Sachdev-Ye-Kitaev Non-Fermi-Liquid Correlations in Nanoscopic Quantum Transport

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 $T^{3/2}$ in the inelastic cotunneling channel, separated from the conventional Fermi liquid $T^2$ 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.

Figure 1

Main: Temperature dependence of the direct tunneling contribution to the conductance. An exponential suppression at temperatures $T<E_C$ gives way to a $T^{-1/2}$ power law at larger temperatures. Left-hand inset: Diagram of the direct tunneling process. Black lines are Green functions in the lead ($l$) and the dot ($d$), fat dots are tunneling vertexes at times ${\tau }_{1,2}$, respectively, and the red dashed line represents the charging correlation $D({\tau }_1-{\tau }_2)$, Eq. (5). Right-hand inset: Energy dependence of the average tunneling density of states on the dot at $T=0$.

Figure 2

Main: Schematic temperature dependence of the inelastic cotunneling contribution to the conductance. Inset: Inelastic cotunneling diagram, where a particle enters the dot from the left lead, while another particle exits to the right a short time $\sim E_C^{-1}$ after, and NFL “particle-hole” excitation with the energy $\sim T$ is left behind on the dot.

Figure 3

Summary of the different regimes characterized by algebraic or exponential temperature dependence of the linear conductance through a quantum device with a narrow single-particle band $W$.