Geometric orbital susceptibility: quantum metric without Berry curvature

TL;DR

This paper reveals that the orbital magnetic susceptibility in electron gases is influenced by quantum geometric properties of Bloch states, specifically the quantum metric tensor, even without Berry curvature, affecting magnetic responses in tight-binding models.

Contribution

It explicitly relates orbital susceptibility to the quantum metric tensor in two-band models, highlighting the importance of geometric effects beyond Berry curvature.

Findings

Interband effects are crucial even when Berry curvature is zero.

Quantum metric induces strong paramagnetism in flat band models.

Geometric properties significantly influence magnetic susceptibility.

Abstract

The orbital magnetic susceptibility of an electron gas in a periodic potential depends not only on the zero field energy spectrum but also on the geometric structure of cell-periodic Bloch states which encodes interband effects. In addition to the Berry curvature, we explicitly relate the orbital susceptibility of two-band models to a quantum metric tensor defining a distance in Hilbert space. Within a simple tight-binding model allowing for a tunable Bloch geometry, we show that interband effects are essential even in the absence of Berry curvature. We also show that for a flat band model, the quantum metric gives rise to a very strong orbital paramagnetism.