Noise signatures of a charged Sachdev-Ye-Kitaev dot in mesoscopic transport

TL;DR

This work develops a unified linear-response framework to study charge and heat transport and their fluctuations in a mesoscopic charged SYK dot weakly coupled to a lead. By employing full counting statistics within a Keldysh formalism, it expresses currents and all noise components in terms of a dot T-matrix and the Coulomb/Schwarzian soft modes, enabling explicit scaling analyses across conformal and Schwarzian regimes and in the presence of Coulomb blockade. The authors identify universal relations between transport and noise coefficients, introduce extended Lorenz numbers, and reveal non-Fermi-liquid signatures via Lorenz ratios that differ from Fermi-liquid values. They demonstrate that certain noise-to-transport ratios saturate to regime-dependent constants, providing robust experimental markers, and show that shot-noise measurements can substitute thermoelectric probes for detecting SYK physics. The framework offers a general approach to identifying non-Fermi-liquid behavior in mesoscopic transport and can guide experiments on graphene quantum dots realizing SYK-like dynamics.

Abstract

We investigate quantum noise in a mesoscopic quantum dot serving as a realization of the charged Sachdev-Ye-Kitaev (SYK) model weakly coupled to a fermionic lead via a tunnel contact. We find noise signatures under voltage and temperature biases that can serve as clear markers of the SYK physics in experiments with related setups. We develop a linear response theory that treats all types of noise on the same footing and generalizes a concept of transport coefficients for charge and heat currents, as well as relations between them, to equilibrium noise power. Within this theory, we find characteristic scaling of the noise coefficients with temperature in all regimes that can be relevant for experimental realizations of the SYK dots, find a set of universal constants, with their values being unique to the SYK physics, that connect these coefficients, and characterize noise manifestations of the Coulomb blockade. Beyond SYK systems, these results may serve as a general framework for identification of non-Fermi-liquid signatures in mesoscopic transport and provide additional observables for experiments on thermoelectric phenomena.

Figures (7)

• Figure 1: Considered setup: A quantum dot of size $l$ has $N$ fermions with the SYK interactions $J_{ij;kl}$ between them. This dot is at finite temperature $T$, and it possesses finite charging energy $E_C$ and spectral asymmetry $\mathcal{E}$. This system is coupled to a metallic lead with voltage bias $\Delta V$ and temperature difference $\Delta T$ through a tunnel contact with tunneling amplitudes $\lambda_{mq}$.
• Figure 2: Charge delta-T noise $S^{\Delta T}_c(T,\mathcal{E})$ vs heat delta-T noise $S^{\Delta T}_h(T,\mathcal{E})$ vs charge conductance $G(T,\mathcal{E})$ in the conformal regime as functions of temperature. $T_0$ is the Schwarzian energy scale, $T_0\simeq J/(N\log N)=J/100$, $E_C/T_0=10$, $N=30$. Solid blue line: $S_{c}^{\Delta T}(T,\mathcal{E}=0.0)$; solid red line: $S_{c}^{\Delta T}(T,\mathcal{E}=0.1)$; dashed green line: $S_{h}^{\Delta T}(T,\mathcal{E}=0.0)$; dashed orange line: $S_{h}^{\Delta T}(T,\mathcal{E}=0.1)$; dotted black line: $G(\mathcal{E}=0.0)$; dotted magenta line: $G(\mathcal{E}=0.1)$. Charge conductance lines are multiplied by a factor $0.67$, heat delta-T noise lines are multiplied by a factor $0.14$ (see explanation in the text). All entities with $\mathcal{E}=0.1$ are additionally multiplied by a factor $0.5$ for better visual separation. All lines are in units of $S^{\Delta T}_{0,c}=\lambda^2e^2/v_F$, $S^{\Delta T}_{0,h}=\lambda^2T^2/v_F$,$G_T^{(0)}=\lambda^2e^2/v_F$, $T_0=J/100$.
• Figure 3: Charge shot noise $S^{SN}_c(T,\mathcal{E})$ vs heat shot noise $S_h^{SN}(T,\mathcal{E})$ vs thermoelectric coefficient $G_T(T,\mathcal{E})$ in the conformal regime as functions of temperature. $T_0$ is the Schwarzian energy scale, $T_0\simeq J/(N\log N)=J/100$, $E_C/T_0=10$, $N=30$. Solid blue line: $S_{c}^{SN}(T,\mathcal{E}=0.1)$; solid red line: $S_{c}^{SN}(T,\mathcal{E}=0.2)$; dashed green line: $S_{h}^{SN}(T,\mathcal{E}=0.1)$; dashed orange line: $S_{h}^{SN}(T,\mathcal{E}=0.2)$; dotted black line: $G_T(\mathcal{E}=0.1)$; dotted magenta line: $G_T(\mathcal{E}=0.2)$. Charge shot noise lines are multiplied by a factor $2.59$, heat shot noise lines are multiplied by a factor $-0.41$ (see explanation in the text); all entities with $\mathcal{E}=0.2$ are additionally multiplied by a factor $0.5$ for better visual separation. All lines are in units of $S^{SN}_{0,c}=\lambda^2e^3/v_F$, $S^{SN}_{0,h}=\lambda^2e T^2/v_F$, $G_T^{(0)}=\lambda^2e/v_F$, $T_0=J/100$.
• Figure 4: Ratio between the charge shot noise $S^{SN}_c$ and the thermoelectric coefficient $G_T$ when charging energy $E_C$ is negligible. $E_C/T_0=0.01$, conformal regime ($N\rightarrow \infty$). Blue solid line - $\mathcal{E}=0.1$, red solid line - $\mathcal{E}=0.2$. Dashed lines are corresponding asymptotic values: orange dashed line is $0.3814$, green dashed line is $0.3672$. Inset: The same ratios in the Schwarzian regime (without charging energy renormalization), $N=30$, dashed magenta line is $0.3345$, dashed black line is $0.3264$.
• Figure 5: Asymptotic ratios between noise and transport coefficients as functions of the spectral asymmetry $\mathcal{E}$ when charging energy $E_C$ is negligible. $T/E_C=300$, conformal regime. Blue dotted line: ratio between charge shot noise and thermoelectric coefficient, $S_{c}^{SN}/G_T$; red dashed line: ratio between charge shot noise and heat shot noise, $S_{c}^{SN}/S_{h}^{SN}$; green solid line: ratio between charge delta-T noise and heat delta-T noise, $S_c^{\Delta T}/S_h^{\Delta T}$; orange dot-dashed line: ratio between charge conductance and heat delta-T noise, $G/S_h^{\Delta T}$. All coefficients are in corresponding dimensionless units.