Electronic transport in nanostructures, such as long molecules or 2D exfoliated flakes, often goes through a nearly degenerate set of single-particle orbitals. Here we show that in such cases a conspiracy of the narrow band and strong e-e interactions may stabilize a non-Fermi-liquid phase in the universality class of the complex Sachdev-Ye-Kitaev (SYK) model. Focusing on signatures in quantum transport, we demonstrate the existence of anomalous power laws in the temperature dependent conductance, including algebraic scaling T3/2 in the inelastic cotunneling channel, separated from the conventional Fermi liquid T2 scaling via a quantum phase transition. The relatively robust conditions under which these results are obtained indicate that the SYK non-Fermi-liquid universality class might not be as exotic as previously thought.
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