Conductance and thermopower fluctuations in interacting quantum dots

TL;DR

This paper investigates conductance and thermopower fluctuations in an interacting quantum dot modeled with SYK-like interactions, revealing how these fluctuations are influenced by the interplay of hopping and interaction strengths across different regimes.

Contribution

It extends previous work by analyzing sample-to-sample fluctuations in conductance and thermopower, showing how SYK interactions suppress fluctuations and how smaller hopping influences these fluctuations.

Findings

SYK interactions reduce conductance and thermopower fluctuations.

Fluctuations are controlled by hopping strength in certain regimes.

Distinct fluctuation regimes depend on temperature and interaction parameters.

Abstract

We model an interacting quantum dot of electrons by a Hamiltonian with random and all-to-all single particle hopping (of r.m.s. strength $t$) and two-particle interactions (of r.m.s. strength $J$). For $t \ll J$, such a model has a regime exhibiting the non-quasiparticle physics of the Sachdev-Ye-Kitaev model at temperatures $E_{\rm coh} \ll T \ll J$, and that of a renormalized Fermi liquid at $T \ll E_{\rm coh}$, where $E_{\rm coh} = t^2 / J$. Extending earlier work has computed the mean thermoelectric properties of such a dot weakly coupled to two external leads, we compute the sample-to-sample fluctuations in the conductance and thermopower of such a dot, and describe several distinct regimes. In all cases, the effect of the SYK interactions is to reduce the strength of the sample-to-sample fluctuations. We also find that in the regime where the mean transport co-efficients are determined only by the value of $J$ at leading order, the sample-to-sample fluctuations can be controlled by the influence of the smaller $t$.