A pressure-induced topological phase with large Berry curvature in Pb
 
 1−
 x
 
 Sn
 
 x
 
 Te

Liang, Tian; Kushwaha, Satya; Kim, J.; Gibson, Quinn; Lin, Jingjing; Kioussis, Nicholas; Cava, R. J.; Ong, N. P.

doi:10.1126/sciadv.1602510

Cited by 67 publications

(38 citation statements)

References 32 publications

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“…A recent transport experiment discovered a solid-state material that exhibits continuous BI-WSM phase transitions [42]. Our paper reveals the universal critical properties of this continuous phase transition through the electric conductance.…”

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confidence: 61%

Unconventional scaling theory in disorder-driven quantum phase transition

2018

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We clarify novel forms of scaling functions of conductance, critical conductance distribution and localization length in a disorder-driven quantum phase transition between band insulator and Weyl semimetal phases. Quantum criticality of the phase transition is controlled by a clean-limit fixed point with spatially anisotropic scale invariance. We argue that the anisotropic scale invariance is reflected on unconventional scaling function forms in the quantum phase transition. We verify the proposed scaling function forms in terms of transfer-matrix calculations of conductance and localization length in a tight-binding model.Scaling theories play a central role in the studies of Anderson localization [1,2] as well as other disorder-driven quantum phase transitions. Inspired by the finite size scaling theory by the gang of four [3], scaling theories of localization length [4,5], and conductance [6,7] have been developed and become the core of our current understandings of the localization phenomena. The theories facilitate numerical studies of the phenomena, that establish a rich variety of the universality classes [8][9][10][11][12]. All the Wigner-Dyson universality classes are characterized and distinguished from one another by critical and dynamical exponents, and critical conductance distribution (CCD) [13][14][15][16]. Meanwhile, all of them obey the similar scaling functions;Here Q is a (properly normalized) dimensionless physical quantity, L is a linear dimension of the system size, m is a relevant scaling variable with its scaling dimension ν, and ∆ j (j = 1, 2, · · · ) is an irrelevant scaling variable with negative scaling dimension y j . Naturally one may raise a question by asking "Is there any new disorder-driven quantum phase transition that obeys different forms of scaling functions ?"In this rapid communication, we answer this question affirmatively, by investigating quantum criticality of a disorder-driven phase transition between band insulator (BI) and Weyl semimetal (WSM) phases. We clarify novel forms of scaling functions of conductance, CCD and localization length such as in Eqs. (5), (10), (11), (12), and (13). The criticality of the BI-WSM transition is controlled by a fixed point in the clean limit that has spatially anisotropic scale invariant property [17][18][19][20][21][22][23]. We show that the anisotropic scale invariance results in unconventional forms of scaling functions for conductance, CCD and localization length in the disorder-driven BI-WSM quantum phase transition. Based on numerical simulations on a lattice model with disorders, we demonstrate the validity of the proposed scaling properties.Weyl semimetal (WSM) is a class of three-dimensional semimetal that has a band touching point with linear dis-persions along all the three directions ('Weyl node') [24][25][26][27][28]. The Nielsen-Ninomiya theorem dictates that two band touching points with the linear dispersions must appear in a pair in the first Brillouin zone. When a pair of two Weyl nodes annihilate with each other, t...

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confidence: 61%

Unconventional scaling theory in disorder-driven quantum phase transition

2018

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“…When z is further increased above z T ≈ 0.41, the alloy undergoes a second, topological phase transition, between a trivial insulator and a topological crystalline insulator [61]. The topological transition entails gapless Weyl points close to the L-points of the Brillouin zone [62]. When doped with Tl or In atoms, this alloy becomes superconducting, and the transition temperature exhibits a peak at some intermediate value of z [63].…”

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confidence: 99%

Superconductivity near a Ferroelectric Quantum Critical Point in Ultralow-Density Dirac Materials

Kozii

Ruhman

2019

Phys. Rev. X

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The experimental observation of superconductivity in doped semimetals and semiconductors, where the Fermi energy is comparable to or smaller than the characteristic phonon frequencies, is not captured by the conventional theory. In this paper, we propose a mechanism for superconductivity in ultralow-density three-dimensional Dirac materials based on the proximity to a ferroelectric quantum critical point. We derive a low-energy theory that takes into account both the strong Coulomb interaction and the direct coupling between the electrons and the soft phonon modes. We show that the Coulomb repulsion is strongly screened by the lattice polarization near the critical point even in the case of vanishing carrier density. Using a renormalization group analysis, we demonstrate that the effective electron-electron interaction is dominantly mediated by the transverse phonon mode. We find that the system generically flows towards strong electron-phonon coupling. Hence, we propose a new mechanism to simultaneously produce an attractive interaction and suppress strong Coulomb repulsion, which does not require retardation. For comparison, we perform same analysis for covalent crystals, where lattice polarization is negligible. We obtain qualitatively similar results, though the screening of the Coulomb repulsion is much weaker. We then apply our results to study superconductivity in the low-density limit. We find strong enhancement of the transition temperature upon approaching the quantum critical point. Finally, we also discuss scenarios to realize a topological p-wave superconducting state in covalent crystals close to the critical point. :1901.11064v2 [cond-mat.supr-con] CONTENTS arXiv

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“…Following the discoveries of time-reversal symmetry-protected Z 2 topological insulator states in both 2D and 3D [1][2][3], intensive efforts have been devoted to searching for new types of topological band insulators protected by crystal symmetries, or topological crystalline insulators (TCI) [4]. Although the large number of crystalline space group symmetries suggests the possibility of a wealth of TCI states, for a long time, the theoretically known TCIs were largely limited to crystals with mirror reflections [4][5][6][7] and glide mirror reflections [8,9], such as the SnTe family of IV-VI semiconductors [10][11][12][13][14][15][16][17][18].…”

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Topological crystalline insulator states in the Ca2As family

Zhou¹,

Hsu²,

Chang³

et al. 2018

Phys. Rev. B

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Topological crystalline insulators (TCI) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have provided powerful guidelines to search for TCIs in real materials. Using density functional theory, we identify a class of new TCI states in the tetragonal lattice of the Ca2As material family. On both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries. We show that a particular lattice distortion can single out the newly proposed topological protection by the rotational symmetry. As a result, the Dirac points of the topological surface states are moved to generic locations in momentum space away from any high symmetry lines. Such topological surface states have not been seen before. Moreover, the other family members, including Ca2Sb, Ca2Bi and Sr2Sb, feature different topological surface states due to their distinct topological invariants. We thus further propose topological phase transitions in the pseudo-binary systems such as (Ca1−xSrx)2As and Ca2AsxSb1−x. Our work reveals rich and exotic TCI physics across the Ca2As family of materials, and suggests the feasibility of materials database search methods to discover new TCIs.

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A pressure-induced topological phase with large Berry curvature in Pb _{1−
x} Sn _x Te

Abstract: Under pressure, the semiconductor PbSnTe transitions from an insulator to a Weyl metal that displays a large Berry curvature.

Cited by 67 publications

References 32 publications

Unconventional scaling theory in disorder-driven quantum phase transition

Unconventional scaling theory in disorder-driven quantum phase transition

Superconductivity near a Ferroelectric Quantum Critical Point in Ultralow-Density Dirac Materials

Topological crystalline insulator states in the Ca2As family

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A pressure-induced topological phase with large Berry curvature in Pb 1− x Sn x Te

Abstract: Under pressure, the semiconductor PbSnTe transitions from an insulator to a Weyl metal that displays a large Berry curvature.

Cited by 67 publications

References 32 publications

Unconventional scaling theory in disorder-driven quantum phase transition

Unconventional scaling theory in disorder-driven quantum phase transition

Superconductivity near a Ferroelectric Quantum Critical Point in Ultralow-Density Dirac Materials

Topological crystalline insulator states in the Ca2As family

Contact Info

Product

Resources

About

A pressure-induced topological phase with large Berry curvature in Pb _{1−
x} Sn _x Te