Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal

Abstract

We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by {\em chiral symmetry} and characterized by the topological winding number $N$. We derive the asymptotic chiral-symmetric boundary conditions and find that there are $N+1$ universal classes of them. The class determines the numbers of flat-band edge states on either side off the node in the 1D spectrum and the winding number $N$ gives the {\em total} number of edge states. We then show that the edge states of chiral nodal semimetals are {\em robust}: they persist in a finite-size {\em stability region} of parameters of chiral-asymmetric terms. This significantly extends the notion of 2D and 3D topological nodal semimetals. We demonstrate that the Luttinger model with a quadratic node for $j=\frac{3}{2}$ electrons is a 3D topological semimetal in this new sense and predict that $\alpha$-Sn, HgTe, possibly Pr${}_2$Ir${}_2$O${}_7$, and many other semimetals described by it are topological and exhibit surface states.

v1: 5 pages Main Text, 8 pages Supplementary Material, 2 figures. v2: 5 pages Main Text, 13 pages Supplementary Material, 2+2 figures; Sec V of Supplementary Material added, on chiral-asymmetric boundary conditions, with examples. v3: identical to the published version

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Cited by in corpus (22)

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• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State
• Testing Topological Protection of Edge States in Hexagonal Quantum Spin Hall Candidate Materials
• Relativistic Gurzhi effect in channels of Dirac materials
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Robustness and Universality of Surface States in Dirac Materials
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram
• Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system
• Escape from black holes in materials: Type II Weyl semimetals and generic edge states
• Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
• Edge states in a two-dimensional non-symmorphic semimetal
• New solutions for graphene with scalar potentials by means of generalized intertwining
• Critical phenomena at the complex tensor ordering phase transition
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Surface spectra of Weyl semimetals through self-adjoint extensions
• Topological Luttinger semimetallic phase accompanied with surface states realized in silicon
• Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces
• Impurities in 3D quadratic band-touching Luttinger semimetals : Friedel and RKKY oscillations
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems