Andreev or Majorana, Cooper finds out

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. Notably, for Majorana bound states the same sign reversal does not occur. Our results highlight the relevance of measuring the full current-phase relation of a Cooper pair transistor for clarifying the nature of zero-energy bound states in candidate systems for topological superconductors and provide an initial step towards integrating Majorana qubits in superconducting circuits.

Cited by in corpus (6)

• Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires
• Supercurrent detection of topologically trivial zero-energy states in nanowire junctions
• Weak measurement protocols for Majorana bound state identification
• Distinguishing trivial and topological zero energy states in long nanowire junctions
• Absence of supercurrent sign reversal in a topological junction with a quantum dot
• Josephson current via an isolated Majorana zero mode