Transient dynamics of the nonequilibrium Majorana resonant level model

The Majorana resonant level model 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 time scale, 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 $\left|\Delta \right|<\Gamma /2$. In the opposite case of strong detuning $\left|\Delta \right|>\Gamma /2$ 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 $\left(\Delta =0\right)$ setup upon increasing the voltage or/and temperature.

Figure 1

Full current through the constriction at zero temperature for different voltages $V$ and dot offset energies $\Delta$. The current is measured in units of $G_0\Gamma /2$ where $G_0=2e^2/h$ is the conductance quantum.

Figure 2

Population of the dot at zero temperature for different voltages $V$ and dot offset energies $\Delta$. The dotted line corresponds to the resonant case $\Delta =0$.