Spectrum collapse of disordered Dirac Landau levels as non-Hermitian topological phase transition

We investigate disorder effects on Landau levels in Dirac semimetals. It is found that disorder induces the spectrum collapse of Landau levels; i.e., the disappearance of the energy gaps between $n$-th and $-n$-th levels under a finite external magnetic field. By treating the magnetic field as a synthesized dimension of momentum, the spectrum collapse can be associated with a non-Hermitian topological phase transition.