Conductance and thermopower fluctuations in interacting quantum dots

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 tJ, such a model has a regime exhibiting the nonquasiparticle physics of the Sachdev-Ye-Kitaev (SYK) model at temperatures EcohTJ, and that of a renormalized Fermi liquid at TEcoh, where Ecoh=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 J at leading order, the sample-to-sample fluctuations can be controlled by the influence of the smaller t.