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arXiv:2309.05741 · Physical review. B./Physical review. B

Conductance and thermopower fluctuations in interacting quantum dots

Henry Shackleton, Laurel E. Anderson, Philip Kim, Subir Sachdev A

Published Jun 4, 2024• 7 citations
arXivHTMLPDF

Abstract

We model an interacting quantum dot of electrons by a Hamiltonian with random and all-to-all single-particle hopping (of root-mean-square strength $t$) and two-particle interactions (of root-mean-square strength $J$). For $t\ensuremath{\ll}J$, such a model has a regime exhibiting the nonquasiparticle physics of the Sachdev-Ye-Kitaev (SYK) model at temperatures ${E}_{\mathrm{coh}}\ensuremath{\ll}T\ensuremath{\ll}J$, and that of a renormalized Fermi liquid at $T\ensuremath{\ll}{E}_{\mathrm{coh}}$, where ${E}_{\mathrm{coh}}={t}^{2}/J$. 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 coefficients 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 $t$.

DOI
10.1103/physrevb.109.235109

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We study the electric and thermoelectric transport through a spinful complex Sachdev-Ye-Kitaev (SYK) quantum dot coupled to metallic leads, forming a N-SYK-N junction, by the Keldysh field theory approach. Unlike traditional equilibrium approaches, our formulation treats the system as an open, interacting quantum conductor under non-equilibrium conditions, without resorting to the replica trick. Starting from the exact Keldysh-Dyson equations, we derive analytical results for the tunneling and zero-temperature limits and perform a numerical analysis in the linear-response regime. We characterize the dependence of conductance, thermoelectric coefficient, and Seebeck effect on the particle-hole asymmetry parameter and coupling strength to the leads. Our results reveal distinctive non-Fermi liquid signatures of the SYK model in transport properties and identify coupling regimes where thermoelectric effects are enhanced, suggesting experimentally accessible fingerprints of SYK physics in mesoscopic systems.
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