Berry Phase and Quantum Oscillation from Multi-orbital Coadjoint-orbit Bosonization

TL;DR

This paper develops a multi-orbital bosonization framework revealing how Berry curvature influences quantum oscillations and magnetization in Fermi surfaces, including effects in interacting systems.

Contribution

It introduces a coadjoint orbit-based effective field theory for multi-orbital fermions, incorporating Berry phase effects into quantum oscillation phenomena.

Findings

Berry curvature causes phase shifts in de Haas-van Alphen oscillations.

The phase shift persists in interacting systems, replacing single-particle Berry phase with anomalous Hall conductance.

Berry curvature modifies the amplitude of quantum oscillations.

Abstract

We develop an effective field theory for a multi-orbital fermionic system using the method of coadjoint orbits for higher-dimensional bosonization. The dynamical bosonic fields are single-particle distribution functions defined on the phase space. We show that when projecting to a single band, Berry curvature effects naturally emerge. In particular, we consider the de Haas-van Alphen effect of a 2d Fermi surface, and show that the oscillation of orbital magnetization in an external field is offset by the Berry phase accumulated by the cyclotron around the Fermi surface. Beyond previously known results, we show that this phase shift holds even for interacting systems, in which the single-particle Berry phase is replaced by the static anomalous Hall conductance. Furthermore, we obtain the correction to the amplitudes of de Haas-van Alphen oscillations due to Berry curvature effects.