Two-dimensional topological semimetal states in monolayers Cu$_2$Ge, Fe$_2$Ge, and Fe$_2$Sn

TL;DR

This study uses first-principles calculations to explore diverse 2D topological semimetal states in Cu$_2$Ge, Fe$_2$Ge, and Fe$_2$Sn monolayers, revealing how symmetry and magnetism influence their exotic electronic properties.

Contribution

It identifies and characterizes different topological semimetal states in three related monolayers, highlighting the role of symmetry and magnetic orientation in their electronic structures.

Findings

Cu$_2$Ge exhibits massive Dirac nodal lines

Fe$_2$Ge shows massive Weyl points

Fe$_2$Sn has massless Weyl nodal lines

Abstract

Recent experimental realizations of the topological semimetal states in several monolayer systems are very attractive because of their exotic quantum phenomena and technological applications. Based on first-principles density-functional theory calculations including spin-orbit coupling, we here explore the drastically different two-dimensional (2D) topological semimetal states in three monolayers Cu$_2$Ge, Fe$_2$Ge, and Fe$_2$Sn, which are isostructural with a combination of the honeycomb Cu or Fe lattice and the triangular Ge or Sn lattice. We find that (i) the nonmagnetic (NM) Cu$_{2}$Ge monolayer having a planar geometry exhibits the massive Dirac nodal lines, (ii) the ferromagentic (FM) Fe$_2$Ge monolayer having a buckled geometry exhibits the massive Weyl points, and (iii) the FM Fe$_2$Sn monolayer having a planar geometry and an out-of-plane magnetic easy axis exhibits the massless Weyl nodal lines. It is therefore revealed that mirror symmetry cannot protect the four-fold degenerate Dirac nodal lines in the NM Cu$_{2}$Ge monolayer, but preserves the doubly degenerate Weyl nodal lines in the FM Fe$_{2}$Sn monolayer. Our findings demonstrate that the interplay of crystal symmetry, magnetic easy axis, and band topology is of importance for tailoring various 2D topological states in Cu$_2$Ge, Fe$_2$Ge, and Fe$_2$Sn monlayers.