Strong Topological Insulator Research Articles

Topologically protected surface states in a centrosymmetric superconductor β-PdBi2.

The topological aspects of electrons in solids can emerge in real materials, as represented by topological insulators. In theory, they show a variety of new magneto-electric phenomena, and especially the ones hosting superconductivity are strongly desired as candidates for topological superconductors. While efforts have been made to develop possible topological superconductors by introducing carriers into topological insulators, those exhibiting indisputable superconductivity free from inhomogeneity are very few. Here we report on the observation of topologically protected surface states in a centrosymmetric layered superconductor, β-PdBi2, by utilizing spin- and angle-resolved photoemission spectroscopy. Besides the bulk bands, several surface bands are clearly observed with symmetrically allowed in-plane spin polarizations, some of which crossing the Fermi level. These surface states are precisely evaluated to be topological, based on the Z2 invariant analysis in analogy to three-dimensional strong topological insulators. β-PdBi2 may offer a solid stage to investigate the topological aspect in the superconducting condensate.

Distinct Topological Crystalline Phases in Models for the Strongly Correlated Topological Insulator SmB_{6}.

SmB_{6} was recently proposed to be both a strong topological insulator and a topological crystalline insulator. For this and related cubic topological Kondo insulators, we prove the existence of four different topological phases, distinguished by the sign of mirror Chern numbers. We characterize these phases in terms of simple observables, and we provide concrete tight-binding models for each phase. Based on theoretical and experimental results for SmB_{6} we conclude that it realizes the phase with C_{k_{z}=0}^{+}=+2, C_{k_{z}=π}^{+}=+1, C_{k_{x}=k_{y}}^{+}=-1, and we propose a corresponding minimal model.

Three-dimensional topological insulators in the supercubane-like lattice: Phase diagram, surface state and spin texture

We study a tight-binding model of the supercubane-like lattice with spin–orbit coupling. By evaluating the Z2 topological indices, we find that the supercubane-like lattice can support strong topological insulator and the phase diagrams of the lattice with different filling fractions are present. Strong topological insulators with Z2 invariants (1;000) and (1;111) can be realized for 1/8 filling fraction and semimetals can be obtained for 1/8, quarter and half filling fractions. We analyze and discuss the characteristics of these topological insulators and their surface states. Spin textures of surface states are also evaluated for 11¯1 slab geometry.

Patterns of electromagnetic response in topological semimetals

Topological semimetals are gapless states of matter which have robust and unique electromagnetic responses and surface states. In this paper, we consider semimetals which have point like Fermi surfaces in various spatial dimensions $D=1,2,3$ which naturally occur in the transition between a weak topological insulator and a trivial insulating phase. These semimetals include those of Dirac and Weyl type. We construct these phases by layering strong topological insulator phases in one dimension lower. This perspective helps us understand their effective response field theory that is generally characterized by a 1-form $b$ which represents a source of Lorentz violation and can be read off from the location of the nodes in momentum space and the helicities/chiralities of the nodes. We derive effective response actions for the 2D and 3D Dirac semi-metals, and extensively discuss the response of the Weyl semimetal. We also show how our work can be used to describe semi-metals with Fermi-surfaces with lower co-dimension as well as to describe the topological response of 3D topological crystalline insulators.

Features of coherent phonons of the strong topological insulator Bi2Te3

Femtosecond laser pulses have been used to generate and detect fully symmetric (A 1g ) and doubly degenerate (E g ) coherent phonons in the topological insulator Bi2Te3. The isotropic detection of the low-symmetry E g modes has been obtained in the case of excitation in the near infrared range (λ = 1300 nm) and these modes have not been observed in the case of excitation with λ = 830 nm. The comparison of the amplitudes and initial phases of the coherent phonons indicates that the mechanisms of the excitation of fully symmetric (A 1g ) and doubly degenerate (E g ) modes in the topological insulator are different.

Gapless topological superconductors: Model Hamiltonian and realization

The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two dimensional Hamiltonians that yield an unusual class $D$ topological superconductor with a gapless bulk spectrum but well-localized Majorana edge states. We perform a numerical analysis for a representative model of this phase and suggest a concrete physical realization by analyzing the effect of magnetic impurities on the surface of strong topological insulators.

Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN.

Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu3PdN can host a three-dimensional (3D) topological node-line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by the coexistence of time-reversal and inversion symmetry. There are three node-line circles in total due to the cubic symmetry. Drumheadlike surface flat bands are also derived. When SOC is included, each node line evolves into a pair of stable 3D Dirac points as protected by C4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na3Bi and Cd3As2, both having only one pair of Dirac points. Once C4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z2 indices.

Interacting Surface States of Three-Dimensional Topological Insulators.

We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite sign for electrons with opposite spin. Assuming density-density contact interactions, we find superconducting and anomalous (quantum) Hall phases for attractive and repulsive interactions, respectively, as well as chiral fermion and chiral Majorana fermion boundary modes between different phases. Our setup is preeminently adapted to the search for topologically ordered surface terminations that could be microscopically stabilized by tailored surface interaction profiles.

Homotopy theory of strong and weak topological insulators

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.

Spin Chirality Tuning and Topological Semimetals in Strained HgTe(x)S(1-x).

By means of detailed electronic structure calculations, we show that strained HgTe(x)S(1-x) alloys show a surprisingly rich topological phase diagram. In the strong topological insulator phase, the spin chirality of the topological nontrivial surface states can be reversed by adjusting the alloy concentration x and the strain. On top of this, we predict two semimetallic topological phases, namely, a Dirac semimetal and a Weyl semimetal. The topological phases are characterized by their Z2 invariants and their mirror Chern numbers.

Surface states of perovskite iridatesAIrO3: Signatures of a topological crystalline metal with nontrivialZ2index

There have been increasing efforts in realizing topological metallic phases with nontrivial surface states. It was suggested that orthorhombic perovskite iridates are classified as a topological crystalline metal (TCM) with flat surface states protected by lattice symmetries. Here we perform first-principles electronic structure calculations for epitaxially stabilized orthorhombic perovskite iridates. Remarkably, two different types of topological surface states are found depending on surface directions. On side surfaces, flat surface states protected by lattice symmetries emerge, manifesting the topological crystalline character. On the top surface, on the other hand, an unexpected Dirac cone appears, indicating surface states protected by a time-reversal symmetry, which is confirmed by the presence of a nontrivial topological $\mathbb{Z}_2$ index. These results suggest that the orthorhombic iridates are unique systems exhibiting both lattice- and global-symmetry-protected topological phases and surface states. Transitions to weak and strong topological insulators and implications of surface states in light of angle resolved photoemission spectroscopy are also discussed.

Virtual topological insulators with real quantized physics

A concrete strategy is presented for generating strong topological insulators in $d+{d}^{\ensuremath{'}}$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and ${d}^{\ensuremath{'}}$ the virtual dimensions. It consists of seeking $d$-dimensional representations of operator algebras which are usually defined in $d+{d}^{\ensuremath{'}}$ dimensions where topological elements display strong topological invariants. The invariants are shown, however, to be fully determined by the physical dimensions, in the sense that their measurement can be done at fixed virtual coordinates. We solve the bulk-boundary correspondence and show that the boundary invariants are also fully determined by the physical coordinates. We analyze the virtual Chern insulator in $1+1$ dimensions realized in Y. E. Kraus et al., Phys. Rev. Lett. 109, 106402 (2012) and predict quantized forces at the edges. We generate a topological system in $(3+1)$ dimensions, which is predicted to have quantized magnetoelectric response.

Magnetically Controlled Electronic Transport Properties of a Ferromagnetic Junction on the Surface of a Topological Insulator* *Supported by National Natural Science Foundation of China under Grant Nos. 11174088, 11175067, 11274124

We have investigated the transport properties of the Dirac fermions through a ferromagnetic barrier junction on the surface of a strong topological insulator. The current-voltage characteristic curve and the tunneling conductance are calculated theoretically. Two interesting transport features are predicted: observable negative differential conductances and linear conductances tunable from unit to nearly zero. These features can be magnetically manipulated simply by changing the spacial orientation of the magnetization. Our results may contribute to the development of high-speed switching and functional applications or electrically controlled magnetization switching.

Quasiparticle interference patterns in a topological superconductor

In light of recent proposals to realize a topological superconductor on the surface of strong topological insulators, we study impurity and vortex scattering in two dimensional topological superconductivity. We develop a theory of quasiparticle interference in a model of the surface of a three dimensional strong topological insulator with a pairing term added. We consider a variety of different scatterers, including magnetic and nonmagnetic impurity as well as a local pairing order parameter suppression associated with the presence of a vortex core. Similar to the case of a surface of a three dimensional topological insulator without pairing, our results for non-magnetic impurity can be explained by the absence of back scattering, as expected for a Dirac cone structure. In the superconducting case, doping away from the Dirac point leads to a doubling of the contours of constant energy. This is in contrast to the unpaired case where the chemical potential simply adds to the bias voltage and shifts the energy. This doubling of contours results in multiplying the number of possible scattering processes in each energy. Interestingly, we find that some processes are dominant in the impurity case while others are dominant in the vortex case. Moreover, the two types of processes lead to a different dependence on the chemical potential.

Strongly interacting Majorana fermions

Interesting phases of quantum matter often arise when the constituent particles -- electrons in solids -- interact strongly. Such strongly interacting systems are however quite rare and occur only in extreme environments of low spatial dimension, low temperatures or intense magnetic fields. Here we introduce a new system in which the fundamental electrons interact only weakly but the low energy effective theory is described by strongly interacting Majorana fermions. The system consists of an Abrikosov vortex lattice in the surface of a strong topological insulator and is accessible experimentally using presently available technology. The simplest interactions between the Majorana degrees of freedom exhibit an unusual nonlocal structure that involves four distinct Majorana sites. We formulate simple lattice models with this type of interaction and find exact solutions in certain physically relevant one- and two-dimensional geometries. In other cases we show how our construction allows for the experimental realization of interesting spin models previously only theoretically contemplated.

Low-temperature thermal transport at the interface of a topological insulator and ad-wave superconductor

We consider the low-temperature thermal transport properties of the 2D proximity-induced superconducting state formed at the interface between a 3D strong topological insulator (TI) and a d-wave superconductor (dSC). This system is a playground for studying massless Dirac fermions, as they enter both as quasiparticles of the dSC and as surface states of the TI. For TI surface states with a single Dirac point, the four nodes in the interface-state quasiparticle excitation spectrum coalesce into a single node as the chemical potential, $\mu$, is tuned from above the impurity scattering rate ($|\mu| \gg \Gamma_0$) to below ($|\mu| \ll \Gamma_0$). We calculate, via Kubo formula, the universal limit ($T \rightarrow 0$) thermal conductivity, $\kappa_0$, as a function of $\mu$, as it is tuned through this transition. In the large and small $|\mu|$ limits, we obtain disorder-independent, closed-form expressions for $\kappa_0/T$. The large-$|\mu|$ expression is exactly half the value expected for a d-wave superconductor, a demonstration of the sense in which the TI surface topological metal is half of an ordinary 2D electron gas. Our numerical results for intermediate $|\mu|$ illustrate the nature of the transition between these limits, which is shown to depend on disorder in a well-defined manner.

Diagnosing a strong topological insulator by quantum oscillations

We show how quantum oscillation measurements of surface states in an insulator may allow to diagnose a strong topological insulator and distinguish it from its weak or topologically trivial counterpart. The criterion is defined by the parity of the number of fundamental frequencies in the surface-state quantum oscillation spectrum: an even number of frequencies implies a weak or a topologically trivial insulator, whereas an odd number points to a strong topological insulator. We also discuss various aspects and issues related to applying this criterion in practice.

Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid 3He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.

Dimensional crossover and cold-atom realization of topological Mott insulators.

Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.

Topological effects on the magnetoconductivity in topological insulators

Three-dimensional strong topological insulators (TIs) guarantee the existence of a 2-D conducting surface state which completely covers the surface of the TI. The TI surface state necessarily wraps around the TI's top, bottom, and two sidewalls, and is therefore topologically distinct from ordinary 2-D electron gases (2DEGs) which are planar. This has several consequences for the magnetoconductivity $\Delta \sigma$, a frequently studied measure of weak antilocalization which is sensitive to the quantum coherence time $\tau_\phi$ and to temperature. We show that conduction on the TI sidewalls systematically reduces $\Delta \sigma$, multiplying it by a factor which is always less than one and decreases in thicker samples. In addition, we present both an analytical formula and numerical results for the tilted-field magnetoconductivity which has been measured in several experiments. Lastly, we predict that as the temperature is reduced $\Delta \sigma$ will enter a wrapped regime where it is sensitive to diffusion processes which make one or more circuits around the TI. In this wrapped regime the magnetoconductivity's dependence on temperature, typically $1/T^2$ in 2DEGs, disappears. We present numerical and analytical predictions for the wrapped regime at both small and large field strengths. The wrapped regime and topological signatures discussed here should be visible in the same samples and at the same temperatures where the Altshuler-Aronov-Spivak (AAS) effect has already been observed, when the measurements are repeated with the magnetic field pointed perpendicularly to the TI's top face.