Transient dynamics of the nonequilibrium Majorana resonant level model

TL;DR

This paper investigates the transient behavior of the Majorana resonant level model, revealing how contact transparency, voltage, and temperature influence the relaxation dynamics and oscillatory patterns of current and population functions.

Contribution

It provides a detailed analysis of the time evolution of the MRLM after switching on tunneling, highlighting the dominant role of contact transparency and the effects of detuning, voltage, and temperature.

Findings

Relaxation time is governed by inverse contact transparency  independent of other parameters.

Weak detuning results in oscillations determined by voltage; strong detuning causes beating patterns.

Temperature influences the current similarly to hybridization, affecting the approach to resonant behavior.

Abstract

The Majorana resonant level model (MRLM) describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga--Luttinger liquids. We analyze the time evolution of the electric current and of the population function after an instantaneous switching on of the tunneling coupling. We find that the only timescale, which governs the relaxation of the initial dot preparation is the inverse contact transparency $\Gamma$, whatever the dot offset energy $\Delta$, applied bias voltage or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning $|\Delta|<\Gamma/2$. In the opposite case of strong detuning $|\Delta|>\Gamma/2$ a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant ($\Delta=0$) setup upon increasing the voltage or/and temperature.