Multifractality at the Weyl-semimetal–diffusive-metal transition for generic disorder

Abstract

A Weyl semimetal is a three dimensional topological gapless phase. In the presence of strong enough disorder it undergoes a quantum transition towards a diffusive metal phase whose universality class depends on the range of disorder correlations. Similar to other quantum transitions driven by disorder, the critical wave functions at the semimetal-diffusive metal transition exhibit multifractality. Using renormalization group methods we study the corresponding multifractal spectrum as a function of the range of disorder correlations for generic disorder including random scalar and vector potentials. We also discuss the relation between the geometric fluctuations of critical wave functions and the broad distribution of the local density of states (DOS) at the transition. We derive a new scaling relation for the typical local DOS and argue that it holds for other disorder-driven transitions in which both the average and typical local DOS vanish on one side of the transition. As an illustration we apply it to the recently discussed unconventional quantum transition in disordered semiconductors with power-law dispersion relation near the band edge.

Ballistic transport in disordered Dirac and Weyl semimetals

“…However, in the presence of disorder, the problem of DOS is complicated because the "rare events" might introduce a small but finite DOS [5][6][7][8][9][10]. It is still an open question that the DOS at the nodal point is finite or not; in other words, we have not reached a clear agreement whether "disordered PNSM" exists or not [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The problem seems difficult to resolve, since the investigation of the vanishing DOS exactly at the nodal point is difficult both theoretically and experimentally.…”

Coherent forward scattering as a robust probe of multifractality in critical disordered media

“…For instance, it is well established that 3d disordered lattices undergo a genuine disorder-driven metal-insulator transition (MIT), associated with a mobility edge in the spectrum, separating the insulating phase with localized eigenstates from the conducting phase with extended eigenstates. Near the critical point of such disorder driven transitions, eigenstates φ α (with energy ω α ) can display multifractal behavior, for instance at the MIT in Anderson model [16][17][18] and graphs [19][20][21], but also for Weyl-semimetal-diffusive transition [22]. They are extended but non-ergodic, and characterized by the anomalous scaling of their moments I q (E):…”

Fermi arcs and surface criticality in dirty Dirac materials

“…However, we expect that their actual values are different similar to the Anderson transition in a semi-infinite systems[68]. The multifractality of critical surface states is also expected to differ from that in the bulk[69,70].Acknowledgments. -We would like to thank David…”