Bosonized theory of de Haas-van Alphen quantum oscillation in Fermi liquids

TL;DR

This paper develops a bosonized effective field theory for 2D Fermi liquids to analyze the de Haas-van Alphen effect, deriving new analytic results that differ from traditional formulas and exploring disorder effects.

Contribution

It introduces a coadjoint-orbit bosonization approach to solve the oscillatory self energy problem in 2D Fermi liquids, providing a new framework for analyzing quantum oscillations.

Findings

Derived analytic expressions for dHvA behavior at various temperatures.

Identified deviations from Lifshitz-Kosevich formula in 2D Fermi liquids.

Discussed the impact of disorder on quantum oscillations.

Abstract

The de Haas-van Alphen effect (dHvA) of a 2d Fermi liquid remains poorly understood, due to the $\sim\mathcal{O}(1)$ contribution to the oscillations of grand potential from the oscillatory part of the fermionic self energy, which has no known closed-form solution. In this work, we solve this problem via coadjoint-orbit bosonization of the Fermi surface. Compared with the fermionic formalism, the issue of the oscillatory self energy is circumvented. As an effective field theory, Landau parameters $F_{n}$ directly enter the theory. We use the bosonized theory to derive the energies of cyclotron resonance and specific heat, which are consistent with Fermi liquid theory. Via a mode expansion, we show that the problem of dHvA is reduced to 0+1D quantum mechanics. We obtain analytic expressions for the behavior of dHvA at low and high temperatures, which deviate from the well-known Lifshitz-Kosevich formula. We contrast this behavior with that of 3d Fermi liquids, for which we show such deviations are parametrically small. We discuss the effects of disorder on dHvA within the bosonized theory.