Disordered double Weyl node: Comparison of transport and density of states calculations

Sbierski, Bjoern; Trescher, Maximilian; Bergholtz, Emil J.; Brouwer, Piet W.

doi:10.1103/physrevb.95.115104

Cited by 27 publications

(19 citation statements)

References 40 publications

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“…We verify the approximation that the internode scattering time is the relevant transport time, and thereby our results, by numerically calculating the conductance using a transfer matrix representation 34,41 of the solutions of the Weyl equation H ψ = E ψ, previously employed for disordered Weyl nodes in the absence of a magnetic field [42][43][44][45] . A random scattering potential with correlations as in Eq.…”

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confidence: 60%

Strongly angle-dependent magnetoresistance in Weyl semimetals with long-range disorder

Behrends

Bardarson

2017

Phys. Rev. B

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The chiral anomaly in Weyl semimetals states that the left- and right-handed Weyl fermions, constituting the low energy description, are not individually conserved, resulting, for example, in a negative magnetoresistance in such materials. Recent experiments see strong indications of such an anomalous resistance response; however, with a response that at strong fields is more sharply peaked for parallel magnetic and electric fields than expected from simple theoretical considerations. Here, we uncover a mechanism, arising from the interplay between the angle-dependent Landau-level structure and long-range scalar disorder, that has the same phenomenology. In particular, we analytically show, and numerically confirm, that the internode scattering time decreases exponentially with the angle between the magnetic field and the Weyl node separation in the large field limit, while it is insensitive to this angle at weak magnetic fields. Since, in the simplest approximation, the internode scattering time is proportional to the anomaly-related conductivity, this feature may be related to the experimental observations of a sharply peaked magnetoresistance

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confidence: 60%

Strongly angle-dependent magnetoresistance in Weyl semimetals with long-range disorder

Behrends

Bardarson

2017

Phys. Rev. B

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“…The above outcome can also be stated in a slightly different words as follows. times [101][102][103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119][120]. However, the role of randomness on BdG-Weyl/Dirac quasiparticles is still at an early stage of exploration (see however Refs.…”

Section: External Strain and S + D Pairingmentioning

confidence: 99%

Topological superconductivity of spin- 3/2 carriers in a three-dimensional doped Luttinger semimetal

et al. 2019

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We investigate topological Cooper pairing, including gapless Weyl and fully gapped class DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter describes effective spin-3/2 carriers near a quadratic band touching and captures the normal-state properties of the 227 pyrochlore iridates and half-Heusler alloys. Electron-electron interactions may favor non-s-wave pairing in such systems, including even-parity d-wave pairing. We argue that the lowest energy d-wave pairings are always of complex (e.g., d + id) type, with nodal Weyl quasiparticles. This implies (E) ∼ |E| 2 scaling of the density of states (DoS) at low energies in the clean limit, or (E) ∼ |E| over a wide critical region in the presence of disorder. The latter is consistent with the T -dependence of the penetration depth in the half-Heusler compound YPtBi. We enumerate routes for experimental verification, including specific heat, thermal conductivity, NMR relaxation time, and topological Fermi arcs. Nucleation of any d-wave pairing also causes a small lattice distortion and induces an s-wave component; this gives a route to strain-engineer exotic s+d pairings. We also consider odd-parity, fully gapped p-wave superconductivity. For hole doping, a gapless Majorana fluid with cubic dispersion appears at the surface. We invent a generalized surface model with ν-fold dispersion to simulate a bulk with winding number ν. Using exact diagonalization, we show that disorder drives the surface into a critically delocalized phase, with universal DoS and multifractal scaling consistent with the conformal field theory (CFT) SO(n)ν , where n → 0 counts replicas. This is contrary to the naive expectation of a surface thermal metal, and implies that the topology tunes the surface renormalization group to the CFT in the presence of disorder. arXiv:1708.07825v2 [cond-mat.mes-hall]A. Even parity pairing: scenarios and main results Even-parity local pairings are represented by anomalous local bilinears of the spin-3/2 fermion field. Local or intra-unit cell pairings can be mediated by short-range interactions, such as spin exchange scattering. For superconductivity at low densities in an LSM, momentumdependent pairing interactions can be strongly suppressed relative to local ones. The mechanism for this is virtual renormalization from higher energies, as may also occur in bilayer graphene (a "two-dimensional LSM") [58][59][60][61] or structurally similar bilayer silicene [62]. The local pairing amplitudes couple to j = 0 and j = 2 spin SU(2) tensor operators.Although the even-parity pairings are local bilinears in the LSM, we focus on the situation where the superconductivity itself manifests mainly near the Fermi surface. The Fermi surface is assumed to reside at finite carrier density away from charge neutrality. The projection of the j = 0 (j = 2) pairing onto the conduction or valence bands give rise to momentum-independent (dependent) s-wave (d-wave) superconductivity on the Fermi surface [51,56]. Both channels are band-pseudospin singlets...

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“…Data collapse in Figs. 8, 13 In the lattice implementation, we set ξ ¼ 4a, where a is the lattice constant, leading to a strong suppression of intervalley scattering by a factor exp ½−ðΔkÞ 2 ξ 2 =2 < 10 −34 , where Δk ¼ π=a is the separation between two Weyl nodes [105]. Now we proceed with the numerical analysis of the average DOS using KPM in a cubic lattice with linear dimension L ¼ 160 in each direction.…”

Section: Appendix F: Correlated Disordermentioning

confidence: 99%

Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality

2018

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Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal (WSM)-insulator quantum-critical point. But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point. The field-theoretic predictions for the correlation length exponent ν ¼ 2 and dynamic scaling exponent z ¼ 5=4 at this multicritical point are in good agreement with the ones extracted numerically, yielding ν ¼ 1.98 AE 0.10 and z ¼ 1.26 AE 0.05, from the scaling of the average density of states (DOS). Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT. We here demonstrate that in the presence of generic but strong disorder, the WSM-metal QPT is ultimately always characterized by the exponents ν ¼ 1 and z ¼ 3=2 (to one-loop order), originating from intranode or chiralsymmetric (e.g., regular and axial potential) disorder. We here anchor such emergent chiral superuniversality through complementary renormalization-group calculations, controlled via ϵ expansions, and numerical analysis of average DOS across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy. The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Grüneisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid, are discussed.

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Disordered double Weyl node: Comparison of transport and density of states calculations

Cited by 27 publications

References 40 publications

Strongly angle-dependent magnetoresistance in Weyl semimetals with long-range disorder

Strongly angle-dependent magnetoresistance in Weyl semimetals with long-range disorder

Topological superconductivity of spin- 3/2 carriers in a three-dimensional doped Luttinger semimetal

Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality

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