Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics

Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042102. doi: 10.1103/PhysRevE.92.042102. Epub 2015 Oct 5.


We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasimomentum space, the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider web in contrast to the Hofstadter butterfly for unbiased motion.