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

Abstract

Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolved task. Here we report such findings in the level statistics and the fractal nature of electron wavefunction around Weyl nodes of disordered WSMs. The nearest-neighbor level spacing follows a new universal distribution $P_c(s)=C_1{s}^2\exp [-C_2{s}^{2-{\gamma }_0}]$ 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. Numerically, we find ${\gamma }_0=0.62\pm 0.07$. In contrast to the Bloch wavefuntions of clean WSMs that uniformly distribute over the whole space of ($D=3$) at large length scale, the wavefunction of disordered WSMs at a Weyl node occupies a fractal space of dimension $D=2.18\pm 0.05$. The finite size scaling of the inverse participation ratio suggests that the correlation length of wavefunctions at Weyl nodes ($E=0$) diverges as $\xi \propto |E{|}^{-\nu }$ with $\nu =0.89\pm 0.05$. In the ergodic limit,the level number variance ${\Sigma }_2$ around Weyl nodes increases linearly with the average level number $N$, ${\Sigma }_2=\chi N$, where $\chi =0.2\pm 0.1$ is independent of system sizes and disorder strengths.

arXiv comment6 pages, 4 figures

References in corpus (8)

• Superconductivity in Cu_xTiSe_2
• Prediction of the Weyl semimetal in the orthorhombic MoTe2
• Evidence for an excitonic insulator phase in 1T-TiSe${}_2$
• Is 1T-TaS${}_2$ a 40 year old quantum spin liquid?
• Non-thermal separation of electronic and structural orders in a persisting charge density wave
• Charge density wave and superconducting dome in TiSe2 from electron-phonon interaction
• Semimetal to semimetal charge density wave transition in 1T-TiSe${}_2$
• Spontaneous exciton condensation in 1T-TiSe2: a BCS-like approach

Cited by in corpus (3)

• Hole- and electron-injection driven phase transitions in transition metal dichalcogenides and beyond: A unified understanding
• Superconducting Sn-Intercalated TaSe${}_2$: Structural Diversity Obscured by Routine Characterization Techniques
• Charge Density Modulation and Defect Ordering in Na${}_x$MnBi${}_y$ magnetic semimetal