Andreev or Majorana, Cooper finds out

TL;DR

This paper investigates how zero-energy Majorana or Andreev bound states in a mesoscopic superconductor island affect the critical supercurrent and its phase relation, providing insights for identifying topological states and advancing quantum computing.

Contribution

It demonstrates that the critical supercurrent's periodicity and phase relation reveal the nature of zero-energy bound states, distinguishing Majorana from Andreev states in superconducting circuits.

Findings

Critical supercurrent transitions from 2e- to 1e-periodicity with zero-energy states.

Sign reversal in current-phase relation occurs for Andreev but not for Majorana states.

Measurement of current-phase relation helps identify topological superconducting states.

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.