Quantum multicriticality in disordered Weyl semimetals

Abstract

In electronic band structure of solid state material, two band touching points with linear dispersion appear in pair in the momentum space. When they annihilate with each other, the system undergoes a quantum phase transition from three-dimensional Weyl semimetal (WSM) phase to a band insulator phase such as Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a 'magnetic dipole' like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases, renormalized WSM phase, CI phase, and diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized Weyl semimetal (WSM) phase turns out to be a direct phase transition whose critical exponent ν = 0.80 ± 0.01. We interpret these numerical results by a renormalization group analysis on the critical theory.

Precipitating ordered skyrmion lattices from helical spaghetti and granular powders

“…In other systems such as MnSi, which possess stronger magnetocrystalline anisotropy, the crystalline axes clearly determine the skyrmion lattice orientation, even under rotation. [13,40] Outside of the skyrmion stability window, rotation of the sample promotes an oriented helix, destroying any precursor state, as shown in Figure S5. Rotation-induced promotion of the skyrmion phase along both high and low-symmetry axes suggests that the skyrmion-ordering mechanism is independent of the initial orientation of the magnetic field relative to the magnetocrystalline easy/hard axes.…”

“…The contrast between the response of MnSi (Supplemental Materials and Refs. [13] and [40]) and (Fe, Co)Si to field rotation emphasizes the role of the magnetocrystalline anisotropy in skyrmion formation.…”

“…under rotation. [13,40] In these works, it was reported that the SANS pattern for MnSi undergoes a sixfold to 12-fold to six-fold sequential transformation when passing through low and high-symmetry axes.…”

Critical behavior of Anderson transitions in three-dimensional orthogonal classes with particle-hole symmetries

“…Recent material discoveries of Weyl [10][11][12][13] and nodal line Dirac semimetals [14][15][16][17][18][19][20] stimulate intensive studies on non-Anderson-type disorder-driven quantum phase transitions [21][22][23]. Their universal critical properties are characterized by unconventional critical exponents [24][25][26][27][28][29][30] and scaling forms [31], indicating new universality classes of the disorder-driven quantum phase transitions.…”

Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems

“…When d > 2α, on the other hand, it is robust against weak disorder below the critical strength, leading to the disorder-driven QCP. Since d = 3 and α = 1 for Weyl SMs, disordered Weyl SMs have the QCP [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Here, we should note that the critical behavior is correct only up to rare-event effects [38,39].…”