For the IV-VI semiconductor family we derive an exact relation between the microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl topological surface state wave function, thus obtaining a fully microscopic surface state. We find that the balance of spin-orbit interaction and crystal field in the bulk, and the band bending at the surface, can profoundly influence the surface state spin-momentum locking. As a manifestation of this we predict that the spin texture of the $M$-point Dirac cones of SnTe can be tuned through an unexpectedly rich sequence of spin textures -- warped helical with winding number $\pm 1$, $k_x$ linear, hyperbolic, and $k_y$ linear -- e.g. by tuning the band bending at the surface.
Deploying an analytical atomistic model of the bulk band structure of the IV-VI semiconductors we connect the spin structure of the topological surface state to the crystal field and spin orbit coupling parameters of the bulk material. While the Dirac-Weyl (or equivalently, Rashba) type topological surface state is often assumed universal, we show that the physics of the surface state is strikingly non-universal. To see this explicitly we calculate the RKKY interaction, which may be viewed as a probe of this surface state spin structure, finding its \emph{qualitative form} depends on the value…
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 …
In commonly employed models for 2D topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to consider this feature, the occurrence of gapless states, a result of the band inversion process under protection of the symmetries. Similarly, the band inversion process might even be perceived as necessary to induce 2D topological phase transitions. To clarify these misleading perspectives, we propose a simple model with a flexible Chern number to demonstrate that…
Weak topological insulators possess a symmetry related set of Dirac-Weyl cones in the surface Brillouin zone, implying misorientation between the principle axis of the low energy manifold of the bulk and the surface normal. We show that this feature of weak topological insulators comes with a hidden richness of surface spin textures, and that by misorientation a helical texture can become an unusual hyperbolic spin texture. We illustrate this effect by comparison of the $M$-point and $Γ$-point Dirac-Weyl cones on the (111) surface of the crystalline topological insulator SnTe.
The valley-Chern and spin-valley-Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which have the same Chern and spin-Chern numbers but different valley-Chern and spin-valley-Chern numbers. The edge state between them is topologically trivial in the tight-binding model but is shown to be as robust as the topological edge. We construct Y-junctions made of topological edges. They satisfy the topological Kirchhoff law, where the topological charges…
Seeking the criterion for diagnosing topological phases in real materials has been one of the major tasks in topological physics. Currently, bulk-boundary correspondence based on spectral measurements of in gap topological boundary states and the fractional corner anomaly derived from the measurement of the fractional spectral charge are two main approaches to characterize topologically insulating phases. However, these two methods require a complete band-gap with either in-gap states or strict spatial symmetry of the overall sample which significantly limits their applications to more general…
Magneto-optics based current imaging technique compares the nature of topological current distribution in a single crystal and thin film of topological insulator material, Bi2Se3. The single crystal, at low temperatures, has uniform topological surface current sheets which are about 3.6 nm thick. With increasing temperature, the current partially diverts into the crystal bulk and concomitantly, the sheet break up into a patchy network of high and low current density regions. The temperature dependence of the high current density areas shows that the surface to bulk transformation in the crysta…
Topological insulators are bulk semiconductors that manifest in-gap massless Dirac surface states due to the topological bulk-boundary correspondence principle [1-3]. These surface states have been a subject of tremendous ongoing interest, due both to their intrinsic properties and to higher order emergence phenomena that can be achieved by manipulating the interface environment [4-11]. Here, angle resolved photoemission (ARPES) spectromicroscopy and supplementary scanning tunneling microscopy (STM) are performed on the model topological insulator Bi2Se3 to investigate the interplay of crystal…
To date, spin generation in three-dimensional topological insulators is primarily modeled as a single-surface phenomenon, attributed to the momentum-spin locking on each individual surface. In this article we propose a mechanism of spin generation where the role of the insulating yet topologically non-trivial bulk becomes explicit: an external electric field creates a transverse pure spin current through the bulk of a three-dimensional topological insulator, which transports spins between the top and bottom surfaces. Under sufficiently high surface disorder, the spin relaxation time can be ext…
We demonstrate that the metallic topological surface states wrap on all sides the 3D topological crystalline insulator SnTe. This is achieved by studying oscillatory quantum magneto-transport and magnetization at tilted magnetic fields which enables us to observe simultaneous contributions from neighbouring sample sides. Taking into account pinning of the Fermi energy by the SnTe reservoir we successfully describe theoretically the de Haas-van Alphen oscillations of magnetization. The determined π-Berry phase of surface states confirms their Dirac fermion character. We independently observe os…
We report transport studies on a three dimensional, 70 nm thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semi-metallic HgTe, which thus becomes a three dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states.
Bulk boundary correspondence in topological materials allows to study their bulk topology through the investigation of their topological boundary modes. However, for classes that share similar boundary phenomenology, the growing diversity of topological phases may lead to ambiguity in the topological classification of materials. Such is the current status of bulk bismuth. While some theoretical models indicate that bismuth possesses a trivial topological nature, other theoretical and experimental studies suggest non-trivial topological classifications such as a strong or a higher order topolog…
High surface-mobility, which is attributable to topological protection, is a trademark of three-dimensional topological insulators (3DTIs). Exploiting surface-mobility indicates successful application of topological properties for practical purposes. However, the detection of the surface-mobility has been hindered by the inevitable bulk conduction. Even in the case of high-quality crystals, the bulk state forms the dominant channel of the electrical current. Therefore, with electrical transport measurement, the surface-mobility can be resolved only below-micrometer-thick crystals. The evaluati…
We report a theoretical study of electron spin resonance in bulk topological insulators, such as Bi2Se3, Bi2Te3 and Sb2Te3. Using the effective four-band model, we find the electron energy spectrum in a static magnetic field and determine the response to electric and magnetic dipole perturbations, represented by oscillating electric and magnetic fields perpendicular to the static field. We determine the associated selection rules and calculate the absorption spectra. This enables us to separate the effective orbital and spin degrees of freedom and to determine the effective g-factors for elect…
We introduce a topological theory to study quasiparticles in interacting and/or disordered many-body systems, which have a finite lifetime due to inelastic and/or elastic scattering. The one-body quasiparticle Hamiltonian includes both the Bloch Hamiltonian of band theory and the self-energy due to interactions, which is non-Hermitian when quasiparticle lifetime is finite. We study the topology of non-Hermitian quasiparticle Hamiltonians in momentum space, whose energy spectrum is complex. The interplay of band structure and quasiparticle lifetime is found to have remarkable consequences in ze…
We study coherent transport in density tunable micro-devices patterned from thin films of the topological insulator (TI) Bi2Se3. The devices exhibit pronounced electric field effect, including ambipolar modulation of the resistance with an on/off ratio of 500%. We show that the weak antilocalization (WAL) correction to conductance is sensitive to the number of coherently coupled channels, which in a TI includes the top and bottom surface and the bulk carriers. These are separated into coherently independent channels by the application of gate voltage and at elevated temperatures. Our results a…
We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk scattering matrix elements and confirm the importance of bulk-surface coupling in transport and photoemission experiments, assessing its dependence on temperature, carrier density, film thickness and particle-hole asymmetry.
We study in this paper time-reversal $δ$-impurity scattering effects in the bulk of topological insulators (TI) in two and three dimensions. Specifically we consider how impurity scattering strength is affected by the bulk band structure of topological insulators. An interesting band inversion effect associated with the change of the system from ordinary to topological insulator is pointed out. Experimental consequences of our findings are discussed.
We investigate the shift current bulk photovoltaic response of materials close to a band inversion topological phase transition. We find that the bulk photocurrent reverses direction across the band inversion transition, and that its magnitude is enhanced in the vicinity of the phase transition. These results are demonstrated with first principles DFT calculations of BiTeI and CsPbI$_3$ under hydrostatic pressure, and explained with an analytical model, suggesting that this phenomenon remains robust across disparate material systems.
We investigate the bulk band structures and the surface states of Bi2Se3 and Bi2Te3 topological insulators using first-principles many-body perturbation theory based on the GW approximation. The quasiparticle self-energy corrections introduce significant changes to the bulk band structures, while their effect on the band gaps is opposite in the band-inversion regime compared to the usual situation without band inversion. Parametrized "scissors operators" derived from the bulk studies are then used to investigate the electronic structure of slab models which exhibit topologically protected surf…
We analyze the finite lifetimes of the topologically protected electrons in the surface state of Bi2Te3 and Bi2Se3 due to elastic scattering off surface vacancies and as a function of energy. The scattering rates are decomposed into surface-to-surface and surface-to-bulk contributions, giving us new fundamental insights into the scattering properties of the topological surface states (TSS). If the number of possible final bulk states is much larger than the number of final surface states, then the surface-to-bulk contribution is of importance, otherwise the surface-to-surface contribution domi…
As-grown topological insulators (TIs) are typically heavily-doped $n$-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just 0.15 times the band gap, in good agreement with experimental data. At lower temperatures activated transp…
Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral topological characteristics are extended from edge states to corner states. However, the chiral symmetry protecting the corner states is often broken in genuine materials, leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant. Here, we show that a local artificial gauge flux can serve as a robust probe…
Topological insulators are predicted to present novel surface transport phenomena, but their experimental studies have been hindered by a metallic bulk conduction that overwhelms the surface transport. We show that a new topological insulator, Bi2Te2Se, presents a high resistivity exceeding 1 Ohm-cm and a variable-range hopping behavior, and yet presents Shubnikov-de Haas oscillations coming from the surface Dirac fermions. Furthermore, we have been able to clarify both the bulk and surface transport channels, establishing a comprehensive understanding of the transport in this material. Our re…
The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined by the bulk topological invariants. To obtain robust transport on the edge, we need to make volumetric changes to many bulk atoms to control the properties of a few edge atoms in a lower dimension. We suggest here that we can do the reverse in some cases: the properties of the edge can guarantee chiral transport phenomena in some bulk modes, achieving pheno…
Topological insulators (TIs) are predicted to be composed of an insulating bulk state along with conducting channels on the boundary of the material. In Bi2Se3, however, the Fermi level naturally resides in the conduction band due to intrinsic doping by selenium vacancies, leading to metallic bulk states. In such non-ideal TIs it is not well understood how the surface and bulk states behave under environmental disorder. In this letter, based on transport measurements of Bi2Se3 thin films, we show that the bulk states are sensitive to environmental disorder but the surface states remain robust.
Although, the long-standing debate on the resistivity anomaly in ZrTe$_{5}$ somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe$_{5}$ to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe$_{5}$ …
We demonstrate that the layered room temperature ferromagnet Fe7Se8 and the topological insulator Bi2Se3 form crystallographically oriented bulk composite intergrowth crystals. The morphology of the intergrowth in real space and reciprocal space is described. Critically, the basal planes of Bi2Se3 and Fe7Se8 are parallel and hence the good cleavage inherent in the bulk phases is retained. The intergrowth is on the micron scale. Both phases in the intergrowth crystals display their intrinsic bulk properties: the ferromagnetism of the Fe7Se8 is anisotropic, with magnetization easy axis in the pl…
In this report, it is shown that Cr doped into the bulk and Cr deposited on the surface of Bi2Se3 films produced by molecular beam epitaxy (MBE) have strikingly different effects on both the electronic structure and chemical environment.
An important challenge in the field of topological materials is to carefully disentangle the electronic transport contribution of the topological surface states from that of the bulk. For Bi$_2$Te$_3$ topological insulator samples, bulk single crystals and thin films exposed to air during fabrication processes are known to be bulk conducting, with the chemical potential in the bulk conduction band. For Bi$_2$Te$_3$ thin films grown by molecular beam epitaxy, we combine structural characterization (transmission electron microscopy), chemical surface analysis as function of time (x-ray photoelec…
The characteristics of topological insulators are manifested in both their surface and bulk properties, but the latter remain to be explored. Here we report bulk signatures of pressure-induced band inversion and topological phase transitions in Pb$_{1-x}$Sn$_x$Se ($x=$0.00, 0.15, and 0.23). The results of infrared measurements as a function of pressure indicate the closing and the reopening of the band gap as well as a maximum in the free carrier spectral weight. The enhanced density of states near the band gap in the topological phase give rise to a steep interband absorption edge. The change…
We consider the analogy between the topological phase transition which occurs as a function of spatial coordinate on a surface of a non-trivial insulator, and the one which occurs in the bulk due to the change of internal parameters (such as crystal field and spin-orbit coupling). In both cases the system exhibits a Dirac cone, which is the universal manifestation of topological phase transition, independently on the type of driving parameters. In particular, this leads to a simple way of determining the topological class based solely on the bulk information even for the systems with translati…
We perform \textit{ab initio} investigations of the bulk and surface band structures of LaSb and LaBi and resolve the existing disagreements about the topological property of LaSb, considering LaBi as a reference. We examine the bulk band structure for band inversion, along with the stability of surface Dirac cones (if any) to time-reversal-preserving perturbations, as a strong diagnostic test for determining the topological character of LaSb, LaBi and LaSb-LaBi multilayer. A detailed \textit{ab initio} investigation of a multilayer consisting of alternating unit cells of LaSb and LaBi shows t…
This review introduces known candidates for bulk topological superconductors and categorizes them with time-reversal symmetry (TRS) and gap structures. Recent studies on two archetypal topological superconductors, TRS-broken Sr2RuO4 and TRS-preserved CuxBi2Se3, are described in some detail.
We evaluate quantum corrections to conductivity in an electrically gated thin film of a three-dimensional (3D) topological insulator (TI). We derive approximate analytical expressions for the low-field magnetoresistance as a function of bulk doping and bulk-surface tunneling rate. Our results reveal parameter regimes for both weak localization and weak antilocalization, and include diffusive Weyl semimetals as a special case.
Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems characterized by Chern or spin-Chern topological invariants. These established examples of topological physics, however, do not exhaust all possible topological phases, and recently a new class of topological metamaterials characterized by bulk polarization has been introduced. In addition to edge conduction, these systems have been shown to host higher-order to…
A long-standing issue in topological insulator research has been to find a material that provides an ideal platform for characterizing topological surface states without interference from bulk electronic states and can reliably be fabricated as bulk crystals. This material would be a bulk insulator, have a surface state Dirac point energy well isolated from the bulk valence and conduction bands, have high surface state electronic mobility, and be growable as large, high quality bulk single crystals. Here we show that this major materials obstacle in the field is overcome by crystals of lightly…
High quality thin films of the topological insulator (Bi$_{0.4}$Sb$_{0.6}$)$_2$Te$_3$ have been deposited on SrTiO$_3$ (111) by molecular beam epitaxy. Their electronic structure was investigated by in situ angle-resolved photoemission spectroscopy and in situ scanning tunneling spectroscopy. The experimental results reveal striking similarities with relativistic ab-initio tight binding calculations. We find that ultrathin slabs of the three-dimensional topological insulator (Bi$_{0.4}$Sb$_{0.6}$)$_2$Te$_3$ display topological surface states, surface states with large weight on the outermost T…
ZrSiS is the most intensively studied topological nodal-line semimetal candidate, which is proposed to host multiple nodal lines in its bulk electronic structure. However, previous angle-resolved photoemission spectroscopy (ARPES) experiments with vacuum ultraviolet lights mainly probed the surface states. Here using bulk-sensitive soft X-ray ARPES, we acquire the bulk electronic states of ZrSiS without any interference from surface states. Our results clearly show two groups of three-dimensional bulk nodal lines located on high-symmetry planes and along high-symmetry lines in the bulk Brillou…
Hydrogen, the smallest and most abundant element in nature, can be efficiently incorporated within a solid and drastically modify its electronic state - it has been known to induce novel magnetoelectric effects in complex perovskites and modulate insulator-to-metal transition in a correlated Mott oxide. Here we demonstrate that hydrogenation resolves an outstanding challenge in chalcogenide classes of three-dimensional (3D) topological insulators and magnets - the control of intrinsic bulk conduction that denies access to quantum surface transport. With electrons donated by a reversible bindin…
Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological pro…
Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a topological invariant that describes the distribution of floppy, zero-energy edge modes. Here, we show that applying force at a point in the bulk of these lattices generates a directional mechanical response, in which stress or strain is induced only on one side of the force. This provides both a bulk metric for mechanical polarization and a design principle to c…
Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit quantized electro-magnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean field theory, a method that incorporates quantum-many-body effects and allows us to evaluate the magneto-electric topological response coefficient in cor…
Unconventional surface states protected by non-trivial bulk orders are sources of various exotic quantum transport in topological materials. One prominent example is the unique magnetic orbit, so-called Weyl orbit, in topological semimetals where two spatially separated surface Fermi-arcs are interconnected across the bulk. The recent observation of quantum Hall states in Dirac semimetal Cd3As2 bulks have drawn attention to the novel quantization phenomena possibly evolving from the Weyl orbit. Here we report surface quantum oscillation and its evolution into quantum Hall states in Cd3As2 thin…
In the past few years materials with protected gapless surface (edge) states have risen to the central stage of condensed matter physics. Almost all discussions centered around topological insulators and superconductors, which possess full quasiparticle gaps in the bulk. In this paper we argue systems with topological stable bulk nodes offer another class of materials with robust gapless surface states. Moreover the location of the bulk nodes determines the Miller index of the surfaces that show (or not show) such states. Measuring the spectroscopic signature of these zero modes allows a phase…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without bulk closure and exhibits as an obstruction of higher-dimensional boundary states. Here, we report the first experimental realization of three-dimensional surface-obstructed topological insulators with using acoustic crystals. Our acoustic measurements demonstrate unambiguously the emergence of one-dimensional topological hinge states in the middle of the bu…
