Kondo Memory in Driven Strongly Correlated Quantum Dots

We investigate the real-time current response of strongly correlated quantum dot systems under sinusoidal driving voltages. By means of an accurate hierarchical equations of motion approach, we demonstrate the presence of prominent memory effects induced by the Kondo resonance on the real-time current response. These memory effects appear as distinctive hysteresis line shapes and self-crossing features in the dynamic current-voltage characteristics, with concomitant excitation of odd-number overtones. They emerge as a cooperative effect of quantum coherence—due to inductive behavior—and electron correlations—due to the Kondo resonance. We also show the suppression of memory effects and the transition to classical behavior as a function of temperature. All these phenomena can be observed in experiments and may lead to novel quantum memory applications.

Figure 1

Current versus voltage for a QD driven by an ac voltage of amplitude $e{V}_0=\Delta$ and frequency $\Omega$. The arrows indicate the circulating directions of the loops. The dashed green curve in (a) depicts the steady-state $I–V$ characteristics. The insets plot the corresponding current (in $e\Delta /h$) versus time (in $h/\Delta$). The other parameters are $U=-2{ϵ}_d=4\Delta$, $W=20\Delta$, and $T=0.2\Delta$.

Figure 2

(a)–(c) Current versus voltage for QDs of ${ϵ}_d=-U/2=-2\Delta$, $-6\Delta$, and $-10\Delta$, under the ac bias voltage of $e{V}_0=0.5\Delta$ and $\Omega =0.3\Delta$, and at $T=0.1\Delta$. The inset of (b) shows $A^{\mathrm{eq}}(\omega )$ for ${ϵ}_d=-2\Delta$, $-6\Delta$, and $-10\Delta$ from up to down. The inset of (c) plots $A(\omega ;V)$ under stationary voltages of $eV=0.1\Delta$, $0.5\Delta$, $\Delta$, and $1.5\Delta$ from up to down at $\omega =0$, for the QD of ${ϵ}_d=-6\Delta$. (d) Steady-state $dI/dV$ versus the stationary voltage of $V=V_L=-V_R$, where the data are scaled by their values at $V=0$. The inset shows the corresponding $A^{\mathrm{eq}}(\omega )/A^{\mathrm{eq}}(0)$.

Figure 3

(a) Dynamic $I\mathrm{\text{−}}V$ characteristics, (b) real-time current response, (c) steady-state $dI/dV$ versus $V$, and (d) imaginary part of the current spectrum of a QD with $U=-2{ϵ}_d=12\Delta$ at various $T$. The inset of (a) magnifies the self-crossing of the ac $I\mathrm{\text{−}}V$ curve near $V=-V_0$ at $T=0.1\Delta$, and that of (b) displays the full peaks of $\mathrm{Im}[I(\omega )]$ at $\omega =\Omega$. The other parameters are $W=20\Delta$, $e{V}_0=\Delta$, and $\Omega =0.3\Delta$.

Figure 4

Dynamic $I\mathrm{\text{−}}V$ characteristics of QDs of various ${ϵ}_d$. The displayed current is $I(t)=[{\overline{I}}_R(t)-{\overline{I}}_L(t)]/2$. The other parameters are $U=12\Delta$, $T=0.1\Delta$, $W=20\Delta$, $e{V}_0=0.5\Delta$, and $\Omega =0.3\Delta$.