Anderson Localization and the Quantum Phase Diagram of Three Dimensional Disordered Dirac Semimetals

Pixley, J. H.; Goswami, Pallab; Sarma, S. Das

doi:10.1103/physrevlett.115.076601

Cited by 114 publications

(207 citation statements)

References 57 publications

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“…In all of these numerical calculations, the CCFS inequality ν ≥ 2=d is well satisfied. It is important to mention that totally independent from this SM to DM transition, at a much larger disorder strength, the Anderson localization transition has been established in some of these models [28,35]. The current work is entirely in the low-disorder regime (where the SM-DM-avoided QCP resides) and has nothing to do with the high-disorder Anderson localization transition from a DM phase to an Anderson insulator phase [28], which occurs at roughly W l =t ¼ 3.75 for the model under consideration with Gaussian disorder (see the Appendix).…”

Section: Introductionmentioning

confidence: 95%

“…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%

“…The goal of the current work is to settle this question definitively. Although the disordered Dirac-Weyl systems have been theoretically studied very extensively in the literature [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], essentially all of this work, except for a very recent one (Ref. [27]), study the properties of the disorder-driven SM-DM quantum phase transition, taking it for granted that such a disorder-induced QCP indeed exists in three dimensions following the predictions of the perturbative field theory.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

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“…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%

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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“…Flat bands are typical characteristics of localized resonant wave modes that are interesting and important in both quantum and classical systems. 22,23 In this paper, we study the dispersion relations of a two-dimensional (2D) AC consisting of a square array of honey-coated air cylinders immersed in a water host. We find that at the BZ center a quadratic band is tangent to a flat band, with the latter being the fingerprint of locally resonant modes.…”

Section: Introductionmentioning

confidence: 99%

Flat band degeneracy and near-zero refractive index materials in acoustic crystals

Mei

2016

AIP Advances

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A Dirac-like cone is formed by utilizing the flat bands associated with localized modes in an acoustic crystal (AC) composed of a square array of core-shell-structure cylinders in a water host. Although the triply-degeneracy seems to arise from two almost-overlapping flat bands touching another curved band, the enlarged view of the band structure around the degenerate point reveals that there are actually two linear bands intersecting each other at the Brillouin zone center, with another flat band passing through the same crossing point. The linearity of dispersion relations is achieved by tuning the geometrical parameters of the cylindrical scatterers. A perturbation method is used to not only accurately predict the linear slopes of the dispersions, but also confirm the linearity of the bands from first principles. An effective medium theory based on coherent potential approximation is developed, and it shows that a slab made of the AC carries a near-zero refractive index around the Dirac-like point. Full-wave simulations are performed to unambiguously demonstrate the wave manipulating properties of the AC structures such as perfect transmission, unidirectional transmission and wave front shaping.

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Anderson Localization and the Quantum Phase Diagram of Three Dimensional Disordered Dirac Semimetals

Cited by 114 publications

References 57 publications

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

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

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

Flat band degeneracy and near-zero refractive index materials in acoustic crystals

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