Nematic order in topological SYK models

TL;DR

This paper investigates how SYK-type interactions influence topological phases in multi-orbital models, revealing a rich phase diagram with non-Fermi liquids and nematic exciton condensates, relevant to correlated topological materials.

Contribution

It introduces a novel analysis of SYK interactions in topological lattice models, uncovering new phases and symmetry effects in strongly correlated topological matter.

Findings

Identification of a non-Fermi liquid phase at high temperature.

Discovery of an exciton condensate with nematic transport at low temperature.

Spectral and transport properties showing topological and interaction effects.

Abstract

We study a class of multi-orbital models based on those proposed by Venderbos, Hu, and Kane which exhibit an interplay of topology, interactions, and fermion incoherence. In the non-interacting limit, these models exhibit trivial and Chern insulator phases with Chern number $C \geq 1$ bands as determined by the relative angular momentum of the participating orbitals. These quantum anomalous Hall insulator phases are separated by topological transitions protected by crystalline rotation symmetry, featuring Dirac or quadratic band-touching points. Here we study the impact of Sachdev-Ye-Kitaev (SYK) type interactions on these lattice models. Given the random interactions, these models display `average symmetries' upon disorder averaging, including a charge conjugation symmetry, so they behave as interacting models in topological class $\mathbf{D}$ enriched by crystalline rotation symmetry. The phase diagram of this model features a non-Fermi liquid at high temperature and an `exciton condensate' with nematic transport at low temperature. We present results from the free-energy, spectral functions, and the anomalous Hall resistivity as a function of temperature and tuning parameters. Our results are broadly relevant to correlated topological matter in multiorbital systems, and may also be viewed, with a suitable particle hole transformation, as an exploration of strong interaction effects on mean-field topological superconductors.