Hourglasslike nodal net semimetal in Ag2BiO3

Abstract

Based on first-principles calculation and analysis of crystal symmetries, we propose a kind of hourglass-like nodal net (HNN) semimetal in centrosymmetric Ag2BiO3 that is constructed by two hourglass-like nodal chains (HNCs) at mutually orthogonal planes in the extended Brillouin zone (BZ) when the weak spin-orbit coupling (SOC) mainly from the 6s orbital of Bi atoms is ignored. The joint point in the nodal net structure is a special double Dirac point located at the BZ corner. Different from previous HNN [Bzdušek et al., Nature 538, 75 (2016)] where the SOC and double groups nonsymmorphic symmetries are necessary, and also different from the accidental nodal net, this HNN structure is inevitably formed and guaranteed by spinless nonsymmorphic symmetries, and thus robust against any symmetry-remaining perturbations. The Fermi surface in Ag2BiO3 consisting of a torus-like electron pocket and a torus-like hole pocket may lead to unusual transport properties. A simple four-band tight-binding model is built to reproduce the HNN structure. For a semi-infinite Ag2BiO3, the "drumhead" like surface states with nearly flat dispersions are demonstrated on (001) and (100) surfaces, respectively. If such weak SOC effect is taken into consideration, this HNN structure will be slightly broken, left a pair of hourglass-like Dirac points at the two-fold screw axis. This type of hourglass-like Dirac semimetal is symmetry-enforced and does not need band inversion anymore. Our discovery provides a new platform to study novel topological semimetal states from nonsymmorphic symmetries.

Recent advances in 2D, 3D and higher-order topological photonics

“…However, the nodal lines rely on accidental degeneracies and are therefore prone to be broken or removed by perturbations that even preserve such symmetries as structural variation. In contrast, a nodal line that arises from an hourglass-shaped dispersion of four bands is robust against perturbations that preserve the symmetries 171,172 . An hourglass nodal line was experimentally observed in a photonic crystal possessing three glide mirror symmetries and C 4 symmetry (Fig.…”

Observation of Hourglass Nodal Lines in Photonics

“…Among them, Weyl semimetals requiring breaking of either time-reversal or inversion symmetry are robust under general perturbations, as all three Pauli matrices have been involved exhaustively. Nodal line semimetals [27][28][29][30][31][32][33][34][35][36] To overcome the fragileness of the typical nodal line semimetals, hourglass nodal line (HNL) [37,38] is proposed, which is formed by hourglass-shaped band dispersion around a loop in the momentum space as shown in FIG. 1(b).…”

Research progress on topological nodal line semimetals

“…因此节线半金属还需要额外 的对称性约束哈密顿量 [35,36] , 在晶体对称性的约束下, , 体系会在整个倒空间形成Kramers 简并, 因此节线相会消失 [16] . [37][38][39] . 第四种是由于体系在高对称线上 存在高维的不可约表示或共表示所形成的节线相, 此 类节线一般会穿过整个布里渊区并且能带会在整条高 对称线上都简并 [40] .…”

“…此外, 当存在滑移面时, 体系 的倒空间也有可能出现一维的节线 [ 3 8 , 6 7 , 6 8 ] . 在材 料方面很多非磁性节线半金属已经被理论和实验所 证实, 例如三维的拓扑节线半金属有Ag 2 BiO 3 [39] , Cu-TeO 3 [69] , X 3 SiTe 6 (X=Ta, Nb) [70] , PbO 2 [71] , IVX 2 (IV=C, Si, Ge, Sn, Pb; X=S, Se, Te) [72] , ZrO [73] , 单质铍 [74] , ZrSiS [75,76] 等; 二维材料有Cu 2 Si [58] [77] . 当不考虑自旋轨道耦合时,…”