Disorder and Metal-Insulator Transitions in Weyl Semimetals

Abstract

The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arcs surface states. We study the effects of disorder and localization in WSMs and find three exotic phase transitions. (I) Two Weyl nodes near the Brillouin zone boundary can be annihilated pairwise by disorder scattering, resulting in the opening of a topologically nontrivial gap and a transition from a WSM to a three-dimensional (3D) quantum anomalous Hall state. (II) When the two Weyl nodes are well separated in momentum space, the emergent bulk extended states can give rise to a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (III) Two Weyl nodes can emerge near the zone center when an insulating gap closes with increasing disorder, enabling a direct transition from a normal band insulator to a WSM. We determine the phase diagram by numerically computing the localization length and the Hall conductivity, and propose that the exotic phase transitions can be realized on a photonic lattice.PACS numbers: 72.15. Rn, 73.20.Fz, Topological quantum states of matter have emerged as an important and growing field in condensed matter and materials physics recently [1,2]. The Weyl semimetal (WSM) is a newly proposed quantum state of the kind that breaks time-reversal symmetry or inversion symmetry [3][4][5][6][7][8][9][10]. A WSM exhibits a set of paired zero-energy Weyl nodes (linearly touching points of conduction and valence bands) in its bulk spectrum and Fermi arcs excitations localized on the surface. A number of candidate materials have been predicted to be WSMs, including pyrochlore iridates and magnetic topological insulator multilayers [3][4][5][6]. Recently, following the theoretical prediction [7], angle resolved photoemission experiments confirmed that TaAs is a WSM by the observation of the Fermi arcs surface states [8]. Both the Weyl nodes and the Fermi arcs have been observed in NbAs using a combination of soft X-ray and ultraviolet photoemission experiments [9]. Furthermore, the Weyl points have been predicted and subsequently observed remarkably in gyroid photonic crystals [10].In this Letter, we study both numerically and analytically the stability of the gapless Weyl nodes and Fermi arcs against random potential scattering and the novel disorder-induced metal-insulator transitions in WSM systems. Previous studies have concentrated on the properties of a single Weyl node, assuming that the disorder potential is smooth enough to avoid scattering between different nodes [11][12][13][14]. Indeed, a system with a single Weyl node is not subject to Anderson localization even for strong disorder [15]. However, the theorem of Nielsen and Ninomiya states that gapless Weyl nodes with opposite chirality must appear in pairs [16]. Thus, it is essential to study the localization properties of a pair of Weyl nodes since they can be annihilated pairwise when approaching each other in momentum space or by strong intervalley scattering [17,18]. To this end, we study a model syste...

Quantum multicriticality in disordered Weyl semimetals

“…Being derived by the k · p expansion around high symmetric points, the dipole model does not carry any information of global k-space topology in its gapped phase side. Thus, scaling properties revealed in this paper can be equally applicable to the other QMCP that is encompassed by oridinary three-dimensional band insulator, WSM and, DM phases [24][25][26][27].…”

Disorder Effect on Chiral Edge Modes and Anomalous Hall Conductance in Weyl Semimetals

“…56,57) In a manner similar to this, the boundary between the semimetal phase and the diffusive metal phase is shown to be modified by it in Weyl semimetals. [44][45][46] The above result indicates that, even within a semimetal phase, the mass renormalization significantly affects the property of edge excitations. An incomplete quantization of G H in the region of W/A 4 indicates that chiral edge modes are destabilized owing to disorder.…”

Global phase diagram of disordered type-II Weyl semimetals

“…In the case of m z < −t z , two Weyl nodes are annihilated at the Brillouin zone (BZ) boundary. Two bands are gapped and the band inversion gives us the three-dimensional quantum anomalous Hall (3D QAH) state 22 . On the contrary, in the case of m z > t z , two Weyl nodes are annihilated pairwise at the center of the BZ and then we have a normal insulator (NI) phase.…”

“…However, comparing to WSM1 (without the tilt term) whose global phase diagram have been thoroughly investigated [22][23][24][25] , disorder-induced phase transitions for tilted WSM, especially WSM2, have not been paid much attention yet. The diffusive phase has been reported in the presence of disorder for single tilted type-I Weyl cone 26 .…”