Revisiting the magnetic responses of bilayer graphene from the perspective of the quantum distance

TL;DR

This paper explores how quantum geometry influences magnetic responses in quadratic band crossing semimetals, revealing that wave function geometry significantly alters Landau levels and quantum Hall effects beyond energy dispersion similarities.

Contribution

It introduces a tunable quantum geometric parameter, the maximum quantum distance, to study its impact on magnetic properties in a general two-band model, connecting free electron and bilayer graphene behaviors.

Findings

Quantum geometry drastically affects Landau levels.

Quantum Hall responses differ despite identical dispersions.

Charge carriers exhibit distinct magnetic responses due to wave function geometry.

Abstract

We study the influence of the quantum geometry on the magnetic responses of quadratic band crossing semimetals. More explicitly, we examine the Landau levels, quantum Hall effect, and magnetic susceptibility of a general two-band Hamiltonian that has fixed isotropic quadratic band dispersion but with tunable quantum geometry, in which the interband coupling is fully characterized by the maximum quantum distance $d_\mathrm{max}$. By continuously tuning $d_\mathrm{max}$ in the range of $0\leq d_\mathrm{max}\leq 1$, we investigate how the magnetic properties of the free electron model with $d_\mathrm{max}=0$ evolve into those of the bilayer graphene with $d_\mathrm{max}=1$. We demonstrate that despite sharing the same energy dispersion $\epsilon(p) =\pm\frac{p^2}{2m}$, the charge carriers in the free electron model and bilayer graphene exhibit entirely distinct Landau levels and quantum Hall responses due to the nontrivial quantum geometry of the wave functions.