Recently, intrinsic antiferromagnetic topological insulator MnBi2Te4 has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi2Te4. However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 meV, which vanishes as the sample becomes paramagnetic with increasing temperature. The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy. Combining these results, the magnetism-induced gap in topological surface states of MnBi2Te4 is revealed.
Identification and control of topological phases in topological thin films offer great opportunity for fundamental research and the fabrication of topology-based devices. Here, combining molecular beam epitaxy, angle-resolved photoemission spectroscopy and ab-initio calculations, we investigate the electronic structure evolution in (Bi1-xInx)2Se3 films with thickness from 2 to 13 quintuple layers. We identify several phases with their characteristic topological nature and evolution between them, i.e., dimensional crossover from a three-dimensional topological insulator with gapless surface sta…
Since the advent of topological insulators hosting symmetry-protected Dirac surface states, efforts have been made to gap these states in a controllable way. A new route to accomplish this was opened up by the discovery of topological crystalline insulators (TCIs) where the topological states are protected by real space crystal symmetries and thus prone to gap formation by structural changes of the lattice. Here, we show for the first time a temperature-driven gap opening in Dirac surface states within the TCI phase in (Pb,Sn)Se. By using angle-resolved photoelectron spectroscopy, the gap form…
The studies of topological insulators and topological semimetals have been at frontiers of condensed matter physics and material science. Both classes of materials are characterized by robust surface states created by the topology of the bulk band structures and exhibit exotic transport properties. When magnetism is present in topological materials and breaks the time-reversal symmetry, more exotic quantum phenomena can be generated, e.g. quantum anomalous Hall effect, axion insulator, large intrinsic anomalous Hall effect, etc. In this research update, we briefly summarize the recent research…
Based on density functional theory (DFT), we investigate the electronic properties of bulk and single-layer ZrTe$_4$Se. The band structure of bulk ZrTe$_4$Se can produce a semimetal-to-topological insulator (TI) phase transition under uniaxial strain. The maximum global band gap is 0.189 eV at the 7\% tensile strain. Meanwhile, the Z$_2$ invariants (0; 110) demonstrate conclusively it is a weak topological insulator (WTI). The two Dirac cones for the (001) surface further confirm the nontrivial topological nature. The single-layer ZrTe$_4$Se is a quantum spin Hall (QSH) insulator with a band g…
In a magnetic topological insulator, nontrivial band topology conspires with magnetic order to produce exotic states of matter that are best exemplified by quantum anomalous Hall (QAH) insulators and axion insulators. Up till now, such magnetic topological insulators are obtained by doping topological insulators with magnetic atoms. The random magnetic dopants, however, inevitably introduce disorders that hinder further exploration of quantum effects in the material. Here, we resolve this dilemma by probing quantum transport in MnBi$_2$Te$_4$ thin flake - a topological insulator with intrinsic…
Helical edge modes are characteristic of topological insulators in two dimensions. This paper demonstrates that helical edge modes remain across transitions to ordinary insulators or to semimetals under certain condition. Straight and zigzag edges are considered in a tight-binding model on square lattice. We focus on the case of indirect gap in bulk topological insulators, and obtain the spectrum of edge modes on both sides of transitions. For straight edge, the helical edge mode in topological insulators with strong particle-hole asymmetry has a reentrant region in momentum space. Edge modes …
To realize novel topological phases and to pursue potential applications in low-energy consumption spintronics, the study of magnetic topological materials is of great interest. Starting from the theory of nonmagnetic topological quantum chemistry [Bradlyn et al., Nature 547, 298 (2017)], we have obtained irreducible (co)representations and compatibility relations (CRs) in momentum space, and we constructed a complete list of magnetic band (co)representations (MBRs) in real space for other MSGs with anti-unitary symmetries (i.e. type-III and type-IV MSGs). The results are consistent with the m…
The magnetic proximity effect is a fundamental feature of heterostructures composed of layers of topological insulators and magnetic materials since it underlies many potential applications in devices with novel quantum functionality. Within density functional theory we study magnetic proximity effect at the 3D topological insulator/magnetic insulator (TI/MI) interface in Bi$_2$Se$_3$/MnSe(111) system as an example. We demonstrate that a gapped ordinary bound state which spectrum depends on the interface potential arises in the immediate region of the interface. The gapped topological Dirac st…
It is shown that, contrary to the naive expectation, single particle spectral gaps can be opened on the surface states of three dimensional topological insulators by using commensurate out- and in-plane antiferromagnetic or ferrimagnetic insulating thin films.
We have performed angle-resolved photoemission spectroscopy on (PbSe)5(Bi2Se3)3m, which forms a natural multilayer heterostructure consisting of a topological insulator (TI) and an ordinary insulator. For m = 2, we observed a gapped Dirac-cone state within the bulk-band gap, suggesting that the topological interface states are effectively encapsulated by block layers; furthermore, it was found that the quantum confinement effect of the band dispersions of Bi2Se3 layers enhances the effective bulk-band gap to 0.5 eV, the largest ever observed in TIs. In addition, we found that the system is no …
We study a general problem how the gap in a nonmagnetic band insulator closes by tuning a parameter. We review our recent results on the classification of all the possible gap closing in two and three dimensions. We show that they accompany the change of Z_2 topological numbers, and that the gap closings correspond to phase transitions between the quantum spin Hall and the insulator phases. Interestingly, in inversion-asymmetric three-dimensional systems there appears a gapless phase between the quantum spin Hall and insulator phases. This gapless phase is due to a topological nature of gap-cl…
Non-trivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one and two-dimensional topological superconductors. Here, we generate such representations with topologically protected domain-wall modes in a classical analogue of the Kitaev superconducting chain, with a particle-hole like symmetry and a Z2 topological invariant. The mid-gap modes are found to exhibit distinct fusion channels and rich non-Abelian braiding properties, which are investigated using a T-junction setup. We employ the adiabatic theorem to explicitly calculate the br…
The recent discovery of antiferromagnetic (AFM) topological insulator (TI) MnBi$_2$Te$_4$ has triggered great research efforts on exploring novel magnetic topological physics. Based on first-principles calculations, we find that the manipulation of magnetic orientation and order not only significantly affects material symmetries and orbital hybridizations, but also results in variant new magnetic topological phases in MnBi$_2$Te$_4$. We thus predict a series of unusual topological quantum phase transitions that are magnetically controllable in the material, including phase transitions from AFM…
Functional manipulation of graphene is an important topic in view of both fundamental researches and practical applications. In this study, we show that intercalation of 5$d$ transition metals in epitaxial graphene on SiC is a promising approach to realize topologically nontrivial phases with a finite band gap in graphene. Using first-principles calculations based on density functional theory, we show that the Re- and Ta-intercalated graphene become two-dimensional topological insulators which exhibit linear Dirac cones and quadratic bands with topological band gaps, respectively. The appearan…
Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond the conventional topological paradigms. Here, we discover experimentally that the nonsymmorphic $p4g$ acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, while the second band gap exhibits quadrupole topology with anomalous Wannier…
We propose new two-dimensional (2D) topological insulators (TIs) in functionalized germanenes (GeX, X=H, F, Cl, Br or I) using first-principles calculations. We find GeI is a 2D TI with a bulk gap of about 0.3 eV, while GeH, GeF, GeCl and GeBr can be transformed into TIs with sizeable gaps under achievable tensile strains. A unique mechanism is revealed to be responsible for large topologically-nontrivial gap obtained: owing to the functionalization, the $σ$ orbitals with stronger spin-orbit coupling (SOC) dominate the states around the Fermi level, instead of original $π$ orbitals with weaker…
In intrinsic magnetic topological insulators, Dirac surface state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here we use molecular beam epitaxy to grow intrinsic MnBi2Te4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that in high defect regions, the Dirac m…
The bosonic analogues of topological insulators have been proposed in numerous theoretical works, but their experimental realization is still very rare, especially for spin systems. Recently, two-dimensional (2D) honeycomb van der Waals (vdW) ferromagnets have emerged as a new platform for topological spin excitations. Here, via a comprehensive inelastic neutron scattering study and theoretical analysis of the spin-wave excitations, we report the realization of topological magnon insulators in CrXTe$_3$ (X=Si, Ge) compounds. The nontrivial nature and intrinsic tunability of the gap opening at …
Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states to be generated, including the quantum anomalous Hall effect (QAHE) and axion insulator states. Magnetic doping and magnetic proximity are viewed as being useful means of exploring the interaction between topology and magnetism. However, the inhomogeneity of magnetic doping leads to complicated magnetic ordering and small exchange gaps, and consequently the …
The magnetoelectric effect predicted in topological insulators makes heterostructures that combine magnetic materials and such insulators promising candidates for spintronics applications. Here, we theoretically consider a setup that exhibits two well-separated interfaces between a topological insulator and a ferromagnetic insulator. We show that there is a topological magnetic dipole-dipole interaction stemming from long-range Coulomb interactions. We analytically derive the magnetization dynamics at the two interfaces and discuss how the long-range coupling can be applied to non-locally indu…
Using Landau level spectroscopy, we determine the temperature dependence of the energy band gap in zirconium pentatelluride (ZrTe$_5$). We find that the band gap reaches $E_g=(5 \pm 1)$ meV at low temperatures and increases monotonously when the temperature is raised. This implies that ZrTe$_5$ is a weak topological insulator, with non-inverted ordering of electronic bands in the center of the Brillouin zone. Our magneto-transport experiments performed in parallel show that the resistivity anomaly in ZrTe$_5$ is not connected with the temperature dependence of the band gap.
The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in solid-state materials. Topological quantum chemistry has enabled the understanding of and the search for paramagnetic topological materials. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC), here we perform a high-throughput search for magnetic topological materials based on first-principles calculations. We use as our starting point the Magnetic Materials Database on th…
We report transport measurements of strained InAs/In$_{x}$Ga$_{1-x}$Sb composite quantum wells (CQWs) in the quantum spin Hall phase, focusing on the control of the energy gap through structural parameters and an external electric field. For highly strained CQWs with $x = 0.4$, we obtain a gap of 35 meV, an order of magnitude larger than that reported for binary InAs/GaSb CQWs. Using a dual-gate configuration, we demonstrate an electrical-field-driven topological phase transition, which manifests itself as a re-entrant behavior of the energy gap. The sizeable energy gap and high bulk resistivi…
The interplay between magnetism and non-trivial topology in magnetic topological insulators (MTI) is expected to give rise to a variety of exotic topological quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the topological axion states. A key to assessing these novel properties is to tune the Fermi level in the exchange gap of the Dirac surface band. MnBi$_2$Te$_4$ possesses non-trivial band topology with intrinsic antiferromagnetic (AFM) state that can enable all of these quantum states, however, highly electron-doped nature of the MnBi$_2$Te$_4$ crystals obstructs the e…
Surface magnetism and its correlation with the electronic structure are critical to understand the gapless topological surface state in the intrinsic magnetic topological insulator MnBi$_2$Te$_4$. Here, using static and time resolved angle-resolved photoemission spectroscopy (ARPES), we find a significant ARPES intensity change together with a gap opening on a Rashba-like conduction band. Comparison with a model simulation strongly indicates that the surface magnetism on cleaved MnBi$_2$Te$_4$ is the same as its bulk state. The coexistence of surface ferromagnetism and a gapless TSS uncovers t…
We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states. We obtain, by explicit and exhaustive construction, the topological classification of electronic band insulators that are magnetically ordered for each one of the 1421 magnetic space groups in three dimensions. We have also computed the symmetry-based indicators for each nontrivial class, and, by doing so, establish the complete mapping from symmetry repres…
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the topology of a gapped Hamiltonian is investigated from the viewpoint of its onsite/crystal symmetry. On the other hand, topological physics also appears in semimetals, whose gapless points can be characterized by topological invariants. Stimulated by this background, we shed light on the topology of nodal superconductors. In this paper, we review our modern top…
For topological magnon spectra, determining and explaining the presence of a gap at a magnon crossing point is a key to characterize the topological properties of the system. An inelastic neutron scattering study of a single crystal is a powerful experimental technique that is widely employed to probe the magnetic excitation spectra of topological materials. Here, we show that when the scattering intensity rapidly disperses in the vicinity of a crossing point, such as a Dirac point, the apparent topological gap size is extremely sensitive to experimental conditions including sample mosaic, res…
Gapped systems with glide symmetry can be characterized by a Z_2 topological invariant. We study the magnetic photonic crystal with a gap between the second and third lowest bands, which is characterized by the nontrivial glide-Z_2 topological invariant that can be determined by symmetry-based indicators. We show that under the space group No. 230 (Ia-3d), the topological invariant is equal to half of the number of photonic bands below the gap, and therefore, the band gap between the second and third lowest bands is always topologically nontrivial, and to realize the topological phase, we need…
The discovery of intrinsic magnetic topological order in $\rm MnBi_2Te_4$ has invigorated the search for materials with coexisting magnetic and topological phases. These multi-order quantum materials are expected to exhibit new topological phases that can be tuned with magnetic fields, but the search for such materials is stymied by difficulties in predicting magnetic structure and stability. Here, we compute over 27,000 unique magnetic orderings for over 3,000 transition metal oxides in the Materials Project database to determine their magnetic ground states and estimate their effective excha…
The superconductor PdTe$_2$ is known to host bulk Dirac bands and topological surface states. The coexistence of superconductivity and topological surface states makes PdTe$_2$ a promising platform for exploring topological superconductivity and Majorana bound states. In this work, we report the layer-by-layer molecular beam epitaxy growth and spectroscopic characterization of high quality PdTe$_2$ films with thickness down to 3 monolayers (ML). In the 3 ML PdTe$_2$ film, we observed spin-polarized surface resonance states, which are isolated from the bulk bands due to the quantum size effects…
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well known to possess a half quantum Hall effect. Furthermore, it has been known that the surface of a weak 3D topological insulator gapped by a charge density wave exhibits a half quantum spin Hall effect. To generalize these results to all Altland-Zirnbauer symmetry classes of topological insulators and superconductors, we reproduce the classification table for th…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected edge states in energy spectra in topological phases. Here we predict a new topological phase that emerges through closing a gap of bands constructed by energy bands, instead of through closing an energy gap with preserved symmetries. From this perspective, topological phases may arise from topological properties of the "bands of bands" associated with their gap…
