Strong Topological Insulator Research Articles

A weak topological insulator state in quasi-one-dimensional bismuth iodide.

The major breakthroughs in understanding of topological materials over the past decade were all triggered by the discovery of the Z2-type topological insulator-a type of material that is insulating in its interior but allows electron flow on its surface. In three dimensions, a topological insulator is classified as either 'strong' or 'weak'1,2, and experimental confirmations of the strong topological insulator rapidly followed theoretical predictions3-5. By contrast, the weak topological insulator (WTI) has so far eluded experimental verification, because the topological surface states emerge only on particular side surfaces, which are typically undetectable in real three-dimensional crystals6-10. Here we provide experimental evidence for the WTI state in a bismuth iodide, β-Bi4I4. Notably, the crystal has naturally cleavable top and side planes-stacked via van der Waals forces-which have long been desirable for the experimental realization of the WTI state11,12. As a definitive signature of this state, we find a quasi-one-dimensional Dirac topological surface state at the side surface (the (100) plane), while the top surface (the (001) plane) is topologically dark with an absence of topological surface states. We also find that a crystal transition from the β-phase to the α-phase drives a topological phase transition from a nontrivial WTI to a normal insulator at roughly room temperature. The weak topological phase-viewed as quantum spin Hall insulators stacked three-dimensionally13,14-will lay a foundation for technology that benefits from highly directional, dense spin currents that are protected against backscattering.

Emergence of Topological insulator and Nodal line semi-metal states in XX\u2032Bi (X\u2009=\u2009Na, K, Rb, Cs; X\u2032\u2009=\u2009Ca, Sr)

In this article, we predict the emergence of non-trivial band topology in the family of XX′Bi compounds having Poverline{6}2m (# 189) space group. Using first principles calculations within hybrid functional framework, we demonstrate that NaSrBi and NaCaBi are strong topological insulator under controlled band engineering. Here, we propose three different ways to engineer the band topology to get a non-trivial order: (i) hydrostatic pressure, (ii) biaxial strain (due to epitaxial mismatch), and (iii) doping. Non-triviality is confirmed by investigating bulk band inversion, topological Z2 invariant, surface dispersion and spin texture. Interestingly, some of these compounds also show a three dimensional topological nodal line semi-metal (NLS) state in the absence of spin orbit coupling (SOC). In these NLS phases, the closed loop of band degeneracy in the Brillouin zone lie close to the Fermi level. Moreover, a drumhead like flat surface state is observed on projecting the bulk state on the [001] surface. The inclusion of SOC opens up a small band gap making them behave like a topological insulator.

Quantum fluctuation in thermopower at the topological phase transition in CaSrX (X: Si, Ge, Sn, Pb) studied from first principles theory

The present density functional calculations propose the compounds CaSrX (X: Si, Ge, Sn, Pb) as strong topological insulators, with appreciable thermoelectric properties. Emergence of Dirac semi-metallic states has been observed in CaSrX (X: Si, Ge, Sn, Pb), which is induced by uni-axial strain along ‘b’ axis. CaSrSi and CaSrGe evolved as normal semiconductors with uni-axial strain. The trivial and non-trivial topological phases are evaluated by band inversion and Z2 topological invariants. A comprehensive analysis of thermopower, electrical conductivity scaled by relaxation time at these Dirac semi-metallic states exposes the highly oscillating behaviour, which gives insight to quantum oscillations driven by uni-axial strain. Further the thermoelectric properties at strong topological insulating states and normal insulating states have been summarized, which reveals the potential thermoelectric properties of these materials.

Angle resolved photoemission spectroscopy studies on three dimensional strong topological insulators and magnetic topological insulators

<sec> The discovery of topological materials – condensed matter systems that have nontrivial topological invariants – marked the commencement of a new era in condensed matter physics and materials science. Three dimensional topological insulators (3D TIs) are one of the first discovered and the most studied among all topological materials. The bulk material of the TIs have the characteristics of the insulator, having a complete energy gap. Their surface electronic states, on the other hand, have the characteristics of a conductor, with energy band passes continuously through the Fermi surface. The conductivity of this topological surface state (TSS) is protected by the time reversal symmetry of the bulk material. The TSS is highly spin-polarized and form a special spin-helical configuration that allows electrons with specific spin to migrate only in a specific direction on the surface. By this means, surface electrons in TIs can " bypass” the influence of local impurities, achieving a lossless transmission of spin-polarized current. The existence of TIs directly leads to a variety of novel transport, magnetic, electrical, and optical phenomena, such as non-local quantum transport, quantum spin Hall effect, etc., promising wide application prospects. Recently, several research groups have searched all 230 non-magnetic crystal space groups, exhausting all the found or undiscovered strong/weak TIs, topological crystalline insulators (TCI), and topological semimetals. This series of work marks that theoretical understanding of non-magnetic topological materials has gone through a period of one-by-one prediction and verification, and entered the stage of the large-area material screening and optimization.</sec><sec> Parallel to non-magnetic TIs, magnetic topological materials constructed by ferromagnetic or antiferromagnetic long range orders in topological systems have always been an important direction attracting theoretical and experimental efforts. In magnetic TIs, the lack of time reversal symmetry brings about new physical phenomena. For example, when a ferromagnetic order is introduced into a three-dimensional TI, the Dirac TSS that originally intersected at one point will open a magnetic gap. When the Fermi surface is placed just in the gap, the quantum anomalous Hall effect can be implemented. At present, the research on magnetic topology systems is still in the ascendant. It is foreseeable that these systems will be the main focus and breakthrough point of topology material research in the next few years. </sec><sec> Angle-resolved photoemission spectroscopy (ARPES) is one of the most successful experimental methods of solid state physics. Its unique <i>k</i>-space-resolved single-electron detection capability and simple and easy-to-read data format make it a popular choice for both theoretists and experimentalists. In the field of topological materials, ARPES has always been an important experimetnal technique. It is able to directly observe the bulk and surface band structure of crystalline materials, and in a very intuitive way. With ARPES, it is incontrovertible to conclude whether a material is topological, and which type of topological material it belongs to.</sec><sec> This paper reviews the progress of ARPES research on TIs since 2008, focusing on the experimental energy band characteristics of each series of TIs and the general method of using ARPES to study this series of materials. Due to space limitations, this paper only discusses the research progress of ARPES for strong 3D TIs (focusing on the Bi<sub>2</sub>Se<sub>3</sub> series) and magnetic TIs (focusing on the MnBi<sub>2</sub>Te<sub>4</sub> series). Researches involving TCIs, topological Kondo insulators, weak 3D TIs, topological superconductors and heterostructures based on topological insulators will not be discussed. This paper assumes that the reader has the basic knowledge of ARPES, so the basic principles and system components of ARPES are not discussed.</sec>

Magnetic and topological transitions in three-dimensional topological Kondo insulator☆☆Supported by the National Natural Science Foundation of China under Grant Nos 11764010, 11504061, 11564008, 11704084, and 11704166, the Natural Science Foundation of Guangxi Province under Grant Nos 2017GXNSFAA198169 and 2017GXNSFBA198115, and the SPC-Lab Research Fund under Grant No XKFZ201605.

Using an extended slave-boson method, we draw a global phase diagram summarizing both magnetic phases and paramagnetic (PM) topological insulators (TIs) in a three-dimensional topological Kondo insulator (TKI). By including electron hopping (EH) up to the third neighbors, we identify four strong TI (STI) phases and two weak TI (WTI) phases. Then, the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH, f-electron energy level, and hybridization constant. We also find an insulator–metal transition from an STI phase that has surface Fermi rings and spin textures in qualitative agreement with the TKI candidate SmB6. In the weak hybridization regime, antiferromagnetic (AF) order naturally arises in the phase diagrams. Depending on how the magnetic boundary crosses the PM topological transition lines, AF phases are classified into the AF topological insulator (AFTI) and the non-topological AF insulator, according to their indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTIs showing distinguishable surface dispersions around their Dirac points.

Experimental observation of conductive edge states in weak topological insulator candidate HfTe5

The quantum spin Hall (QSH) effect is widely studied as a novel quantum state in condensed matter physics over the past decade. Recently, it is predicted that the transition metal pentatelluride XTe5 (X = Zr, Hf) has a large bandgap in its bulk form and a single layer of XTe5 is a QSH insulator candidate. However, the topological nature of the bulk material is still under debate because it is located close to the phase boundary of a strong topological insulator and a weak topological insulator (WTI). Here, using angle-resolved photoemission spectroscopy and scanning tunneling microscopy (STM)/scanning tunneling spectroscopy, we systematically studied the electronic structures of bulk HfTe5. Both the large bulk bandgaps and conductive edge states in the vicinity of the step edges in HfTe5 were observed, strongly suggesting a WTI phase in bulk HfTe5. Moreover, our STM experiment for the first time reveals the bulk band bending due to the broken symmetry near the step edge, making it an ideal platform for studying the development of edge states in the WTI and QSH insulator.

Fractional Angular Momentum at Topological Insulator Interfaces.

Recently, two fundamental topological properties of a magnetic vortex at the interface of a superconductor (SC) and a strong topological insulator (TI) have been established: The vortex carries both a Majorana zero mode relevant for topological quantum computation and, for a time-reversal invariant TI, acharge of e/4. This fractional charge is caused by the axion term in the electromagnetic Lagrangian of the TI. Here we determine the angular momentum J of the vortices, which in turn determines their mutual statistics. Solving the axion-London electrodynamic equations including screening in both a SC and a TI, we find that the elementary quantum of angular momentum of the vortex is -n^{2}ℏ/8, where n is the flux quantum of the vortex line. Exchanging two elementary fluxes thus changes the phase of the wave function by -π/4.

Classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator

Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a -classification formula for these states. By calculating the index, the antiferromagnetic insulating states are classified into AFTI or non-topological antiferromagnetic insulator (nAFI) in different parameter regions. On the antiferromagnetic surfaces in AFTI, we find topologically protected gapless Dirac cones inside the bulk gap, leading to metallic Fermi rings exhibiting helical spin texture with weak spin-momentum locking. Depending on model parameters, the magnetic transitions take place either between AFTI and strong topological insulator, or between nAFI and weak topological insulator. By varying some model parameters, we find a topological transition between AFTI and nAFI, driving by closing of bulk gap. Our work may account for the pressure-induced magnetism in TKI compound SmB6, and helps to explore richer AFTI phases in heavy-fermion systems as well as in other strong-correlated systems.

Topological phases in the TaSe3 compound

Based on first-principles calculations, we show that stoichiometric TaSe3, synthesized in space group P21/m, belongs to a three-dimensional (3D) strong topological insulator (TI) phase with Z2 invariants (1;100). The calculated surface spectrum shows clearly a single Dirac cone on surfaces, with helical spin texture at a constant energy contour. To check the stability of the topological phase, strain effects have been systematically investigated, showing that many topological phases survive in a wide range of the strains along both the a- and c-axes, such as strong TI (STI), weak TI (WTI) and Dirac semimetal phases. TaSe3 provides us an ideal platform for experimental study of topological phase transitions. More interestingly, since superconductivity in TaSe3 has been reported for a long time, the co-existence of topological phases and superconducting phase suggests that TaSe3 is a realistic system to study the interplay between topological and superconducting phases in the future.

Giant planar Hall effect in the Dirac semimetal ZrTe5−δ

Recently, giant planar Hall effect originating from chiral anomaly has been predicted in nonmagnetic Dirac/Weyl semimetals. ZrTe5 is considered to be an intriguing Dirac semimetal at the boundary of weak topological insulators and strong topological insulators, though this claim still remains controversial. Here, we report the observation in ZrTe5 of the giant planar Hall resistivity that shows two different magnetic-field dependences as predicted by theory and a maximum at the Lifshitz transition temperature. We found that the giant planar Hall resistivity fades out with decreasing the thickness of ZrTe5 nanoplates, which may be ascribed to the vanishing of the 3D nature of the samples. In addition, we have observed a nontrivial Berry phase, chiral-anomaly-induced negative longitudinal magnetoresistance, and a giant in-plane anisotropic magnetoresistance in these ZrTe5 nanoplates. All the experimental observations demonstrated coherently that ZrTe5 is a Dirac semimetal.

Quantum transport in a compensated semimetal W2As3 with nontrivial Z2 indices

We report a topological semimetal W2As3 with a space group C2/m. Based on the first-principles calculations, band crossings are partially gapped when spin-orbit coupling is included. The Z2 indices at the electron filling are [1;111], characterizing a strong topological insulator and topological surface states. From the magnetotransport measurements, nearly quadratic field dependence of magnetoresistance (MR) (B || [200]) at 3 K indicates an electron-hole compensated compound whose longitudinal MR reaches 115 at 3 K and 15 T. In addition, multiband features are detected from the high-magnetic-field Shubnikov-de Haas (SdH) oscillation, Hall resistivity, and band calculations. A nontrivial pi Berry's phase is obtained, suggesting the topological feature of this material. A two- band model can fit well the conductivity and Hall coefficient. Our experiments manifest that the transport properties of W2As3 are in good agreement with the theoretical calculations.

Towards microscopic control of the magnetic exchange coupling at the surface of a topological insulator

Magnetically doped topological insulators may produce novel states of electronic matter, where for instance the quantum anomalous Hall effect state can be realized. Pivotal to this goal is a microscopic control over the magnetic state, defined by the local electronic structure of the dopants and their interactions. We report on the magnetic coupling among Mn or Co atoms adsorbed on the surface of the topological insulator Bi2Te3. Our findings uncover the mechanisms of the exchange coupling between magnetic atoms coupled to the topological surface state in strong topological insulators. The combination of x-ray magnetic circular dichroism and ab initio calculations reveals that the sign of the magnetic coupling at short adatom–adatom distances is opposite for Mn with respect to Co. For both elements, the magnetic exchange reverses its sign at a critical distance between magnetic adatoms, as a result of the interplay between superexchange, double exchange and Ruderman–Kittel–Kasuya–Yoshida interactions.

Topological semimetals and insulators in three-dimensional honeycomb materials

Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combination of time-reversal and inversion symmetries and are accompanied by topologically protected "drumhead" surface states. In the bulk, these nodal line systems exhibit Landau level quantization and flat bands upon applying a magnetic field. In the presence of spin-orbit coupling, these topological semimetals are found to generically form (strong) topological insulators. This comprehensive classification of the electronic band structures of three-dimensional honeycomb systems might serve as guidance for future material synthesis.

Distinct multiple fermionic states in a single topological metal

Among the quantum materials that have recently gained interest are the topological insulators, wherein symmetry-protected surface states cross in reciprocal space, and the Dirac nodal-line semimetals, where bulk bands touch along a line in k-space. However, the existence of multiple fermion phases in a single material has not been verified yet. Using angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations, we systematically study the metallic material Hf2Te2P and discover properties, which are unique in a single topological quantum material. We experimentally observe weak topological insulator surface states and our calculations suggest additional strong topological insulator surface states. Our first-principles calculations reveal a one-dimensional Dirac crossing—the surface Dirac-node arc—along a high-symmetry direction which is confirmed by our ARPES measurements. This novel state originates from the surface bands of a weak topological insulator and is therefore distinct from the well-known Fermi arcs in semimetals.

Interaction approach to anomalous spin texture in warped topological insulators

Interactions between the surface and the bulk in a strong topological insulator (TI) cause a finite lifetime of the topological surface states (TSS) as shown by the recent experiments. On the other hand, interactions also induce unitary processes, which, in the presence of anisotropy and the spin-orbit coupling (SOC), can induce non-trivial effects on the spin texture. Recently, such effects were observed experimentally in the $Bi_2X_3$ family, raising the question that the hexagonal warping (HW) may be linked with new spin-related anomalies. The most remarkable among which is the 6-fold periodic canting of the in-plane spin vector. Here, we show that, this anomaly is the result of a {\it triple cooperation between the interactions, the SOC and the HW}. To demonstrate it, we formulate the spin-off-diagonal self energy. A unitary phase with an even symmetry develops in the latter and modulates the spin-1/2 vortex when the Fermi surface is anisotropic. When the anisotropy is provided by the HW, a 6-fold in-plane spin-canting is observed. Our theory suggests that the spin-canting anomaly in $Bi_2X_3$ is a strong evidence of the interactions. High precision analysis of the spin-texture is a promising support for further understanding of the interactions in TIs.

Experimental and theoretical study of topology and electronic correlations in PuB4

We synthesize single crystals of ${\mathrm{PuB}}_{4}$ using an Al-flux technique. Single-crystal diffraction data provide structural parameters for first-principles density functional theory (DFT) calculations. By computing the density of states, the ${Z}_{2}$ topological invariant using the Wilson loop method, and the surface electronic structure from slab calculations, we find that ${\mathrm{PuB}}_{4}$ is a nonmagnetic strong topological insulator with a band gap of 254 meV. Our magnetic susceptibility, heat capacity, and resistivity measurements are consistent with this analysis, albeit with a smaller gap of 35 meV. DFT plus dynamical mean-field theory calculations show that electronic correlations reduce the size of the band gap, and provide better agreement with the value determined by resistivity. These results demonstrate that ${\mathrm{PuB}}_{4}$ is a promising actinide material to investigate the interplay of electronic correlations and nontrivial topology.

Multiple topological electronic phases in superconductor MoC

The search for a superconductor with non-s-wave pairing is important not only for understanding unconventional mechanisms of superconductivity but also for finding new types of quasiparticles such as Majorana bound states. Materials with both topological band structure and superconductivity are promising candidates as $p+ip$ superconducting states can be generated through pairing the spin-polarized topological surface states. In this work, the electronic and phonon properties of the superconductor molybdenum carbide (MoC) are studied with first-principles methods. Our calculations show that nontrivial band topology and superconductivity coexist in both structural phases of MoC, namely, the cubic $\alpha$ and hexagonal $\gamma$ phases. The $\alpha$ phase is a strong topological insulator and the $\gamma$ phase is a topological nodal line semimetal with drumhead surface states. In addition, hole doping can stabilize the crystal structure of the $\alpha$ phase and elevate the transition temperature in the $\gamma$ phase. Therefore, MoC in different structural forms can be a practical material platform for studying topological superconductivity and elusive Majorana fermions.

Deformation and stability of surface states in Dirac semimetals

The unusual surface states of topological semimetals have attracted a lot of attention. Recently, we showed [PNAS 113, 8648 (2016)] that for a Dirac semimetal (DSM) arising from band-inversion, such as Na$_3$Bi and Cd$_3$As$_2$, the expected double Fermi arcs on the surface are not topologically protected. Quite generally, the arcs deform into states similar to those on the surface of a strong topological insulator. Here we address two questions related to deformation and stability of surface states in DSMs. First, we discuss why certain perturbations, no matter how large, are unable to destroy the double Fermi arcs. We show that this is related to certain extra (particle-hole) symmetry, which is non-generic in materials. Second, we discuss situations in which the surface states are completely destroyed without breaking any symmetry or impacting the bulk Dirac nodes. We are not aware of any experimental or density functional theory (DFT) candidates for a material which is a bulk DSM without any surface states, but our results clearly show that this is possible.

Shubnikov–de Haas oscillations in bulk ZrTe5 single crystals: Evidence for a weak topological insulator

The study of $\mathrm{ZrT}{\mathrm{e}}_{5}$ crystals is revived because of the recent theoretical prediction of topological phase in bulk $\mathrm{ZrT}{\mathrm{e}}_{5}$. However, the current conclusions for the topological character of bulk $\mathrm{ZrT}{\mathrm{e}}_{5}$ are quite contradictory. To resolve this puzzle, we here identify the Berry phase on both $b$- and $c$ planes of high-quality $\mathrm{ZrT}{\mathrm{e}}_{5}$ crystals by the Shubnikov--de-Hass (SdH) oscillation under tilted magnetic field at 2 K. The angle-dependent SdH oscillation frequency, both on $b$- and $c$ planes of $\mathrm{ZrT}{\mathrm{e}}_{5}$, demonstrates the two-dimensional feature. However, phase analysis of SdH verifies that a nontrivial \ensuremath{\pi}-Berry phase is observed in the $c$-plane SdH oscillation, but not in the $b$-plane one. Compared to bulk Fermi surface predicted by the first-principle calculation, the two-dimensional-like behavior of SdH oscillation measured at $b$ plane comes from the bulk electron. Based on these analyses, it is suggested that bulk $\mathrm{ZrT}{\mathrm{e}}_{5}$ at low temperature (\ensuremath{\sim}2 K) belongs to a weak topological insulator, rather than Dirac semimetal or strong topological insulator as reported previously.

Saddle-like topological surface states on the TT′X family of compounds ( T, T′ = Transition metal, X=Si , Ge)

Topological nodal-line semimetals are exotic conductors that host symmetry-protected conducting nodal-lines in their bulk electronic spectrum and nontrivial drumhead states on the surface. Based on first-principles calculations and an effective model analysis, we identify the presence of topological nodal-line semimetal states in the TT'X family of compounds (T, T' = transition metal, X= Si, or Ge) in the absence of spin-orbit coupling (SOC). Taking ZrPtGe as an exemplar system, we show that this material harbors a single nodal line on the $k_y=0$ plane, which is protected by the $M_y$ mirror plane symmetry. Surface electronic structure calculations further reveal the existence of a drumhead surface state nested inside the nodal line projection on the (010) surface with a saddle-like energy dispersion. When the SOC is included, the nodal line gaps out and the system transitions to a strong topological insulator state with $Z_2=(1;000)$. The topological surface state evolves from the drumhead surface state via the sharing of its saddle-like energy dispersion within the bulk energy gap. These features differ remarkably from those of the currently known topological surface states in topological insulators such as Bi$_2$Se$_3$ with Dirac-cone-like energy dispersions.