Emergence of topological phases from the extension of two-dimensional lattice with nonsymmorphic symmetries

TL;DR

This paper constructs 3D tight-binding models from 2D nonsymmorphic lattices to explore various topological semimetallic phases, revealing how symmetries protect different nodal structures and surface states.

Contribution

It introduces a method to generate multiple topological semimetal phases from stacked 2D nonsymmorphic lattices, expanding understanding of symmetry-protected topological features.

Findings

Generation of Dirac and Weyl nodal line semimetals

Protection of nodal lines by mirror symmetry

Emergence of drumhead surface states

Abstract

Young and Kane have given a great insight for 2D Dirac semimetals with nontrivial topology in the presence of nonsymmorphic crystalline symmetry. Based on one of 2D nonsymmorphic square lattice structures they proposed, we further construct a set of 3D minimal tight-binding models via vertically stacking the 2D nonsymmorphic lattice. Specifically, our model provides a platform to generate three topologically semimetallic phases such as Dirac nodal line semimetals, Weyl nodal line semimetals and Weyl semimetals. The off-centered mirror symmetry sufficiently protects nodal lines emerging within mirror-invariant plane with a nontrivial mirror invariant $n_{M\mathbb{Z}}$, whereas twofold screw rotational symmetry protects nontrivial Weyl nodal points with topological charge $C=2$. Interestingly, Weyl nodal loops are generated without mirror symmetry protection, where nontrivial "drumhead" surface states emerge within loops. In the presence of both time-reversal and inversion symmetries, the emergence of weak topological insulator phases is discussed as well.