Distinguishing Quantum Capacitance Signatures of a Topological Majorana Wire from a Normal Wire Segment

Abstract

Majorana zero modes (MZMs) are spatially separated, near-zero-energy excitations expected at the ends of a topological superconducting (TS) wire. A quantum-dot interferometer can be used to probe the quantum capacitance of the TS wire, and the location and magnitude of the capacitance resonances provide information about the MZMs, while their magnetic flux dependence probes coherent coupling to the two Majorana modes. It has been recently shown that, a gapless (i.e., $\Delta=0$) wire segment can also exhibit flux-dependent quantum capacitance oscillations through Aharonov-Bohm interference and, with suitable tuning, can reproduce a Majorana-like response. Here we show that the two mechanisms can be distinguished experimentally. In the gapless normal wire segment, the two parity-dependent signals originate from separate energy resonances corresponding to the lack of generic zero-energy states. By contrast, in the topological wire, the pair of low energy levels with even and odd parity are nearly degenerate in energy, and therefore, the two parity branches remain within the same broader resonance region in the quantum-dot potential, and persist under independent variations of the dot potential and wire chemical potential. Our results show that the experimentally observed quantum capacitance response is distinguished not by a particular flux trace at one optimized point in parameter space, but by its persistence over a finite range of independently controlled parameters, including the quantum-dot potential. This parameter space stability provides a direct means of ruling out the gapless normal wire segment as the origin of the observed Majorana-like response.