Decaying spectral oscillations in a Majorana wire with finite coherence length

TL;DR

This paper explores how finite coherence length affects spectral oscillations in a Majorana wire, revealing different regimes of energy behavior linked to the spatial structure of Majorana states, supported by analytical models.

Contribution

It introduces analytical models explaining the impact of finite coherence length on Majorana bound state spectral oscillations in proximitized wires.

Findings

Different spectral regimes observed: crossings, anticrossings, and energy reduction.

Energy oscillation amplitude decreases with increasing magnetic field.

Distinct $k$-space structures of Majorana states are crucial for different scenarios.

Abstract

Motivated by recent experiments, we investigate the excitation energy of a proximitized Rashba wire in the presence of a position dependent pairing. In particular, we focus on the spectroscopic pattern produced by the overlap between two Majorana bound states that appear for values of the Zeeman field smaller than the value necessary for reaching the bulk topological superconducting phase. The two Majorana bound states can arise because locally the wire is in the topological regime. We find three parameter ranges with different spectral properties: crossings, anticrossings and asymptotic reduction of the energy as a function of the applied Zeeman field. Interestingly, all these cases have already been observed experimentally. Moreover, since an increment of the magnetic field implies the increase of the distance between the Majorana bound states, the amplitude of the energy oscillations, when present, gets reduced. The existence of the different Majorana scenarios crucially relies on the fact that the two Majorana bound states have distinct $k$-space structures. We develop analytical models that clearly explain the microscopic origin of the predicted behavior.