Geometrical Effects in Orbital Magnetism

Within the wave-packet semi classical approach, the Bloch electron energy is derived to second order in the magnetic field and classified into gauge-invariant terms with clear physical meaning, yielding a fresh of the complex behavior of orbital magnetism. The Berry curvature and quantum metric of the Bloch states rise to a geometrical magnetic susceptibility, which can be dominant when bands are filled up to a small energy gap.is also an energy polarization term, which can compete with the Peierls-Landau and Pauli magnetism on a Fermi surface. These, and an additional Langevin susceptibility, can be calculated from each single band, leaving the Van Vleck susceptibility the only term truly from interband coupling.