Revealing universal Majorana fractionalization using differential shot noise and conductance in nonequilibrium states controlled by tunneling phases

TL;DR

This paper investigates the conditions under which universal fractionalization in Majorana quantum dot devices can be observed, highlighting the importance of tunneling phases and device configurations for experimental detection.

Contribution

It reveals that the universal fractionalization of shot noise and conductance occurs only in ideal setups with a single Majorana mode, and introduces a phase-insensitive ratio useful for experiments.

Findings

The ratio of differential shot noise to conductance becomes phase-independent at high bias.

Universal fractional values are observable only when Majorana bound states are well separated.

In realistic devices, tunneling phases significantly affect measurable transport characteristics.

Abstract

Universal fractionalization of quantum transport characteristics in Majorana quantum dot devices is expected to emerge for well separated Majorana bound states. We show that the Majorana universality of the differential shot noise $\partial S^>/\partial V$ and conductance $\partial I/\partial V$ at low bias voltages $V$ arises only in ideal setups with only one Majorana mode entangled with the quantum dot. In realistic devices, where both Majorana modes are entangled with the quantum dot, $\partial S^>/\partial V$ and $\partial I/\partial V$ become very sensitive to tunneling phases and their universal fractional values are hard to observe even for well separated Majorana bound states. In contrast, as revealed here, the ratio $(\partial S^>/\partial V)/(\partial I/\partial V)$ weakly depends on the tunneling phases and is fractional when the Majorana bound states are well separated or integer when they significantly overlap. Importantly, for very large $V$ we demonstrate that this ratio becomes fully independent of the tunneling phases and its universal fractional Majorana value may be observed in state-of-the-art experiments.