Chern numbers and chiral anomalies in Weyl butterflies

Abstract

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

4 pages, 4 figures + supplementary material, version accepted in Phys. Rev. B as a Rapid Communication

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Cited by in corpus (11)

• Interactions remove the quantization of the chiral photocurrent at Weyl points
• Emergent Weyl nodes and Fermi arcs in a Floquet Weyl semimetal
• Floquet chiral magnetic effect
• Landau levels, Bardeen polynomials and Fermi arcs in Weyl semimetals: the who's who of the chiral anomaly
• Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementations
• Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals
• Time-reversal-broken Weyl semimetal in the Hofstadter regime
• Linking topological features of the Hofstadter model to optical diffraction figures
• Topological van Hove singularities at phase transitions in Weyl metals
• Two Types of 3D Quantum Hall Effects in Multilayer WTe${}_2$
• Interaction and temperature effects on the magneto-optical conductivity of Weyl liquids