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Register a new userTowards ideal topological materials: Comprehensive database searches using symmetry indicators
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Topological materials (TMs) showcase intriguing physical properties defying expectations based on conventional materials, and hold promise for the development of devices with new functionalities. While several theoretically proposed TMs have been experimentally confirmed, extensive experimental exploration of topological properties as well as applications in realistic devices have been held back due to the lack of excellent TMs in which interference from trivial Fermi surface states is minimized. We tackle this problem in the present work by applying our recently developed method of symmetry indicators to all non-magnetic compounds in the 230 space groups. An exhaustive database search reveals thousands of TM candidates. Of these, we highlight the excellent TMs, the 258 topological insulators and 165 topological crystalline insulators which have either noticeable full band gap or a considerable direct gap together with small trivial Fermi pockets. We also give a list of 489 topological semimetals with the band crossing points located near the Fermi level. All predictions obtained through standard generalized gradient approximation (GGA) calculations were cross-checked with the modified Becke-Johnson (MBJ) potential calculations, appropriate for narrow gap materials. With the electronic and optical behavior around the Fermi level dominated by the topologically non-trivial bands, these newly found TMs candidates open wide possibilities for realizing the promise of TMs in next-generation electronic devices.
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Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to ascertaining band topology in realistic calculations. Here, we integrate the recently established theory of symmetry indicators of band topology into first-principle band-structure calculations, and test it on a databases of previously synthesized crystals. The combined algorithm is found to efficiently unearth topological materials and predict topological properties like protected surface states. On applying our algorithm to just 8 out of the 230 space groups, we already discover numerous materials candidates displaying a diversity of topological phenomena, which are simultaneously captured in a single sweep. The list includes recently proposed classes of TC insulators that had no previous materials realization as well as other topological phases, including: (i) a screw-protected 3D TC insulator, b{eta}-MoTe2, with gapped surfaces except for 1D helical hinge states; (ii) a rotation-protected TC insulator BiBr with coexisting surface Dirac cones and hinge states; (iii) non-centrosymmetric Z2 topological insulators undetectable using the well-established parity criterion, AgXO (X=Na,K,Rb); (iv) a Dirac semimetal MgBi2O6; (v) a Dirac nodal-line semimetal AgF2; and (vi) a metal with three-fold degenerate band crossing near the Fermi energy, AuLiMgSn. Our work showcases how the recent theoretical insights on the fundamentals of band structures can aid in the practical goal of discovering new topological materials.
Crystalline symmetries play an important role in the classification of band structures, and the rich variety of spatial symmetries in solids leads to various topological crystalline phases (TCPs). However, compared with topological insulators and Dirac/Weyl semimetals, relatively few realistic materials candidates have been proposed for TCPs. Based on our recently developed method for the efficient discovery of topological materials using symmetry indicators, we explore topological materials in five space groups (i.e. SGs87,140,221,191,194), which are indexed by large order strong symmetry based indicators (Z8 and Z12) allowing for the realization of several kinds of gapless boundary states in a single compound. We predict many TCPs, and the representative materials include: Pt3Ge(SG140), graphite(SG194), XPt3 (SG221,X=Sn,Pb), Au4Ti (SG87) and Ti2Sn (SG194). As by-products, we also find that AgXF3 (SG140,X=Rb,Cs) and AgAsX (SG194,X=Sr,Ba) are good Dirac semimetals with clean Fermi surface. The proposed materials provide a good platform to study the novel properties emerging from the interplay between different types of boundary states.
Two-dimensional (2D) topological materials (TMs) have attracted tremendous attention due to the promise of revolutionary devices with non-dissipative electric or spin currents. Unfortunately, the scarcity of 2D TMs holds back the experimental realization of such devices. In this work, based on our recently developed, highly efficient TM discovery algorithm using symmetry indicators, we explore the possible 2D TMs in all non-magnetic compounds in four recently proposed materials databases for possible 2D materials. We identify hundreds of 2D TM candidates, including 205 topological (crystalline) insulators and 299 topological semimetals. In particular, we highlight MoS, with a mirror Chern number of -4, as a possible experimental platform for studying the interaction-induced modification to the topological classification of materials. Our results winnow out the topologically interesting 2D materials from these databases and provide a TM gene pool which for further experimental studies.
We develop a systematic approach for constructing symmetry-based indicators of a topological classification for superconducting systems. The topological invariants constructed in this work form a complete set of symmetry-based indicators that can be computed from knowledge of the Bogoliubov-de Gennes Hamiltonian on high-symmetry points in Brillouin zone. After excluding topological invariants corresponding to the phases without boundary signatures, we arrive at natural generalization of symmetry-based indicators [H. C. Po, A. Vishwanath, and H. Watanabe, Nature Comm. 8, 50 (2017)] to Hamiltonians of Bogoliubov-de Gennes type.
Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states and unusual magneto-transport properties. In this paper, we present a complete classification of all possible nonsymmorphic band degeneracies in hexagonal materials with strong spin-orbit coupling. This includes (i) band crossings protected by conventional nonsymmorphic symmetries, whose partial translation is within the invariant space of the mirror/rotation symmetry; and (ii) band crossings protected by off-centered mirror/rotation symmetries, whose partial translation is orthogonal to the invariant space. Our analysis is based on (i) the algebraic relations obeyed by the symmetry operators and (ii) the compatibility relations between irreducible representations at different high-symmetry points of the Brillouin zone. We identify a number of existing materials where these nonsymmorphic nodal lines are realized. Based on these example materials, we examine the surface states that are associated with the topological band crossings. Implications for experiments and device applications are briefly discussed.
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