Three-dimensional Topological Insulator Research Articles

Field-free anomalous junction and superconducting diode effect in spin-split superconductor/topological insulator junctions

We study the transport properties of a diffusive Josephson junction between two spin-split superconductors (SCs) made of SC-ferromagnetic insulator bilayers on top of a three-dimensional topological insulator. We derive the corresponding Usadel equation describing the quasiclassical Green's functions in these systems and first solve the equation analytically in the weak-proximity case. We demonstrate the appearance of an anomalous phase in the absence of an external magnetic field. We also explore nonreciprocal electronic transport. Specifically, we calculate the diode efficiency of the junction $\ensuremath{\eta}$ by solving the Usadel equation. We obtain a sizable diode effect even at zero applied magnetic field. We discuss how the diode efficiency $\ensuremath{\eta}$ depends on the different parameters and find a nonmonotonic behavior of $\ensuremath{\eta}$ with temperature.

Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator Bi2Te3 by angle-resolved photoemission and terahertz spectroscopy

Photoexcited carriers in three-dimensional topological insulators (3D TIs) decay rapidly through the electron-electron and electron-phonon scattering. While most studies focus on such fast dynamics, recent experiments find the slow photovoltage (PV) dynamics arising from the band-bending potentials, in which the optical transitions in two-dimensional electron gas (2DEG) are effective. Although early investigations speculated the existence of multiple band-bending structures from the TI surface to the TI bulk, how PV and 2DEG are correlated in the presence of such multiple band bendings has been less explored. Here, we employ the combination of time- and angle-resolved photoemission spectroscopy (tr-ARPES) and ultrafast time-resolved terahertz (tr-THz) spectroscopy to investigate the PV and 2DEG dynamics in the prototypical topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$. Our tr-ARPES analysis identifies two spatially separated PV dynamics associated with two types of band bending: one is the well-known surface PV, and another PV is formed deep within the bulk, which we call ``internal bulk PV.'' For the surface PV, our tr-THz spectra substantiate that the $\ensuremath{\mu}\mathrm{s}$-long transient signal arises from the surface-PV-induced increase of the TSS and 2DEG carrier density, which appears as a transient blueshift of a Fermi cutoff and an increased ARPES intensity in the tr-ARPES measurements. In contrast, the effect of the internal bulk PV shows only marginal changes in the 2DEG and TSS carrier densities but shifts the entire binding energy of the near-surface bands.

Topology-insensitive axion mass in magnetic topological insulators

We study the axion in three-dimensional topological insulators with magnetic impurities under finite temperature. We find a stable antiferromagnetic ground state and ferromagnetic metastable state. In both magnetic states, the mass of the axion is found to be up to eV scale and it approaches zero near the phase boundary of the magnetic state. This result applies to both normal and topological insulator phases, i.e., the axion mass is insensitive to the topological states, and it will have a direct impact on the targeted mass range of particle axion dark matter in future experiments.

A generic designing rule for realizing quantum anomalous Hall phase in a transition-metal trichalcogenide family

Different from introducing ferromagnetism in three-dimensional (3D) topological insulators, empowering nontrivial band topology with 2D ferromagnetic (2DFM) materials is another way to realize quantum anomalous Hall effect (QAHE). The recently discovered 2DFM insulators provide unprecedented opportunities for realizing such an intriguing quantum phenomenon. Here, by using first-principles approaches, we design a generic rule for realizing QAHE in the transition-metal trichalcogenide family materials of Cr2A2X6 (where A = Si, Ge, Sn; X = S, Se, Te), whose design principle is based on that a 2D topologically trivial magnetic insulator can be converted into a QAH system via proper surface modification. Taking silicene-passivated Cr2Sn2Se6 as an illustration, we show that the Cuire temperature of Cr2Sn2Se6 monolayer can be enhanced up to ∼92 K after silicene passivation. Most strikingly, such a heterostructure harbors QAHE with a band gap of ∼30 meV. Further low-effective model analyses reveal that the topologically nontrivial states are attributed to the honeycomb lattice of Cr atoms. All those results demonstrate that our proposal is general, which opens a new avenue to explore high-temperature QAHE.

Unconventional optical selection rules in ZrTe5 under an in-plane magnetic field

The optical selection rules of an electron system under a magnetic field play key roles in determining its optical properties, from which the band structures and underlying symmetries can be derived. In this Letter, based on a three-dimensional strong topological insulator model describing ZrTe5,we study the Landau levels (LLs) and magneto-optical conductivity under an in-plane magnetic field. We reveal that in the transverse conductivity Re(\sigma_{zz}), the unconventional optical selection rules n\righatarrow n\pm 2 dominate, with n being the LL index. We attribute the unconventional selection rules to the peculiar distribution of parity carried by the LLs, resulting from the chiral symmetry of the sub-Hamiltonians. Moreover, we predict that, if the strong anisotropic system is tuned to be nearly isotropic, the LLs would redistribute and the conventional selection rules n\rightarrow n\pm 1 can be recovered.

Emergent helical edge states in a hybridized three-dimensional topological insulator

As the thickness of a three-dimensional (3D) topological insulator (TI) becomes comparable to the penetration depth of surface states, quantum tunneling between surfaces turns their gapless Dirac electronic structure into a gapped spectrum. Whether the surface hybridization gap can host topological edge states is still an open question. Herein, we provide transport evidence of 2D topological states in the quantum tunneling regime of a bulk insulating 3D TI BiSbTeSe2. Different from its trivial insulating phase, this 2D topological state exhibits a finite longitudinal conductance at ~2e2/h when the Fermi level is aligned within the surface gap, indicating an emergent quantum spin Hall (QSH) state. The transition from the QSH to quantum Hall (QH) state in a transverse magnetic field further supports the existence of this distinguished 2D topological phase. In addition, we demonstrate a second route to realize the 2D topological state via surface gap-closing and topological phase transition mechanism mediated by a transverse electric field. The experimental realization of the 2D topological phase in a 3D TI enriches its phase diagram and marks an important step toward functionalized topological quantum devices.

Green's function approach to interacting higher-order topological insulators

The Bloch wave functions have been playing a crucial role in the diagnosis of topological phases in non-interacting systems. However, the Bloch waves are no longer applicable in the presence of finite Coulomb interaction and alternative approaches are needed to identify the topological indices. In this paper, we focus on three-dimensional higher-order topological insulators protected by $C_4T$ symmetry and show that the topological index can be computed through eigenstates of inverse Green's function at zero frequency. If there is an additional $S_4$ rotoinversion symmetry, the topological index $P_3$ can be determined by eigenvalues of $S_4$ at high symmetry momenta, similar to the Fu-Kane parity criterion. We verify this method using many-body exact diagonalization in higher-order topological insulators with interaction. We also discuss the realization of this higher-order topological phase in tetragonal lattice structure with $C_4T$-preserving magnetic order. Finally, we discuss the boundary conditions necessary for the hinge states to emerge and show that these hinge states exist even when the boundary is smooth and without a sharp hinge.

Topological electronic bands in crystalline solids

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals

Conductivity of Two-Dimensional Small Gap Semiconductors and Topological Insulators in Strong Coulomb Disorder

We are honored to dedicate this article to Emmanuel Rashba on the occasion of his 95 birthday. In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap, $\Delta$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $\Delta$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional narrow gap semiconductor on a substrate containing Coulomb impurities, mostly focusing on the case when amplitude of the random potential $\Gamma \gg \Delta$. We show that the conductivity generically exhibits three regimes and only the highest temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through nearest-neighbor or variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We arrive at a similar disorder driven steep insulator-metal transition in thin films of three-dimensional topological insulators with very large dielectric constant, where due to confinement of electric field internal Coulomb impurities create larger disorder potential. Away from neutrality point this unconventional insulator-to-metal transition is augmented by conventional metal-insulator transition at small impurity concentrations, so that we arrive at disorder-driven re-entrant metal-insulator-metal transition.

Collective Spin Modes in Fermi Liquids with Spin–Orbit Coupling

A combination of spin-orbit coupling and electron-electron interaction gives rise to a new type of collective spin modes, which correspond to oscillations of magnetization even in the absence of the external magnetic field. We review recent progress in theoretical understanding and experimental observation of such modes, focusing on three examples of real-life systems: a two-dimensional electron gas with Rashba and/or Dresselhaus spin-orbit coupling, graphene with proximity-induced spin-orbit coupling, and the Dirac state on the surface of a three-dimensional topological insulator. This paper is dedicated to the 95th birthday of Professor Emmanuel I. Rashba.

DFT-1/2 method applied to 3D topological insulators

In this paper, we present results and describe the methodology of application of DFT-1/2 method for five three-dimensional topological insulators materials that have been extensively studied in last years: Bi2Se3, Bi2Te3, Sb2Te3, CuTlSe2 and CuTlS2. There are many differences between the results of simple DFT calculations and quasiparticle energy correction methods for these materials, especially for band dispersion in the character band inversion region. The DFT-1/2 leads to quite accurate results not only for band gaps, but also for the shape and atomic character of the bands in the neighborhood of the inversion region as well as the topological invariants, essential quantities to describe the topological properties of materials. The methodology is efficient and ease to apply for the different approaches used to obtain the topological invariant Z 2, with the benefit of not increasing the computational cost in comparison with standard DFT, possibilitating its application for materials with a high number of atoms and complex systems.

Disorder-induced topological phase transition in HgCdTe crystals

Using the self-consistent Born approximation, we study a topological phase transition appearing in bulk HgCdTe crystals induced \emph{uncorrelated} disorder due to both randomly distributed impurities and fluctuations in Cd composition. By following the density-of-states evolution, we clearly demonstrate the topological phase transition, which can be understood in terms of the disorder-renormalized mass of Kane fermions. We find that the presence of heavy-hole band in HgCdTe crystals leads to the topological phase transition at much lower disorder strength than it is expected for conventional 3D topological insulators. Our theoretical results can be also applied to other narrow-gap zinc-blende semiconductors such as InAs, InSb and their ternary alloys InAsSb.

Tailoring the surface and interface states in a three-dimensional fragile topological insulator with kagome lattice

Topological insulators, which are insulating in the bulk and conducting on the surface, have attracted great interest in recent years. The recently discovered topological surface and hinge states in three dimensions have provided promising methods for wave manipulation in classical systems. However, the combination of surface states and interface states has yet to be achieved in phononic crystals due to the missing topological surface states. Here, we experimentally demonstrate a fragile topological insulator with a bilayer kagome lattice. We observe the surface states in three different orientations and interface states formed by inversion of layer pseudospin sectors or bands. The combination of surface and interface states is investigated in $\mathsf{X}$-shaped waveguides. Our work may provide a platform for exploring unique acoustic applications based on surface or interface states.

Critical topology and pressure-induced superconductivity in the van der Waals compound AuTe2Br

The study on quantum spin Hall effect and topological insulators formed the prologue to the surge of research activities in topological materials in the past decade. Compared to intricately engineered quantum wells, three-dimensional weak topological insulators provide a natural route to the quantum spin Hall effect, due to the adiabatic connection between them and a stack of quantum spin Hall insulators, and the convenience in exfoliation of samples associated with their van der Waals-type structure. Despite these advantages, both theoretical prediction and experimental identification of weak topological insulators remain scarce. Here, based on first-principles calculations, we show that AuTe2Br locates at the boundary between a strong and a weak topological semimetal state. We identify the key structural parameter that dictates the traversal of the topological transition, which can be easily realized in experiments. More interestingly, the critical topology of AuTe2Br persists up to an applied pressure of ~15.4 GPa before a structural phase transition accompanied by a change of electronic topology and the onset of superconductivity. Our results establish AuTe2Br as a new candidate for an effective tuning between weak and strong topological phases in a single material, with the potential to realize various other topological phases of matter.

Observation of Dirac Hierarchy in Three-Dimensional Acoustic Topological Insulators.

Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional topological corner states in a third-order 3D TI. Our Letter not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.

Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry

We show that the gapless boundary signatures---namely, chiral/helical hinge modes or localized zero modes---of three-dimensional higher-order topological insulators and superconductors with inversion symmetry can be gapped without symmetry breaking upon the introduction of non-Abelian surface topological order. In each case, the fractionalization pattern that appears on the surface is ``anomalous'' in the sense that it can be made consistent with symmetry only on the surface of a three-dimensional higher-order insulator/superconductor. Our results show that the interacting manifestation of higher-order topology is the appearance of ``anomalous gapped boundaries'' between distinct topological orders whose quasiparticles are related by inversion, possibly in conjunction with other protecting symmetries such as time-reversal symmetry and charge conservation.

Nanometric Moiré Stripes on the Surface of Bi2Se3 Topological Insulator.

Mismatch between adjacent atomic layers in low-dimensional materials, generating moiré patterns, has recently emerged as a suitable method to tune electronic properties by inducing strong electron correlations and generating novel phenomena. Beyond graphene, van der Waals structures such as three-dimensional (3D) topological insulators (TIs) appear as ideal candidates for the study of these phenomena due to the weak coupling between layers. Here we discover and investigate the origin of 1D moiré stripes on the surface of Bi2Se3 TI thin films and nanobelts. Scanning tunneling microscopy and high-resolution transmission electron microscopy reveal a unidirectional strained top layer, in the range 14–25%, with respect to the relaxed bulk structure, which cannot be ascribed to the mismatch with the substrate lattice but rather to strain induced by a specific growth mechanism. The 1D stripes are characterized by a spatial modulation of the local density of states, which is strongly enhanced compared to the bulk system. Density functional theory calculations confirm the experimental findings, showing that the TI surface Dirac cone is preserved in the 1D moiré stripes, as expected from the topology, though with a heavily renormalized Fermi velocity that also changes between the top and valley of the stripes. The strongly enhanced density of surface states in the TI 1D moiré superstructure can be instrumental in promoting strong correlations in the topological surface states, which can be responsible for surface magnetism and topological superconductivity.

Temperature-dependent band modification and energy dependence of the electron-phonon interaction in the topological surface state on Bi2Te3

We report the temperature-dependent band structure and energy dependence of the electron-phonon interaction of the topological surface state (TSS) on the three-dimensional topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ using angle-resolved photoemission spectroscopy. Despite the nonrigid-band-like band modification as the temperature increases, the degeneracy at the Dirac point (DP) was robust, indicating topological protection. The electron-phonon coupling parameter depends on the initial-state electron energy, varying from 0.13 (at the DP) to 0.02 (100 meV above the DP), in agreement with reported first-principles calculations. Our findings provide insight into the physical properties derived from TSSs at finite temperatures.

Photo-induced inverse spin Hall effect of the top and bottom Dirac surface states of three-dimensional topological insulators Sb2Te3

Inverse spin Hall effect (ISHE) provides an important way to manipulate and detect spin current via spin–orbit coupling. However, it is difficult to distinguish the ISHE of the top and bottom surface states of topological insulators (TIs). Photo-induced inverse spin Hall effect (PISHE) is a powerful tool to investigate the ISHE of the Dirac surface states of TIs. In this work, PISHE of three-dimensional topological insulators Sb 2 Te 3 with a thickness of 7 and 30 quintuple layer (QL) has been investigated. It is revealed that both of the PISHE currents of the top and bottom surface states are observed in the 7-QL and the 30-QL samples. Besides, a model has been developed to separate the PISHE current of the top and bottom surface states. It is found that the PISHE currents of the top and bottom surface states of the Sb 2 Te 3 films almost do not change with temperature in the range of 77 to 300 K. It is demonstrated that the PISHE current changes linearly with light power, which agrees well with the theoretical model. This study provides a method utilizing circularly polarized light to manipulate and detect the ISHE of the top and bottom surface states of three-dimensional topological insulators. • Both of the PISHE currents of the top and bottom surface states are observed in the 7-QL and the 30-QL Sb 2 Te 3 films. • A model has been developed to separate the PISHE current of the top and bottom surface states. • The PISHE currents of the top and bottom surface states of the Sb 2 Te 3 films almost do not change with temperature in the range of 77 to 300 K.

Magic angle conditions for twisted three-dimensional topological insulators

When two layers of graphene are stacked at a specific ``magic'' twist angle, the Dirac cones hybridize, forming perfectly flat bands. Can Dirac cones at the interface between two stacked and twisted 3D topological insulators exhibit similar band flattening? Ultimately, the generalization from Dirac cones in sublattice space to spin space is not so simple. The authors derive here the necessary conditions to flatten the anomalous Dirac cones, which has implications for realizing tunable interacting topological phases.