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arXiv:2010.13592 · Physical review. B./Physical review. B

Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade

Andrei I. Pavlov, Mikhail N. Kiselev

Published May 7, 2021• 11 citations

Abstract

We present a microscopic theory for quantum thermoelectric and heat transport in the Schwarzian regime of the Sachdev-Ye-Kitaev (SYK) model. As a charged fermion realization of the SYK model in nanostructures, we assume a setup based on a quantum dot connected to the charge reservoirs through weak tunnel barriers. We analyze particle-hole symmetry breaking effects crucial for both Seebeck and Peltier coefficients. We show that the quantum charge and heat transport at low temperatures are defined by the interplay between elastic and inelastic processes such that the inelastic processes provide a leading contribution to the transport coefficients at the temperatures that are smaller compared to the charging energy. We demonstrate that both electric and thermal conductance obey a power law in temperature behavior, while thermoelectric, Seebeck, and Peltier coefficients are exponentially suppressed. This represents selective suppression of only nondiagonal transport coefficients. We discuss the validity of the Kelvin formula in the presence of a strong Coulomb blockade.

DOI: 10.1103/physrevb.103.l201107

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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 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.

Disorder at etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edge states in the graphene electrodes to measure electrical conductance and thermoelectric power across the GQD. In specific temperature ranges, we observe a suppression of electric conductance fluctuations and slowly decreasing thermoelectric power across the GQD with increasing temperature, consistent with recent theory for the SYK regime.

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