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Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolvedtask. Here we report such findings in the level statistics and the fractalnature of electron wavefunction around Weyl nodes of disordered WSMs. Thenearest-neighbor level spacing follows a new universal distribution $P_c(s)=C_1s^2\exp[-C_2 s^{2-\gamma_0}]$ originally proposed for the level statistics ofcritical states in the integer quantum Hall systems or normal dirty metals(diffusive metals) at metal-to-insulator transitions, instead of theWigner-Dyson distribution for diffusive metals. Numerically, we find$\gamma_0=0.62\pm0.07$. In contrast to the Bloch wavefuntions of clean WSMsthat uniformly distribute over the whole space of ($D=3$) at large lengthscale, the wavefunction of disordered WSMs at a Weyl node occupies a fractalspace of dimension $D=2.18\pm 0.05$. The finite size scaling of the inverseparticipation ratio suggests that the correlation length of wavefunctions atWeyl nodes ($E=0$) diverges as $\xi\propto |E|^{-\nu}$ with $\nu=0.89\pm0.05$.In the ergodic limit,the level number variance $\Sigma_2$ around Weyl nodesincreases linearly with the average level number $N$, $\Sigma_2=\chi N$, where$\chi= 0.2\pm0.1$ is independent of system sizes and disorder strengths.

Non-Wigner-Dyson level statistics and fractal wavefunction of disordered Weyl semimetals