Topological quantum chemistry and symmetry-based indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy (
). We report the implementation of a ...publicly accessible catalog of stable and fragile topology in all of the bands both at and away from
in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations, which represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, have enabled the discovery of repeat-topological and supertopological materials, including rhombohedral bismuth and Bi
Mg
. We find that 52.65% of all materials are topological at
, roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topology, and 87.99% of all materials contain at least one stable or fragile topological band.
Abstract
When electric conductors differ from their mirror image, unusual chiral transport coefficients appear that are forbidden in achiral metals, such as a non-linear electric response known as ...electronic magnetochiral anisotropy (eMChA)
1–6
. Although chiral transport signatures are allowed by symmetry in many conductors without a centre of inversion, they reach appreciable levels only in rare cases in which an exceptionally strong chiral coupling to the itinerant electrons is present. So far, observations of chiral transport have been limited to materials in which the atomic positions strongly break mirror symmetries. Here, we report chiral transport in the centrosymmetric layered kagome metal CsV
3
Sb
5
observed via second-harmonic generation under an in-plane magnetic field. The eMChA signal becomes significant only at temperatures below
$${T}^{{\prime} }\approx $$
T
′
≈
35 K, deep within the charge-ordered state of CsV
3
Sb
5
(
T
CDW
≈ 94 K). This temperature dependence reveals a direct correspondence between electronic chirality, unidirectional charge order
7
and spontaneous time-reversal symmetry breaking due to putative orbital loop currents
8–10
. We show that the chirality is set by the out-of-plane field component and that a transition from left- to right-handed transport can be induced by changing the field sign. CsV
3
Sb
5
is the first material in which strong chiral transport can be controlled and switched by small magnetic field changes, in stark contrast to structurally chiral materials, which is a prerequisite for applications in chiral electronics.
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk but conducting surface states that are topologically protected by time-reversal (or spatial) symmetries. ...We extend the notion of three-dimensional topological insulators to systems that host no gapless surface states but exhibit topologically protected gapless hinge states. Their topological character is protected by spatiotemporal symmetries of which we present two cases: (i) Chiral higher-order topological insulators protected by the combination of time-reversal and a fourfold rotation symmetry. Their hinge states are chiral modes, and the bulk topology is
-classified. (ii) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs, and the bulk topology is
-classified. We provide the topological invariants for both cases. Furthermore, we show that SnTe as well as surface-modified Bi
TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.
A very high Chern number
Topologically nontrivial electronic structure can often be characterized by the Chern number, the value of which is related to the magnitude of some of the exotic effects ...predicted to occur in such systems. Many topological phases discovered so far have a Chern number of 1 or 2, but higher values are also theoretically possible. Schröter
et al.
predicted that the chiral material palladium gallium (PdGa) would have a Chern number of 4, and they confirmed that prediction using photoemission experiments. Interestingly, the sign of the Chern number was opposite for the two enantiomers of PdGa.
Science
, this issue p.
179
Angle-resolved photoemission indicates that chiral crystalline PdGa has a Chern number of 4.
Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (
C
). Nodal band crossings with linear dispersion are expected to have at most
|
C
|
=
4
, which sets an upper limit to the magnitude of many topological phenomena in these materials. Here, we show that the chiral crystal palladium gallium (PdGa) displays multifold band crossings, which are connected by exactly four surface Fermi arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.
Magnetic interactions in combination with nontrivial band structures can give rise to several exotic physical properties such as a large anomalous Hall effect, the anomalous Nernst effect, and the ...topological Hall effect (THE). Antiferromagnetic (AFM) materials exhibit the THE due to the presence of nontrivial spin structures. EuCuAs crystallizes in a hexagonal structure with an AFM ground state (Néel temperature ∼ 16 K). In this work, we observe a large topological Hall resistivity of ∼7.4 μΩ-cm at 13 K which is significantly higher than the giant topological Hall effect of Gd2PdSi3 (∼3 μΩ-cm). Neutron diffraction experiments reveal that the spins form a transverse conical structure during the metamagnetic transition, resulting in the large THE. In addition, by controlling the magnetic ordering structure of EuCuAs with an external magnetic field, several fascinating topological states such as Dirac and Weyl semimetals have been revealed. These results suggest the possibility of spintronic devices based on antiferromagnets with tailored noncoplanar spin configurations.
Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline ...insulators (TCIs) and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures — including the theory of topological quantum chemistry (TQC) — researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85 per cent of the known stoichiometric materials host energetically isolated topological bands, and just under two-thirds of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.Solid-state materials have emerged as a platform for probing and manipulating topological phases of matter. This Review surveys topological materials discovery in nonmagnetic crystalline solids, focusing on the role of crystal symmetry and geometry in topological material predictions.
Time Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite ...the numerous demonstrations of 2D topological phases, few examples of 3D topological systems with TRS breaking exist. In this article, we devise a general strategy to design 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRS broken environment with orientable and arbitrarily large Chern vectors. The designs display topologically protected chiral and unidirectional surface states with disjoint equifrequency loops. The resulting crystals present the following characteristics: First, by increasing the Chern number, multiple surface states channels can be supported. Second, the Chern vector can be oriented along any direction simply changing the magnetization axis, opening up larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, by lowering the TRS breaking requirements, the system is ideal for realistic photonic applications where the magnetic response is weak.
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological ...crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.
Efficient and versatile spin-to-charge current conversion is crucial for the development of spintronic applications, which strongly rely on the ability to electrically generate and detect spin ...currents. In this context, the spin Hall effect has been widely studied in heavy metals with strong spin–orbit coupling. While the high crystal symmetry in these materials limits the conversion to the orthogonal configuration, unusual configurations are expected in low-symmetry transition-metal dichalcogenide semimetals, which could add flexibility to the electrical injection and detection of pure spin currents. Here, we report the observation of spin-to-charge conversion in MoTe2 flakes, which are stacked in graphene lateral spin valves. We detect two distinct contributions arising from the conversion of two different spin orientations. In addition to the conventional conversion where the spin polarization is orthogonal to the charge current, we also detect a conversion where the spin polarization and the charge current are parallel. Both contributions, which could arise either from bulk spin Hall effect or surface Edelstein effect, show large efficiencies comparable to the best spin Hall metals and topological insulators. Our finding enables the simultaneous conversion of spin currents with any in-plane spin polarization in one single experimental configuration.
A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The ...double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin‐dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single‐ and double‐valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPG and REPRESENTATIONS DSG). The tool DCOMPREL provides compatibility relations between the irreducible representations of double space groups at different k vectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The program DSITESYM implements the so‐called site‐symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description of and the search for topological insulators.
A new section of computer tools devoted to the double crystallographic groups has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The section includes databases of symmetry operations and irreducible representations of the double point and space groups and programs that compute the compatibility relations, generate relevant information related to the site‐symmetry approach, and calculate band representations and elementary band representations induced from any Wyckoff position of any double space group.
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