Chiral anomaly without Landau levels: From the quantum to the classical regime

Abstract

We study the chiral anomaly in disordered Weyl semimetals, where the broken translational symmetry prevents the direct application of Nielsen and Ninomiya's mechanism and disorder is strong enough that quantum effects are important. In the weak disorder regime, there exist rare regions of the random potential where the disorder strength is locally strong, which gives rise to quasilocalized resonances and their effect on the chiral anomaly is unknown. We numerically show that these resonant states do not affect the chiral anomaly only in the case of a single Weyl node. At energies away from the Weyl point, or with strong disorder where one is deep in the diffusive regime, the chiral Landau level itself is not well defined and the semiclassical treatment is not justified. In this limit, we analytically use the supersymmetry method and find that the Chern-Simons term in the effective action which is not present in nontopological systems gives rise to a nonzero average level velocity which implies chiral charge pumping. We numerically establish that the nonzero average level velocity serves as an indicator of the chiral anomaly in the diffusive limit. arXiv:1805.00485v2 [cond-mat.dis-nn]

Rare-Region-Induced Avoided Quantum Criticality in Disordered Three-Dimensional Dirac and Weyl Semimetals

“…(b) For two flux quanta Φ = 2Φ 0 and one rare state one renormalized chiral Landau level remains. Taken from Ref [127]…”

“…(c) In the presence of a magnetic field two chiral Landau levels with opposite velocity develop (green and blue) along the direction of the magnetic field emanating out of the two Weyl points with different helicities. Taken from Ref [127]…”

Anomaly non-renormalization in interacting Weyl semimetals

“…[21,22]. Interaction [23][24][25][26][27][28][29][30][31][32] and disorder [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] effects in Weyl semimetals have been previously considered, but the issue of the anomaly non-renormalization has not been addressed yet.…”