Protected boundary states in gapless topological phases

Abstract

We systematically study gapless topological phases of (semi-)metals and nodal superconductors described by Bloch and Bogoliubov-de Gennes Hamiltonians. Using K-theory, a classification of topologically stable Fermi surfaces in (semi-)metals and nodal lines in superconductors is derived. We discuss a generalized bulk-boundary correspondence that relates the topological features of the Fermi surfaces and superconducting nodal lines to the presence of protected zero-energy states at the boundary of the system. Depending on the case, the boundary states are either linearly dispersing (i.e. Dirac or Majorana states) or dispersionless, forming two-dimensional surface flat bands or one-dimensional arc surface states. We study examples of gapless topological phases in symmetry classes AIII and DIII, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors. For some cases we explicitly compute the surface spectrum and examine the signatures of the topological boundary states in the surface density of states. We also discuss the robustness of the surface states against disorder.

Are the surface Fermi arcs in Dirac semimetals topologically protected?

“…An important set of questions concerns the topological properties of gapless Fermi systems (3)(4)(5)(6)(7)(8).…”

“…The chiral edge modes of these momentum-space Chern insulators give rise to robust surface Fermi arcs, which end at the projection of bulk Weyl nodes. Unlike the WSM, the bulk-boundary correspondence in topological phase (8) provides no obvious answer for DSMs, because the stability of bulk Dirac nodes requires crystal rotation symmetries (17,18) that are explicitly broken on open side surfaces. It was claimed (25), however, that the surface Fermi arcs in DSMs are perturbatively stable against a weak symmetry-breaking surface potential, and a strong surface potential can destroy them.…”

Patterns of electromagnetic response in topological semimetals

“…All of above work pertains to gapped systems, however, recent theoretical predictions have shown that even materials that are not bulk insulators can harbor robust topological electronic responses,transport properties, and conducting surface/boundary states [31][32][33][34][35][36][37][38][39][40] . This class of materials falls under the name topological semi-metals, and represents another type of non-interacting electronic structure with a topological imprint.…”

“…a Dirac semimetal type with nodes at the time-reversal invariant momenta 44,47,48 , and one with nodes away from those special momenta 45,46 has been reported to be found. In addition to these TSMs there is a large set of symmetry-protected TSMs which rely on additional symmetries for their stability 35 . Finally, we also note that there are superconducting relatives of these semi-metal phases called topological nodal superconductors, or Weyl superconductor phases, that await experimental discovery 35,50,51 , though we will not consider them further.…”

Quasitopological electromagnetic response of line-node semimetals

“…We also note that a version of our stacking construction for gapped phases has also been considered in Ref. 36, while a superconducting version of this, including line nodes, has been considered in [37,38]. Additionally, in very recent work, several proposals for materials that realize linenode TSM states have appeared which utilize magnetic heterostructures [32,39], carbon allotropes [40,41], and inversion symmetric Cu 3 PdN [42,43].…”