Magnetic Bloch bands and Weiss oscillations in Dirac mass superlattices

We study two-dimensional Dirac fermions in a one-dimensional mass superlattice under a perpendicular magnetic field. Using exact solutions for isolated and finite arrays of domain walls, we demonstrate the persistence of Jackiw-Rebbi modes with a field-dependent renormalized velocity. For the periodic case, we adopt a gauge-invariant projection method onto magnetic Bloch states, valid for arbitrary fields and mass profiles, which yields dispersive Landau levels, and confirm its accuracy by comparison with finite arrays spectra. From the miniband spectra we predict modified quantum Hall plateaus and Weiss-like magnetoconductivity oscillations, characterized by a strongly reduced amplitude and a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>π</a:mi> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:math> phase shift compared to electrostatic superlattices.