Counting formula for the pseudo Landau levels visible in an energy spectrum

One interesting feature of Dirac/Weyl systems is that spatial modulation, for instance given by strain, can be regarded as a gauge filed. This “pseudo” gauge field can generate pseudo magnetic field, and enables us to observe magnetic like phenomena such as Landau level formation or quantum oscillations even without external magnetic field. Here, by considering a simplest situation to have finite pseudo magnetic field, we derive a concise formula to count the number of pseudo Landau levels clearly visible in the energy spectrum. The derived formula is numerically verified in a toy model. Equipped with the formula, we also discuss the possible realization of the pseudo Landau levels in existing Dirac materials, particularly in antiperovskite Sr₃SnO series.