Abstract
Weyl semimetals (WS) are a new class of Dirac-type materials exhibiting a phase with bulk energy nodes and an associated vanishing density of states (DOS). We investigate the stability of this nodal DOS suppression in the presence of local impurities and consider whether or not such a suppression can be lifted by impurity-induced resonances. We find that while a scalar (chemical potential type) impurity can always induce a resonance at arbitrary energy and hence lift the DOS suppression at Dirac/Weyl nodes, for many other impurity types (e.g. magnetic or orbital mixing), resonances are forbidden in a wide range of energy. We investigate a four-band tight-binding model of WS adapted from a physical heterostructure construction due to Burkov et al (2011 Phys. Rev. B 84 235126), and represent a local impurity potential by a strength g as well as a matrix structure Λ. A general framework is developed to analyze this resonance dichotomy and make connection with the phase shift picture in scattering theory, as well as to determine the relation between resonance energy and impurity strength g. A complete classification of impurities based on Λ, based on their effect on nodal DOS suppression, is tabulated. We also discuss the differences between continuum and lattice approaches.
Highlights
The history of relativistic (Dirac) fermions in solid state band structures has been known since Wallace [2], who first considered a single layer of hexagonal graphite, i.e. graphene
An effective way to extract the locus of such rapid migrations, which we identify as resonances, is to find the zeros of T −1(ω, g−1) ≡ g−1Λ−1 − G000(ω), where G000(ω) ≡
Inversion-even impurity In this class we have Λ = I, Γ4, or Γμν (μ, ν = 1, 2, 3, 5). Since they all commute with G000, a resonance can be induced at arbitrary energy, i.e. a solution of det T0−0 1 = 0 exists for real g
Summary
The history of relativistic (Dirac) fermions in solid state band structures has been known since Wallace [2], who first considered a single layer of hexagonal graphite, i.e. graphene. In this case, the Weyl node energy is found to be stable for any Λ that does not commute with the local Green’s function, but unstable if it commutes. Impurities commuting with the local Green’s function will disrupt the Weyl node stability Those that do not fully commute yield either a nodal energy stable over the full range of η, or a critical symmetry breaking amplitude ηc – which is fully determined by parameters of the clean system – that splits the η axis into two phases where the nodal energy is stable in one phase and unstable in the other.
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