Fermion parity and quantum capacitance oscillation with partially separated Majorana and quasi-Majorana modes

TL;DR

This paper investigates flux-dependent quantum capacitance oscillations in semiconductor-superconductor heterostructures, revealing that such oscillations can originate from both topological Majorana modes and trivial quasi-Majorana states, complicating their use as topological signatures.

Contribution

It demonstrates that quantum capacitance oscillations are not exclusive to topological Majorana zero modes but can also arise from trivial quasi-Majorana states, challenging their role as definitive topological indicators.

Findings

Oscillations can originate from partially separated Majorana modes with overlap.

Quasi-Majorana modes in trivial phases can produce similar oscillations.

Detection of oscillations alone does not confirm topological Majorana modes.

Abstract

In a recent experiment, flux dependent oscillations of the quantum capacitance were observed in a one dimensional spin-orbit coupled semiconductor superconductor heterostructure connected end to end via a quantum dot and threaded by a magnetic flux. In the topological superconducting phase of the heterostructure, the oscillations corresponding to different fermion parity sectors are shifted by half a period and can serve as a mechanism for fermion parity readout or fusion operations involving a pair of localized, well separated Majorana modes. In this work, we demonstrate that flux induced fermion parity dependent oscillations of the quantum capacitance in a disordered semiconductor superconductor quantum dot system can originate not only from topologically protected, spatially well separated Majorana zero modes (MZMs) localized at the wire ends, but also, generically, from partially separated Majorana modes with significant overlap, as well as from quasi-Majorana modes in the topologically trivial phase, which can be viewed as Andreev bound states whose constituent Majorana wave functions are slightly shifted relative to each other and have nonzero amplitude at opposite ends of the wire. Therefore, while the detection of flux dependent oscillations of quantum capacitance marks an important experimental advance, such observations alone do not constitute evidence of the presence of topological Majorana zero modes.