Bound on resistivity in flat-band materials due to the quantum metric

TL;DR

This paper establishes an upper bound on resistivity in flat-band materials caused by the quantum metric, highlighting its potential dominance in certain topological and semimetal systems, and suggests experimental exploration in rhombohedral trilayer graphene.

Contribution

It links the quantum metric to resistivity bounds in flat-band materials and topological systems, revealing conditions where interband effects dominate conductivity.

Findings

Quantum metric influences resistivity in flat-band materials.

Interband effects can dominate conductivity in certain regimes.

An upper resistivity bound is identified for topological flat-band systems.

Abstract

The quantum metric is a central quantity of band theory but has so far not been related to many response coefficients due to its nonclassical origin. However, within a newly developed Kubo formalism for fast relaxation, the decomposition of the dc electrical conductivity into both classical (intraband) and quantum (interband) contributions recently revealed that the interband part is proportional to the quantum metric. Here, we show that interband effects due to the quantum metric can be significantly enhanced and even dominate the conductivity for semimetals at charge neutrality and for systems with highly quenched bandwidth. This is true in particular for topological flat-band materials of nonzero Chern number, where for intermediate relaxation rates an upper bound exists for the resistivity due to the common geometrical origin of quantum metric and Berry curvature. We suggest to search for these effects in highly tunable rhombohedral trilayer graphene flakes.