Nonequilibrium transport through an interacting monitored quantum dot

Abstract

We study the interplay between strong correlations and Markovian dephasing, resulting from monitoring the charge or spin degrees of freedom of a quantum dot described by a dissipative Anderson impurity model. Using the Auxiliary master equation approach we compute the steady-state spectral function and occupation of the dot and discuss the role of dephasing on Kondo physics. Furthermore, we consider a two-lead setup which allows to compute the steady-state current and conductance. We show that the Kondo steady-state is robust to moderate charge dephasing but not to spin dephasing, which we interpret in terms of dephasing-induced heating of low-energy excitations. Finally, we show universal scaling collapse of the non-linear conductance with a dephasing-dependent Kondo scale.

Figures (6)

• Figure 1: Sketch of the setup for the two leads dissipative Anderson Impurity Model: a quantum dot subjected to Markovian dissipation due to continuous monitoring with strength $\gamma$ and coupled to two large metallic leads via a hybridization $\Gamma_{\rm R,L}$. The two leads are held at different chemical potential leading to a current flowing and nonequilibrium transport.
• Figure 2: Dissipative Anderson Impurity Model - (a) Impurity spectral function at half-filling for interaction strength $U = 8\Gamma$, $V_g=0$, shown for increasing values of the charge dephasing rate $\gamma_{\rm charge}$. (b) Corresponding distribution function $F(\omega)$ as $\gamma_{\rm charge}$ increases. (c) Effective temperature $T_{\rm eff}$ extracted from the distribution function, as a function of $\gamma$ in the charge dephasing case, compared with the spin dephasing case and the Kondo temperature of the non-dissipative Anderson impurity model (taken from Ref. we.lo.23). The leads are held at a finite temperature $T=0.02 \Gamma$, and are modeled with a flat (wide-band) density of states.
• Figure 3: Dissipative Anderson Impurity Model - (a) Differential conductance $G$ as a function of the gate voltage $V_g$ for increasing values of $\gamma_{\rm charge}$ and $\gamma_{\rm spin}$. (b) Differential conductance $G$ a function of the bias voltage for increasing values of $\gamma_{\rm charge}$ and $\gamma_{\rm spin}$. (c) The normalized conductance $G/G_{\rm max}$ displays a universal behavior as a function of the normalized bias $V/V_{K}$, highlighting the universality and scaling behavior across different charge and spin dephasing rate. Here, $G_{\rm max}$ denotes the zero-bias conductance at a given $\gamma$, and $V_{K}$ is defined as the bias voltage at which the conductance drops to half of the value it has with respect to $V=0$ for a given $\gamma$.
• Figure S1: Dissipative Resonant Level model with charge dephasing $L = \sqrt{\gamma_{\rm charge}} \sum_\sigma n_\sigma$. (a) Impurity spectral function for the half-filled dissipative resonant level model, corresponding to $U = 0$, and increasing values of $\gamma_{\rm charge}$ at fixed temperature $T=0.02 \Gamma$. (b) Corresponding distribution function $F(\omega)$ . The solid lines represent results from the auxiliary master equation approach, while the dotted lines show the exact solution obtained via the Keldysh formalism.
• Figure S2: Anderson Impurity Model with spin dephasing $L= \sqrt{\gamma_{\rm spin}} \sum_\sigma \sigma n_\sigma$. (a) Impurity spectral function at half-filling for interaction strength $U = -2\epsilon_d = 8\Gamma$, shown for increasing values of the charge dephasing rate $\gamma_{\rm spin}$. (b) Corresponding distribution function $F(\omega)$ as $\gamma_{\rm spin}$ increases.