Conductance and thermopower fluctuations in interacting quantum dots

Statistical fluctuations of transport quantities in mescoscopic conductors can lead to suprising quantum phenomena, such as universal conductance fluctuations in weakly-interacting quantum dots. Motivated by recent experiments which aim to realize a Sachdev-Ye-Kitaev (SYK) model in the zeroth Landau level of a graphene quantum dot, we analyze the statistical fluctuations in conductance and thermopower of a disordered and strongly-interacting quantum dot. We model this dot 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 ≪ J, such a model has a regime exhibiting the non-quasiparticle physics of the Sachdev-Ye-Kitaev model at temperatures E_coh ≪ T ≪ J, and that of a renormalized Fermi liquid at T ≪ E_coh, where E_coh = t²/J. We find 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.