Berry Curvature-Induced Magnetic Breakdown

The one-band semiclassical approximation is a fundamental tool for analyzing the dynamics of electrons in materials with nonzero Berry curvature. To understand the limits of this approximation in the presence of Berry curvature, we exactly solve a continuum model with infinitely-many bands of constant positive Berry curvature in the presence of a transverse magnetic field. With further support from a semiclassical analysis of this model, we show that the results of the semiclassical approximation are exact over a wide range of parameters, but there is a critical value of the magnetic field where the one-band approximation breaks down, leading to a divergence in the energy spectrum.