to 1e in the island-gate charge. Moreover, for Andreev bound states, the current-phase relation displays a sign reversal when the parity of the charge ground state of the island changes between even and odd. For Majorana bound states the same sign reversal does not occur. Our results highlight that the full current-phase relation of a Cooper pair transistor can depend on the nature of zero-energy bound states in candidate systems for topological superconductors and provide an initial step toward integrating Majorana qubits in superconducting circuits.

Similar papers