Effect of Disorder in a Three-Dimensional Layered Chern Insulator

Liu, Shang; Ohtsuki, Tomi; Shindou, Ryuichi

doi:10.1103/physrevlett.116.066401

Cited by 108 publications

(170 citation statements)

References 42 publications

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“…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.…”

Section: Simulation Of Electron Transportmentioning

confidence: 78%

“…An incomplete quantization of G H in the region of W/A 4 indicates that chiral edge modes are destabilized owing to disorder. A plausible explanation is that a finite-size gap at the Weyl nodes is closed by a strong disorder and hence chiral edge modes located at one side of the system are coupled with those in the opposite side by low-energy bulk states, 46) resulting in the destabilization of chiral edge modes. As ∆G H turns to increase near W/A = 4.3 without being reduced to zero, we observe that the critical strength W c of disorder is W c /A ∼ 4.3 in this case.…”

Section: Simulation Of Electron Transportmentioning

confidence: 99%

“…To find a clear difference between them, we need to consider the density of bulk states at Weyl nodes, which jumps to a finite value from zero at the transition to a diffusive metal phase. [33][34][35][36][37][38][39]46) Note that, in previous studies on this subject, the role of Fermi arc surface states is not explicitly considered, except in Refs. 46, 48, and 49.…”

Section: Introductionmentioning

confidence: 99%

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

Takane

2016

J. Phys. Soc. Jpn.

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Typical Weyl semimetals host chiral surface states and hence show an anomalous Hall response. Although a Weyl semimetal phase is known to be robust against weak disorder, the effect of disorder on chiral states has not been fully clarified so far. We study the behavior of such chiral states in the presence of disorder and its consequences on an anomalous Hall response, focusing on a thin slab of Weyl semimetal with chiral surface states along its edge. It is shown that weak disorder does not disrupt chiral edge states but crucially affects them owing to the renormalization of a mass parameter: the number of chiral edge states changes depending on the strength of disorder. It is also shown that the Hall conductance is quantized when the Fermi level is located near Weyl nodes within a finite-size gap. This quantization of the Hall conductance collapses once the strength of disorder exceeds a critical value, suggesting that it serves as a probe to distinguish a Weyl semimetal phase from a diffusive anomalous Hall metal phase.

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Section: Simulation Of Electron Transportmentioning

confidence: 78%

Section: Simulation Of Electron Transportmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Takane

2016

J. Phys. Soc. Jpn.

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“…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 .…”

Section: Introductionmentioning

confidence: 99%

Global phase diagram of disordered type-II Weyl semimetals

Liu

Jiang

et al. 2017

Phys. Rev. B

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With electron and hole pockets touching at the Weyl node, type-II Weyl semimetal is a newly proposed topological state distinct from its type-I cousin. We numerically study the localization effect for tilted type-I as well as type-II Weyl semimetals and give the global phase diagram. For disordered type-I Weyl semimetal, an intermediate three-dimensional quantum anomalous Hall phase is confirmed between Weyl semimetal phase and diffusive metal phase. However, this intermediate phase is absent for disordered type-II Weyl semimetal. Besides, near the Weyl nodes, comparing to its type-I cousin, type-II Weyl semimetal possesses even larger ratio between the transport lifetime along the direction of tilt and the quantum lifetime. Near the phase boundary between the type-I and the type-II Weyl semimetals, infinitesimal disorder will induce an insulating phase so that in this region, the concept of Weyl semimetal is meaningless for real materials.

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“…Because of the invariable presence of disorder in all solid-state materials, there has been a substantial amount of theoretical activity studying the effect of disorder on noninteracting Dirac and Weyl fermions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Focusing on the undoped (i.e., Fermi energy at E ¼ 0) Dirac point (i.e., the band touching point), the quadratically vanishing density of states at zero energy [ρðEÞ ∼ E 2 ] associated with the linear three-dimensional energy band dispersion places these problems in a different class than that of a conventional metal with a parabolic energy dispersion and a nonzero Fermi energy.…”

Section: Introductionmentioning

confidence: 99%

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

2016

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We numerically study the effect of short-ranged potential disorder on massless noninteracting threedimensional Dirac and Weyl fermions, with a focus on the question of the proposed (and extensively theoretically studied) quantum critical point separating semimetal and diffusive-metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian (H) and exactly calculate the density of states (DOS) near zero energy, using a combination of Lanczos on H 2 and the kernel polynomial method on H. We establish the existence of two distinct types of low-energy eigenstates contributing to the disordered density of states in the weak-disorder semimetal regime. These are (i) typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states and (ii) nonperturbative rare eigenstates that are weakly dispersive and quasilocalized in the real-space regions with the largest (and rarest) local random potential. Using twisted boundary conditions, we are able to systematically find and study these two (essentially independent) types of eigenstates. We find that the Dirac states contribute low-energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasilocalized eigenstates contribute a nonzero background DOS which is only weakly energy dependent near zero energy and is exponentially small at weak disorder. We also find that the expected semimetal to diffusive-metal quantum critical point is converted to an avoided quantum criticality that is "rounded out" by nonperturbative effects, with no signs of any singular behavior in the DOS at the energy of the clean Dirac point. However, the crossover effects of the avoided (or hidden) criticality manifest themselves in a so-called quantum critical fan region away from the Dirac energy. We discuss the implications of our results for disordered Dirac and Weyl semimetals, and reconcile the large body of existing numerical work showing quantum criticality with the existence of these nonperturbative effects.

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Effect of Disorder in a Three-Dimensional Layered Chern Insulator

Cited by 108 publications

References 42 publications

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

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

Global phase diagram of disordered type-II Weyl semimetals

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

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