Composite topological nodal lines penetrating the Brillouin zone in orthorhombic AgF2

Dexi Shao,Pengchao Lu,Jian Sun,Dingyu Xing,Qinyan Gu,Tong Chen,Huaiqiang Wang,Li Sheng

doi:10.1038/s41524-019-0190-3

Abstract

It has recently been found that nonsymmorphic symmetries can bring many exotic band crossings. Here, based on symmetry analysis, we predict that materials with time-reversal symmetry in the space group of Pbca (No. 61) possess rich symmetry-enforced band crossings, including nodal surfaces, fourfold degenerate nodal lines and hourglass Dirac loops, which appear in triplets as ensured by the cyclic permutation symmetry. We take Pbca AgF2 as an example in real systems and studied its band structures with ab initio calculations. Specifically, in the absence of spin-orbit coupling (SOC), besides the above-mentioned band degeneracies, this system features a nodal chain and a nodal armillary sphere penetrating the Brillouin zone (BZ). While with SOC, we find a new configuration of the hourglass Dirac loop/chain with the feature traversing the BZ, which originates from the splitting of a Dirac loop confined in the BZ. Furthermore, guided by the bulk-surface correspondence, we calculated the surface states to explore these bulk nodal phenomena. The evolution of these interesting nodal phenomena traversing the BZ under two specific uniaxial strains is also discussed.

Highlights

Topological materials have attracted great interest both theoretically and experimentally[1,2,3] since the proposal of topological insulators (TIs) in 2005.4 Generally speaking, topological materials can be classified into gapped phases, such as TIs and topological superconductors (TSCs),[1,2] and gapless phases consisting of various topological semimetals (TSMs), such as Weyl semimetals (WSMs),[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] Dirac semimetals(DSMs),[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] nodal-line semimetals (NLSMs),[44,45,46,47,48,49,50,51,52,53] and nodal surface semimetals (NSSMs),[54,55,56,57,58] etc
When spin-orbit coupling (SOC) is taken into consideration, we find one of the closed three nodal hourglass Dirac loops in theory splits into two loops stretching across the Brillouin zone (BZ)
It is evident that the plane kα = π are Θα invariant, and analogous to the well-known Kramers degeneracy, Θα can ensure the above three nodal surfaces encircling the whole BZ

Summary

INTRODUCTION

Topological materials have attracted great interest both theoretically and experimentally[1,2,3] since the proposal of topological insulators (TIs) in 2005.4 Generally speaking, topological materials can be classified into gapped phases, such as TIs and topological superconductors (TSCs),[1,2] and gapless phases consisting of various topological semimetals (TSMs), such as Weyl semimetals (WSMs),[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] Dirac semimetals(DSMs),[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] nodal-line semimetals (NLSMs),[44,45,46,47,48,49,50,51,52,53] and nodal surface semimetals (NSSMs),[54,55,56,57,58] etc. When SOC is taken into consideration, we predict that there is a nodal hourglass Dirac loop on each surface of the BZ. It should be emphasized that all of the above-mentioned nodal configurations are symmetryenforced and appear in triplets as a result of the cyclic permutation symmetry. With both ab initio calculations and tight-binding analysis, we have taken the orthorhombic AgF2 as a candidate material to justify the theoretical predictions. When SOC is taken into consideration, we find one of the closed three nodal hourglass Dirac loops in theory splits into two loops stretching across the BZ. The coexistence of multiple exotic nodal configurations with and without SOC makes this system quite

Shao et al 2

RESULTS AND DISCUSSIONS

METHODS