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arXiv:2401.08050 · Physical Review Letters

Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations

Laurel E. Anderson, Antti Laitinen, Andrew Zimmerman, Thomas Werkmeister, Henry Shackleton, Alexander Kruchkov, Takashi Taniguchi, Kenji Watanabe, Subir Sachdev A, Philip Kim

Published Jun 12, 2024• 13 citations
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Abstract

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.

DOI
10.1103/physrevlett.132.246502

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•Jan 1, 2018•0 citations
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.
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.
We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi-liquid state of such a quantum dot coupled to noninteracting leads. The properties of this setup depend essentially on the ratio ppp between the number of transverse modes in the lead MMM and the number of the fermion degrees of freedom NNN on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the nontrivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear-response conductance acquires distinct p\sqrt{p}p​ and 1/p1/\sqrt{p}1/p​ dependencies for the two phases, respectively, in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak-tunneling regime, we find differential conductance proportional to the inverse square root of the applied voltage bias UUU. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to 1/T1/\sqrt{T}1/T​ for bias energy eUeUeU smaller than temperature scale kBT{k}_{B}TkB​T. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.
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 ttt) and two-particle interactions (of root-mean-square strength JJJ). 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 Ecoh=t2/J{E}_{\mathrm{coh}}={t}^{2}/JEcoh​=t2/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 JJJ at leading order, the sample-to-sample fluctuations can be controlled by the influence of the smaller ttt.
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.
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.
We address the transport properties of a mesoscopic realization of the Sachdev-Ye-Kitaev (SYK) model which is an exactly solvable system of interacting spinless fermions connected to the black hole physics through the holographic principle. Starting with a recent proposal for simulating the SYK model in a graphene flake in an external magnetic field and extending it by considering leads attached to it, we model a realistic transport experiment and calculate directly measurable quantities featuring non-Fermi liquid signatures of the SYK physics. We show that the graphene flake realization is robust in the presence of leads and that measuring the tunneling current across the leads one can experimentally observe a non-Fermi liquid - Fermi liquid transition by tuning the external magnetic field threading the flake. After establishing the transport signatures of the SYK model near equilibrium using linear response framework, we then derive a formula to extend our results for tunneling current using Keldysh formalism to explore the effects of finite bias voltage across the leads, going beyond equilibrium.