Quantum transport in dispersionless electronic bands

TL;DR

This paper investigates quantum transport in perfectly flat electronic bands, revealing that quantum-geometric effects enable enhanced transport and large thermopower in topologically nontrivial flat bands, challenging conventional quasiparticle notions.

Contribution

It demonstrates that quantum-geometric contributions enable transport in flat bands, especially topological ones, and derives related expressions for thermal and thermoelectric properties.

Findings

Quantum-geometric effects enable transport in flat bands.

Large thermopower observed in flat topological bands.

Transport contributions vanish without quantum geometry.

Abstract

Flat electronic bands are counterintuitive: with the electron velocity vanishing, our conventional notions of quasiparticle transport are no longer valid. We here study the quantum transport in the generalized families of perfectly flat bands [PRB 105, L241102 (2022)], and find that while the conventional contributions indeed vanish, the quantum-geometric contribution gives rise to the enhanced electronic transport. This contribution is connected to the Wannier orbital quantization in the perfectly flat bands, and is present only for geometrically-nontrivial bands (for example, flat Chern bands). We find similar expressions for thermal conductance, thermoelectric response, and superfluid weight in the flat bands. In particular, we report the anomalous thermopower associated with flat topological bands reaching values as large as $\frac{k_B}{e}\ln 2$$\approx$60 $\mu$V/k, the quantum unit of thermopower, not expected in conventional dispersive bands.