High-frequency transport and zero-sound in an array of SYK quantum dots

• Published in: SciPost physics Vol. 13; no. 3; p. 073
• Main Authors: Aleksey, Lunkin, Feigel'man, Mikhail
• Format: Journal Article
• Language: English
• Published: SciPost 01.09.2022
• ISSN: 2542-4653; 2542-4653
• DOI: 10.21468/SciPostPhys.13.3.073

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range T \gg T_{FL} T ≫ T F L . We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric \sigma(\omega,p) σ ( ω , p ) and thermal \kappa(\omega,p) κ ( ω , p ) conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter \mathcal{E} ℰ . At low-frequencies \omega \ll T ω ≪ T we find the Lorenz ratio L = \kappa(0,0)/T\sigma(0,0) L = κ ( 0 , 0 ) / T σ ( 0 , 0 ) to be non-universal and temperature-dependent. At \omega \gg T ω ≫ T the conductivity \sigma(\omega,p) σ ( ω , p ) contains a pole with nearly linear dispersion \omega \approx sp\sqrt{\ln\frac{\omega}{T}} ω ≈ s p ln ω T reminiscent of the “zero-sound”, known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.