Topological Nodal-line Semimetals in Two Dimensions with time-reversal symmetry breaking

TL;DR

This paper demonstrates the realization of two-dimensional topological nodal-line semimetals with protected closed nodal lines through symmetry breaking in topological insulators, revealing new phases and potential spintronic applications.

Contribution

It introduces a novel method to achieve 2D TNLSs with closed nodal lines in the presence of spin-orbit coupling by breaking time-reversal symmetry, and explores their topological properties.

Findings

2D TNLSs can be obtained from TIs/TCIs by symmetry breaking.

Nodal lines are protected by crystalline mirror symmetry.

Strong spin Hall effect predicted in 2D TNLSs.

Abstract

Topological nodal-line semimetals (TNLSs) exhibit exotic physical phenomena due to a one-dimensional (1D) band touching line, rather than discrete (Dirac or Weyl) points. While so far proposed two-dimensional (2D) TNLSs possess closed nodal lines (NLs) only when spin-orbit coupling (SOC) is neglected, here using Na$_3$Bi trilayers as an example, we show that 2D TNLSs can been obtained from topological (crystalline) insulators (TI/TCI) by time-reversal symmetry breaking even in the presence of SOC. We further reveal that these obtained NLs are protected by crystalline mirror symmetry, while a mirror symmetry breaking perturbation opens a full gap thus giving rise to a phase transition from 2D TNLS to a quantum anomalous Hall insulator (QAHI). We thereby uncover a close correlation between various topological phases. Remarkably, a strong spin Hall effect, important for transport applications, is predicted in 2D TNLS. Finally, a Na$_2$CrBi trilayer is proposed to realize the 2D TNLS without extrinsic magnetic field. Our work not only proposes a new strategy for realizing 2D TNLSs with truely closed NLs, but also reveals potential applications of TNLS in spintronics.