Level statistics of disordered Weyl semimetalsν

The level statistics and the fractal nature of electron wavefunction around
Weyl nodes of disordered Weyl semimetals are numerically investigated.
The nearest-neighbor level spacing follows a new universal distribution
originally proposed for the level statistics of critical states in the integer
quantum Hall systems or normal dirty metals (diffusive metals) at metal-to-insulator
transitions, instead of the Wigner-Dyson distribution for diffusive metals.
The wavefunction at a Weyl node occupies a fractal space of dimension 2.18,
in contrast to the extended states that spread over the whole space (D=3).
The finite size scaling of the inverse participation ratio (IPR) suggests that the
correlation length of wavefunctions at Weyl nodes (E=0) diverges as ξ∼|E|^-ν
with ν=0.89. In the ergodic limit, the level number variance
around Weyl nodes increases linearly with the average level number N.