Nonequilibrium finite frequency resonances in differential quantum noise driven by Majorana interference

Abstract

Nonequilibrium quantum noise $S^>(\omega,V)$ measured at finite frequencies $\omega$ and bias voltages $V$ probes Majorana bound states in a host nanostructure via fluctuation fingerprints unavailable in average currents or static shot noise. When Majorana interference is brought into play, it enriches nonequilibrium states and makes their nature even more unique. Here we demonstrate that an interference of two Majorana modes via a nonequilibrium quantum dot gives rise to a remarkable finite frequency response of the differential quantum noise $\partial S^>(\omega,V,\Delta\phi)/\partial V$ driven by the Majorana phase difference $\Delta\phi$. Specifically, at low bias voltages there develops a narrow resonance of width $\hbar\Delta\omega\sim\sin^2\Delta\phi$ at a finite frequency determined by $V$, whereas for high bias voltages there arise two antiresonances at two finite frequencies controlled by both $V$ and $\Delta\phi$. We show that the maximum and minimum of these resonance and antiresonances have universal fractional values, $3e^3/4h$ and $-e^3/4h$. Moreover, detecting the frequencies of the antiresonances provides a potential tool to measure $\Delta\phi$ in nonequilibrium experiments on Majorana finite frequency quantum noise.