Chern numbers and chiral anomalies in Weyl butterflies

The Hofstadter butterfly of lattice electrons in a strong magnetic field is a\ncornerstone of condensed matter physics, exploring the competition between\nperiodicities imposed by the lattice and the field. In this work we introduce\nand characterize the Weyl butterfly, which emerges when a large magnetic field\nis applied to a three-dimensional Weyl semimetal. Using an experimentally\nmotivated lattice model for cold atomic systems, we solve this problem\nnumerically. We find that Weyl nodes reemerge at commensurate fluxes and\npropose using wavepackets dynamics to reveal their chirality and location.\nMoreover, we show that the chiral anomaly -- a hallmark of the topological Weyl\nsemimetal -- does not remain proportional to magnetic field at large fields,\nbut rather inherits a fractal structure of linear regimes as a function of\nexternal field. The slope of each linear regime is determined by the difference\nof two Chern numbers in gaps of the Weyl butterfly and can be measured\nexperimentally in time of flight.\n