Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

Abstract

Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50]. Despite this diversity, topological semimetals can be further classified and characterized by the dimensionality of their band crossings in the bulk Brillouin zone (BZ). In a Dirac/Weyl semimetal or an unconventional (higher-fold degenerate) fermion semimetal [41,[43][44][45][46], the conduction and valence bands cross at discrete points in the BZ. Therefore, the dimension of their band crossings is 0D. In a nodal-line semimetal [38], the conduction and valence bands touch along a closed loop, thus the dimension of its band crossing is 1D. In this letter, we propose a number of previously unidentified topological semimetals and identify a candidate material class for the experimental realization. They feature 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain enabled by perpendicular mirror planes. The Hopf link, which consists of two rings that pass through the center of each other, represents the simplest topologically nontrivial link. While originally studied in mathematics and other areas, recently, researchers have applied this concept into topological physics in order to construct novel topological insulators and superconductors [52][53][54], although the role of Hopf link is distinctly different from what is considered here. Here we apply this idea in metals and show that the c...

Composite topological nodal lines penetrating the Brillouin zone in orthorhombic AgF2

“…Topological materials have attracted great interest both theoretically and experimentally 1-3 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), 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. Symmetries play important roles in the classification of topological phases.…”

“…npj Computational Materials (2019)53 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences 1234567890():,;…”

Probing topological properties of a three-dimensional lattice dimer model with neural networks

“…We obtain that on a bipartite (in our case cubic) lattice, hopfions are characterized by an integer topological invarariant, whereas on a non-bipartite lattice (we consider an example of stacked triangular lattice), dimer configurations are characterized by Z 2 invariant. We remark, that this reasoning gave us a hint that on a bipartite lattice, dimer configurations can be characterized by an exact Hopf number [27][28][29][30][31][32][33][34][35][36], which we later verified analytically [37]. However, on a non-bipartite lattice, the neural network is the only known way to obtain the topological classification of dimer configurations.…”

Crystalline topological Dirac semimetal phase in rutile structure β′−PtO2

“…Moreover, as the mirror planes contain the k z axis, the nodal lines should pass through the points (0,0,+k d ) and (0,0,−k d ). Consequently, without SOC, we have an inner nodal chain structure [36,37] as shown in Fig. 2(b).…”