Revisiting the magnetic responses of bilayer graphene from the perspective of quantum distance - Oh, Chang Geun; Rhim, Jun Won; Yang, Bohm Jung (Physical Review B, 2024)
We study the influence of 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 dmax. By continuously tuning dmax in the range of 0≤dmax≤1, we investigate how the magnetic properties of the free-electron model with dmax=0 evolve into those of the bilayer graphene with dmax=1. We demonstrate that despite sharing the same energy dispersion ϵ(p)=±p22m, 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.
Keywords: Band dispersions; Bilayer Graphene; Free electron models; Isotropics; Landau levels; Magnetic response; Quantum distances; Quantum geometry; Quantum hall; Two bands