Thermal and thermoelectric transport in flat bands with non-trivial quantum geometry

TL;DR

This paper investigates thermal and thermoelectric transport in flat bands with non-trivial quantum geometry, deriving formulas and identifying signatures relevant for topological flat band systems.

Contribution

It provides new Kubo formulas for flat band transport properties and reveals topological aspects of the Seebeck coefficient in flat Chern bands.

Findings

Seebeck coefficient in flat Chern bands is topological up to second order in broadening.

Identifies transport signatures in flat Chern bands and the generalized Lieb model.

Saturation of the quantum metric lower bound occurs only in extremal bands with meromorphic Hamiltonian dependence.

Abstract

Although quasiparticles in flat bands have zero group velocity, they can display an anomalous velocity due to the quantum geometry. We address the thermal and thermoelectric transport in flat bands in the clean limit with a small amount of broadening due to inelastic scattering. We derive general Kubo formulas for flat bands in the DC limit up to linear order in the broadening and extract expressions for the thermal conductivity, the Seebeck and Nernst coefficients. We show that the Seebeck coefficient for flat Chern bands is topological up to second order corrections in the broadening. We identify thermal and thermoelectric transport signatures for two generic flat Chern bands and also for the generalized flattened Lieb model, which describes a family of three equally spaced flat Chern bands where the middle one is topologically trivial. Finally, we address the saturation of the quantum metric lower bound for a general family of Hamiltonians with an arbitrary number of flat Chern bands corresponding to SU(2) coherent states. We find that only the extremal bands in this class of Hamiltonians saturate the bound, provided that the momentum dependence of their Hamiltonians is described by a meromorphic function.