Disorder in tilted Weyl semimetals from a renormalization group perspective

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We study the effects of disorder and Coulomb interactions on the physics of three-dimensional type-I Weyl fermions with tilted and anisotropic dispersions in a renormalization group approach. To lowest non-trivial loop order we show that the tendency of the Coulomb interactions to restore the symmetry of the dispersion in the semimetallic region of the phase diagram dominates the stabilization of the tilt and anisotropy favored by weak disorder. We argue that the topology of the renormalization flow of the disorder and Coulomb couplings is essentially determined by gauge invariance, so that these findings continue to hold qualitatively at any order in perturbation theory.

Section: Model Settingmentioning

confidence: 70%

“…We next introduce a tilt into the model of a Weyl fermion perturbed by disorder, as studied before in Ref. 33 . The β functions of interest reduce to…”

Section: B Untilted Interacting Casementioning

confidence: 99%

Interplay of disorder and interactions in a system of subcritically tilted and anisotropic three-dimensional Weyl fermions

Sikkenk

Fritz

2019

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“…With tilt increasing, the transition from type-I to type-II Dirac/Weyl fermions appears. The nonmagnetic disorder in an isolated Weyl cone also enhances the tilt [33,34]. At the same time, it drives a phase transition from the SM phase to compressible diffusive metal (CDM) phase [33,34], which is characterized by the generation of finite zeroenergy scatting rate γ 0 and finite zero-energy density of states (DOS) ρ (0) [33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

“…The nonmagnetic disorder in an isolated Weyl cone also enhances the tilt [33,34]. At the same time, it drives a phase transition from the SM phase to compressible diffusive metal (CDM) phase [33,34], which is characterized by the generation of finite zeroenergy scatting rate γ 0 and finite zero-energy density of states (DOS) ρ (0) [33][34][35][36][37][38][39][40][41][42][43][44][45]. This disorder-induced SMto-CDM phase transition has been widely studied in untilted D/WSMs [35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions

Zhao

Wang

2019

We investigate the mutual influence of tilt, disorder, and Coulomb interaction in a type-I Dirac semimetal (DSM) with x-direction tilt by performing a renormalization group analysis. The interplay between disorder and ordinary tilt generates an effective tilt along the x-direction, which is the physically observable one. There exist two types of disorder which increase the effective tilt and drive a phase transition from the DSM phase to the diffusive metal phase. The diffusive phase transition stops the increase of the effective tilt and the surface of the original Dirac cone in the diffusive metal phase is just slightly tilted. Surprisingly, the Dirac point is replaced by a bulk nodal arc in the diffusive metal phase. The Coulomb interaction suppresses the diffusive phase transition and therefore is harmful to the formation of bulk nodal arc. In contrast, there also exists other two types of disorder which reduce the effective tilt and induce no phase transition. For these two types of disorder, the Coulomb interaction enhances their low-energy relevances. Coexistence of Coulomb interaction with any of them leads to a stable infrared fixed point where the coupling strengths for two kinds of interaction are identical and the effective tilt vanishes. The original tilted Dirac semimetal now reacts like an untilted and interaction-free Dirac semimetal. Our results show that interplay between tilt, disorder, and Coulomb interaction results in rich low-energy properties for the tilted Dirac fermions. *

“…Materials that exhibit such tilted Weyl cones are of type I if the tilt is relatively small and of type II if the cones are overtilted such that the electron and hole dispersions intersect the energy plane of the Weyl node itself [19][20][21] . Moreover, the tilt is affected and can even be generated by disorder and interaction effects [22][23][24] . It is thus of considerable interest to investigate what such a tilt does to the chiral magnetic conductivity of a Weyl (semi)metal.…”

mentioning

confidence: 99%

Anisotropic chiral magnetic effect from tilted Weyl cones

Wurff

Stoof

2017

We determine the antisymmetric current-current response for a pair of (type-I) tilted Weyl cones with opposite chirality. We find that the dynamical chiral magnetic effect depends on the magnitude of the tilt and on the angle between the tilting direction and the wave vector of the magnetic field. Additionally, the chiral magnetic effect is shown to be closely related to the presence of an intrinsic anomalous Hall effect with a current perpendicular to the tilting direction and the electric field. We investigate the nonanalytic long-wavelength limit of the corresponding transport coefficients.PACS numbers: 71.55. Ak, 71.15.Rf Introduction.-In classical electrodynamics, magnetic fields always induce currents that are perpendicular to the magnetic field direction due to the Lorentz force. However, in quantum electrodynamics, a current can also be generated in the same direction as the magnetic field. This was first realized for massless fermions in particle physics 1,2 . It is a consequence of the fact that quantum mechanically a magnetic field quenches the kinetic energy perpendicular to its direction and also spin polarizes the lowest Landau level. As a result massless fermions only obtain a drift velocity along the magnetic field with an opposite sign for opposite chiralities. Inducing an imbalance between the two chiral species then gives a net current along the magnetic field direction known now as the chiral magnetic effect (CME).Massless chiral fermions also occur as low-energy quasiparticles in the recently discovered Weyl (semi)metals 3-7 . These quasiparticles do not move at the speed of light, as in elementary-particle physics, but rather at the Fermi velocity. Additionally, the effective Weyl cones with different chirality are in a real material always connected by the full bandstructure and hence electrons can be transported from one cone to another by applying both an electric and a magnetic field 8 . In particle physics the same phenomenon occurs due to the breaking of chiral symmetry by quantum corrections. This breaking of chiral symmetry due to the renormalization of ultraviolet divergencies is called a chiral anomaly and causes the difference between the numbers of particles with positive and negative chirality to be no longer conserved 9-11 . The main difference with particle physics is that Lorentz invariance is not enforced in a condensed-matter material. This gives, besides a velocity that is smaller than the speed of light, also the possibility that Weyl nodes are separated in energy-momentum space. Splitting them in the momentum direction gives rise to a topological anomalous Hall effect 8 , whereas splitting them in the energy direction is exactly the situation of most interest for the CME 2,12 . Indirect measurements of the chiral magnetic effect have recently been made by the observation of a negative magnetoresistance [13][14][15][16] . Another interesting possibility is tilting the Weyl cones, meaning that the slope of the dispersion relation is not the same in opposite directions ...