Chiral topological insulating phases from three-dimensional nodal loop semimetals

Abstract

We identify a topological Z index for three dimensional chiral insulators with P*T symmetry where two Hamiltonian terms define a nodal loop. Such systems may belong in the AIII or DIII symmetry class. The Z invariant is a winding number assigned to the nodal loop and has a correspondence to the geometric relation between the nodal loop and the zeroes of the gap terms. Dirac cone edge states under open boundary conditions are in correspondence with the winding numbers assigned to the nodal loops. We verify our method with the low-energy effective Hamiltonian of a three-dimensional material of topological insulators in the Bi${}_2$Te${}_3$ family.

5 pages, 4 figures

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Topological nodal line semimetals
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Tunable Weyl Points in Periodically Driven Nodal Line Semimetals
• Topological Weyl Semi-metal from a Lattice Model
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Topological insulating phases from two-dimensional nodal loop semimetals

Cited by in corpus (6)

• Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops
• Floquet multi-Weyl points in crossing-nodal-line semimetals
• Chiral topological insulator of magnons
• $2\pi$-flux loop semimetals
• Broken-symmetry phases of interacting nested Weyl and Dirac loops
• Characterization of Lifshitz transitions in topological nodal line semimetals