Transport properties and thermopower of the spinful Sachdev-Ye-Kitaev dot

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.

💡 Research Summary

This paper presents a comprehensive theoretical study of electrical and thermoelectric transport through a spinful, complex Sachdev-Ye-Kitaev (SYK) quantum dot coupled to two metallic leads, forming an N-SYK-N junction. The primary objective is to characterize the non-equilibrium transport signatures of this strongly interacting, non-Fermi liquid system and identify regimes where distinctive SYK physics becomes experimentally accessible.

The authors employ the Keldysh field theory (KFT) approach, a real-time, non-equilibrium formalism, to tackle this open quantum system problem. A key methodological advantage highlighted is that KFT naturally handles the quenched disorder inherent to the SYK model without resorting to the technically cumbersome replica trick commonly used in equilibrium SYK studies. The model consists of a central SYK dot with random all-to-all four-fermion interactions (strength J) and a particle-hole asymmetry parameter μ, connected to two non-interacting metallic leads via tunneling amplitudes W_L and W_R.

Starting from the microscopic Hamiltonian, the Keldysh action is constructed, and disorder averaging is performed. By introducing bi-local fields representing the dot’s Green’s function and self-energy in a path integral formulation, the authors derive the exact Keldysh-Dyson equations in the large-N limit. For the isolated SYK dot, these reduce to well-known self-consistent equations where the self-energy is proportional to the square of the Green’s function. The analysis then extends to the full junction, where the coupling to the leads introduces additional self-energy contributions (Γ) that broaden the dot’s spectral functions.

The core of the paper investigates the linear-response transport coefficients: the electrical conductance (G), the thermoelectric coefficient (L), and the derived Seebeck coefficient (S = L/(GT)). Analytical results are obtained in limiting cases. At zero temperature, the Seebeck coefficient is shown to be linearly proportional to the asymmetry parameter μ. In the tunneling limit (weak coupling to leads Γ « J), explicit expressions linking transport to the dot’s equilibrium spectral properties are derived.

Numerical analysis at finite temperature reveals the rich dependence of these coefficients on the coupling strength Γ and the asymmetry μ. The main findings are:

1. Non-Fermi Liquid Signatures: The transport properties reflect the underlying non-Fermi liquid nature of the SYK dot, distinct from conventional Fermi-liquid quantum dots.
2. Enhanced Thermoelectric Effects: The thermoelectric response, particularly the Seebeck coefficient, can be significantly enhanced in specific regimes. The most favorable conditions are found in the weak coupling limit (Γ « J) combined with strong particle-hole asymmetry (large |μ|).
3. Experimental Fingerprint: This enhancement in thermopower under weak coupling provides a concrete, measurable signature that could help identify SYK physics in potential mesoscopic realizations, such as in nanostructured materials or quantum simulators.

In conclusion, the work successfully demonstrates the power of the Keldysh field theory for studying non-equilibrium transport in strongly correlated, disordered systems like the SYK model. It provides quantitative predictions for transport observables and pinpoints the parameter space (weak tunneling, strong asymmetry) where the unique SYK behavior—characterized by its strange metallicity and chaos—should be most prominent in thermoelectric measurements, offering valuable guidance for future experiments.