Noises in a two-channel charge Kondo model

Abstract

We investigate fluctuations of electric and heat currents, along with their cross-correlations, in a two-channel charge Kondo circuit driven by either a voltage bias or a temperature gradient applied across the weak link. The ratios of voltage-driven electric/heat noise to the applied voltage $V$ exhibit oscillations with the gate voltage $N$, resembling the behavior of the thermoelectric coefficient $G_T$. In contrast, the ratios of temperature-driven electric/heat noise to the temperature difference $ΔT$ vary with $N$ in a manner analogous to the thermal coefficient $G_H$ or the electric conductance $G$. The mixed noise, which is defined as the correlation function between electric and heat currents, displays behavior opposite to that of the above noises. The logarithmic temperature dependence of these noises signals non-Fermi-liquid behavior, while their oscillations with gate voltage reflect the roles of particle-hole and time-reversal symmetries in thermoelectric transport. Our results demonstrate that the fundamental relations linking voltage- and temperature-induced noises to thermoelectric transport across a tunnel junction persist beyond the Fermi-liquid paradigm.

Figures (5)

• Figure 1: Schematic of a single-electron transistor device in which a large metallic quantum dot (QD) is embedded into two-dimensional electron gas (2DEG) and connects weakly to the left lead (LL) through a tunnel barrier and strongly coupled to the right one (RL) through an almost transparent single-mode quantum point contact (QPC). The QD and the right lead (yellow color) are at potential $\mu_R$ temperature $T_R=T$ while the left lead (red color) is at higher voltage $\mu_L=\mu_R-eV$ and temperature $T_L=T +\Delta T$. The voltage or temperature drops at the weak link. The green patches demonstrate the gate voltage and the voltages controlling the tunnel barrier and the QPC.
• Figure 2: Voltage-driven electric noise $\Delta \mathcal{S}_C^V/(e G_L)$ [panels a) and d)], voltage-driven heat noise $e\Delta \mathcal{S}_Q^V/(E_C^2 G_L)$ [panels b) and e)], and voltage-driven mixed shot noise $\Delta \mathcal{S}_M^V/(E_C G_L)$ [panels c) and f)] over the voltage difference $V$ between two sides of the weak link as a function of the gate voltage $N$. For the plots on the left [a), b), and c)], $T/E_C=0.01$, black, red, and blue lines correspond to $|r|^2=0.06$, $|r|^2=0.08$, and $|r|^2=0.1$. For the plots on the right [d), e), and f)], $|r|^2=0.1$, black, red, and blue lines correspond to $T/E_C=0.008$, $T/E_C=0.01$, and $T/E_C=0.012$.
• Figure 3: Temperature-driven charge noise (delta-T noise) $\Delta \mathcal{S}_C^{\Delta T}/G_L$ [panels a) and d)], temperature-driven heat noise $e^2\Delta \mathcal{S}_Q^{\Delta T}/(E_C^2G_L)$ [panels b) and e)], and temperature-driven mixed noise $e\Delta \mathcal{S}_M^{\Delta T}/(E_C G_L$ [panels c) and f)] over the temperature difference $\Delta T$ between two sides of the weak link $\Delta T/E_C$ as a function of the gate voltage $N$. For the plots on the left [a), b), and c)], $T/E_C=0.01$, black, red, and blue lines correspond to $|r|^2=0.06$, $|r|^2=0.08$, and $|r|^2=0.1$. For the plots on the right [d), e), and f)], $|r|^2=0.1$, black, red, and blue lines correspond to $T/E_C=0.008$, $T/E_C=0.01$, and $T/E_C=0.012$.
• Figure 4: Maximum of voltage-driven electric noise (shot noise) $\Delta\mathcal{S}_{C,max}^V/(eG_L)$ [panel a)], maximum of voltage-driven heat noise $e\Delta\mathcal{S}_{Q,max}^V/(E_C^2G_L)$ [panel b)], maximum of voltage-driven mixed noise $\Delta\mathcal{S}_{M,max}^V/(E_CG_L)$ [panel c)] over the voltage difference $V$ between two sides of the weak link, maximum of temperature-driven electric noise $\Delta\mathcal{S}_{C,max}^{\Delta T}/(G_L)$ [panel d)], maximum of temperature-driven heat noise $e^2\Delta\mathcal{S}_{Q,max}^{\Delta T}/(E_C^2G_L)$ [panel e)], and maximum of temperature-driven mixed noise $e\Delta\mathcal{S}_{M,max}^{\Delta T}/(E_C G_L)$ [panel f)] over the temperature difference $\Delta T$ between two sides of the weak link as functions of temperature $T/E_C$ are plotted. For all plots, black, red, and blue lines are corresponding to $|r|^2=0.06$, $|r|^2=0.08$, and $|r|^2=0.1$.
• Figure 5: Fano factors as functions of the gate voltage $N$: a) $F_C^{V}$, b) $F_Q^{V}$, c) $F_C^{\Delta T}$, and d) $F_Q^{\Delta T}$ are plotted with different temperatures $T/E_C=0.001$, $T/E_C=0.01$, and $T/E_C=0.1$ corresponding to black, red, and blue lines. For all plots, $|r|^2=0.1$.