Node-Surface and Node-Line Fermions From Nonsymmorphic Lattice Symmetries

TL;DR

This paper introduces a new class of topological semimetals in BaMX$_3$ crystals, featuring node-surfaces and node-lines protected by nonsymmorphic symmetries, with potential for material design of such states.

Contribution

It identifies and characterizes topological node-surface and node-line states in BaMX$_3$ crystals using symmetry analysis and first principles calculations, highlighting their protection by nonsymmorphic symmetries.

Findings

Node-surface in BaVS$_3$ protected by nonsymmorphic symmetry.

Spin-orbit coupling reduces node-surface to node-lines in BaTaS$_3$.

Node-lines are robust and symmetry-guaranteed, different from accidental band touchings.

Abstract

We propose a kind of novel topological quantum state of semimetals in a quasi-one-dimensional (1D) crystals BaMX$_3$ (M = V, Nb or Ta; X = S or Se) family by using symmetry analysis and first principles calculation. We find that in BaVS$_3$ the valence and conduction bands are degenerate in the $k_z=\pi/c$ plane ($c$ is the lattice constant along $\hat{z}$ axis) of the Brillouin Zone (BZ). These nodal points form a node-surface and they are protected by a nonsymmorphic crystal symmetry consisting of a two-fold rotation about the $\hat{z}$ axis and a half-translation along the same $\hat{z}$ axis. The band degeneracy in the node-surface is lifted in BaTaS$_3$ by including strong spin-orbit coupling (SOC) of Ta. The node-surface is reduced into 1D node-lines along the high-symmetry paths $k_x=0$ and $k_x$ = $\pm{\sqrt{3}}k_y$ on the $k_z=\pi/c$ plane. These node-lines are robust against SOC and guaranteed by the symmetries of $P6_3/mmc$ space group. These node-line states are entirely different from previous proposals which are based on the accidental band touchings. We also propose a useful material design for realizing topological node-surface and node-line semimetals.