Universal relations between thermoelectrics and noise in mesoscopic transport across a tunnel junction

Abstract

We develop a unified theory of weakly probed differential observables for currents and noise in transport experiments. Our findings uncover a set of universal transport relations between thermoelectric and noise properties of a system probed through a tunnel contact, with the Wiedemann-Franz law being just one example of such universality between charge and heat currents. We apply this theory to various quantum dot systems, including multichannel Kondo, quantum Hall and Sachdev-Ye-Kitaev quantum dots, and demonstrate that each of the microscopic theories is characterized by a set of universal relations connecting conductance and thermoelectrics with noise. Violations of these relations indicate additional energy scales emerging in a system.

Figures (2)

• Figure 1: Lorenz ratio given by Eq. (\ref{['RL']}). Red solid line - Lorenz ratio given by Eq. (\ref{['RLcosh']}). Blue dotted line - a range of Lorenz ratios for an N-channel Kondo/quantum Hall simulator; vertical dotted lines at $\alpha=1$ and $\alpha=3$ depict the range of $\alpha$ for the Kondo/quantum Hall simulator (they values reproduce the results obtained in Kiselev2023Stabler2023KiselevUn2 for these systems). Black square corresponds to the Fermi liquid regime. Gray diamond - SYK in the conformal regime. Downward violet triangle - inelastic tunneling regime for the conformal SYK. Blue star - large-$q$ conformal regime of the double-scaled SYK. Upward cyan triangle - SYK dot in the Schwarzian regime. Green cross - Schwarzian SYK regime with only inelastic tunneling. Dashed lines are used as eyeguides.
• Figure 2: Extended Lorenz ratios as functions of $\alpha$. $R_k$ stands for $R_L$ (solid blue line), $R^{\Delta T}_C$ (dashed red line), $R^{\Delta T}_H$ (dotted black line), $R^V_C$ (dash-dotted green line), $R^V_H$ (short-dotted orange line). All ratios are normalized by the extended Lorenz numbers $L_i$, $i=0,..,4$ such that $R_k=1$ at $\alpha=1$ (Fermi liquid regime, thin vertical dotted line).