Protected Surface States Research Articles

Topological insulators based on the semi-metallic HgCdTe

The review of peculiarity of growth and experimental results of the magneto-transport measurements (longitudinal magneto-resistance Rxx and the Hall resistance Rxy) over a wide interval of temperatures for several samples of Hg1−xCdxTe (x ≈ 0.13–0.15) grown by MBE is presented in this paper. An amazing temperature stability of the SdH-oscillation period and amplitude is observed in the entire temperature interval of measurements up to 50 K. Moreover, the quantum Hall effect (QHE) behaviour of the Hall resistance was shown in the same temperature interval. These peculiarities of the Rxx and Rxy for strained thin layers are interpreted using quantum Hall conductivity (QHC) on topologically protected surface states (TPSS). In the case of not strained layers it is assumed that the QHC on the TPSS contributes also to the conductance of the bulk samples. The experimental results on magneto-transport (QHC and SdH) obtained for the strained 100 nm thickness Hg1−xCdxTe layer are interpreted on the basis of the 8 × 8 kp model and an advantage of the Hg1−xCdxTe as topological insulators is shown. This article is an expanded version of the scientific reports presented at the International Conference on Semiconductor Nanostructures for Optoelectronics and Biosensors 2016 ICSeNOB2016, May 22–25, 2016, Rzeszow, Poland.

Evolution of the topologically protected surface states in superconductor β-Bi2Pd from the three-dimensional to the two-dimensional limit

The recent discovery of topologically protected surface states in the noncentrosymmetric α-BiPd and the centrosymmetric β-Pd has renewed the interest in the Bi–Pd family of superconductors. We employ first-principles calculations to investigate the electronic structure and topological features of β-Pd, in bulk and in thin films of various thicknesses. We find that films of nine or more triple layers could harbor topological surface states with Dirac- and Rashba-like band dispersion.

Magnonic Weyl semimetal and chiral anomaly in pyrochlore ferromagnets

Topological states of matter have been a subject of intensive studies in recent years because of their exotic properties such as the topologically protected edge and surface states. The initial studies were exclusively for electron systems. It is now known that topological states can also exist for other particles. Indeed, topologically protected edge states have already been found for phonons and photons. In spite of active searching for topological states in many fields, the studies in magnetism are relatively rare although topological states are apparently important and useful in magnonics. Here we show that the pyrochlore ferromagnets with the Dzyaloshinskii-Moriya interaction are intrinsic magnonic Weyl semimetals. Similar to the electronic Weyl semimetals, the magnon bands in a magnonic Weyl semimetal are nontrivially crossing in pairs at special points (called Weyl nodes) in momentum space. The equal energy contour around the Weyl nodes gives rise to the Fermi arcs on sample surfaces due to the topologically protected surface states between each pair of Weyl nodes. Additional Weyl nodes and Fermi arcs can be generated in lower energy magnon bands when an anisotropic exchange interaction is introduced.

Nano-Angle Resolved Photoemission Spectroscopy on Topological insulator Sb2Te3 nanowires responsible of quantum transport

Using high-resolution Nano-Angle Resolved Photoemission Spectroscopy (Nano-ARPES), we have determined the electronic structure of the surface and bulk states of topological insulator Sb2Te3 nanowires, which have been also characterized by magnetoresistance measurements. The observed Aharonov-Bohm-type oscillations could be unambiguously related to the transport by topological protected surface states directly recorded by photoemission. We have measured Nano-ARPES on individual nanowires of a few nanometers wide to provide direct evidence of the existence of the nontrivial topological surface states, as well as their doping. Our findings are consistent with theoretical predictions and confirm that the surface states of intrinsically doped unidimensional topological insulator nanowires are responsible for the quantum transport.

Boosting the discovery of 3D topological materials: mixing chemistry with physics via a two-step computational screening strategy

Topological materials in crystal solids, including topological insulators (TIs), topological crystalline insulators (TCIs), topological Dirac semimetals (DSMs), topological Weyl semimetals (WSMs), topological Dirac or Weyl nodal line semimetals (NLSMs) and beyond, are mainly featured with topological, protected non-trivial surface states, and their bulk phases are insulators or semimetals with the proper presence of Dirac cones, Weyl nodes or Dirac nodal lines around the Fermi level. The author suggests a two-step computational screening strategy of 3D topological materials by mixing chemistry with physics with the considerations of fully filled bands and band inversion.

Using gapped topological surface states of Bi2Se3 films in a field effect transistor

Three dimensional topological insulators are insulators with topologically protected surface states that can have a high band velocity and high mobility at room temperature. This suggests electronic applications that exploit these surface states, but the lack of a band gap poses a fundamental difficulty. We report a first principles study based on density functional theory for thin Bi2Se3 films in the context of a field effect transistor. It is known that a gap is induced in thin layers due to hybridization between the top and bottom surfaces, but it is not known whether it is possible to use the topological states in this type of configuration. In particular, it is unclear whether the benefits of topological protection can be retained to a sufficient degree. We show that there is a thickness regime in which the small gap induced by hybridization between the two surfaces is sufficient to obtain transistor operation at room temperature, and furthermore, that the band velocity and spin texture that are important for the mobility are preserved for Fermi levels of relevance to device application.

Surface-state spin textures in strained bulk HgTe: Strain-induced topological phase transitions

The opening of a band gap due to compressive uniaxial strain renders bulk HgTe a strong three-dimensional topological insulators with protected gapless surface states at any surface. By employing a six-band k.p model, we determine the spin textures of the topological surface states of strained HgTe using their close relations with the mirror Chern numbers of the system and the orbital composition of the surface states. We show that at surfaces with C2v point group symmetry an increase in the strain magnitude triggers a topological phase transition where the winding number of the surface state spin texture is flipped while the four topological invariants characterizing the bulk band structure of the material are unchanged.

Massless Dirac fermions in semimetal HgCdTe

Abstract Magneto-transport results obtained for the strained 100 nm thick Hg 1 − x CdxTe (x=0.135) layer grown by MBE on the CdTe/GaAs substrate are interpreted by the 8×8 kp model with the in-plane tensile strain. The dispersion relation for the investigated structure proves that the Dirac point is located in the gap caused by the strain. It is also shown that the fan of the Landau Levels (LL's) energy calculated for topological protected surface states for the studied HgCdTe alloy corresponds to the fan of the LL's calculated using the graphen-like Hamiltonian which gives excellent agreement with the experimental data for velocity on the Fermi level equal to v f ≈ 0.85×106 m/s. That characterized strained Hg 1 − x CdxTe layers (0.13 x 0.14) are a perfect Topological Insulator with good perspectives of further applications.

Landau Levels of Double-Weyl Nodes in a Simple Lattice Model

In the Weyl semimetals, a recently discovered class of bulk materials, inverted band gap closes in the first Brillouin zone at topologically protected points of degeneracy called the Weyl nodes. By using the Chern number formalism it is possible to assign to each of the nodes an integer topological charge Q. While around typical Weyl points the energy disperses linearly in all three directions, double-Weyl nodes (with |Q| = 2) exhibit quadratic dispersion in two directions and linear in the third one. We use a simple 2-band tight-binding lattice model to investigate the dispersion of the Landau levels in the presence of quantizing magnetic field in the vicinity of a double-Weyl node. In the long wavelength limit we obtain analytically the expected presence of two chiral levels. In addition, we find numerous level crossings between the non-chiral Landau levels and the chiral ones, a feature which is distinct from the single node case. Calculations for a finite-size sample, both with periodic and hard-wall boundary conditions (the latter corresponding to slab geometry), show that the two chiral levels hybridize in the conduction band with the two lowest non-chiral Landau levels. In the case of slab geometry these four levels are responsible for the formation of a protected surface state.

Growth, characterization, and transport properties of ternary (Bi1−xSbx)2Te3 topological insulator layers

Ternary (Bi1−xSbx)2Te3 films with an Sb content between 0 and 100% were deposited on a Si(1 1 1) substrate by means of molecular beam epitaxy. X-ray diffraction measurements confirm single crystal growth in all cases. The Sb content is determined by x-ray photoelectron spectroscopy. Consistent values of the Sb content are obtained from Raman spectroscopy. Scanning Raman spectroscopy reveals that the (Bi1−xSbx)2Te3 layers with an intermediate Sb content show spatial composition inhomogeneities. The observed spectra broadening in angular-resolved photoemission spectroscopy (ARPES) is also attributed to this phenomena. Upon increasing the Sb content from x = 0 to 1 the ARPES measurements show a shift of the Fermi level from the conduction band to the valence band. This shift is also confirmed by corresponding magnetotransport measurements where the conductance changes from n- to p-type. In this transition region, an increase of the resistivity is found, indicating a location of the Fermi level within the band gap region. More detailed measurements in the transition region reveals that the transport takes place in two independent channels. By means of a gate electrode the transport can be changed from n- to p-type, thus allowing a tuning of the Fermi level within the topologically protected surface states.

Surface oxidation of the topological insulator Bi2Se3

An understanding of the aging and oxidation of the (0001) surface of Bi2Se3 is critical to a comprehensive physical picture of its topologically protected surface states. Here, the authors contribute new experimental observations about the aging and oxidation process. The authors find that surface aging in ambient conditions occurs in two major steps. Within 2 h of exfoliation, a series of ∼3.2 Å high islands are observed by atomic force microscopy over approximately 10% of the surface. Subsequently, patch growth stops, and oxidation begins after the 2 h and continues until one quintuple layer has been oxidized. X-ray photoelectron spectroscopy shows no sign of oxidation before ∼120 min of exposure to air, and the oxygen 1 s peak, as well as oxidized Se 3d and Bi 4d peaks, are clearly present after ∼190 min of ambient exposure. Variable angle spectroscopic ellipsometry indicates that the oxidation of a full quintuple layer occurs on the time scale of days. These results are in good agreement with the time dependent changes observed in the surface crystal structure by second harmonic generation. In addition to providing the ability to nondestructively measure oxide on the surface of Bi2Se3 crystals, ellipsometry can be used to identify the thickness of Bi2Se3 flakes. With these methods, the authors have constructed a consistent, experimentally based model of aging process at the surface of Bi2Se3.

Dirac cone and pseudogapped density of states in the topological half-Heusler compound YPtBi

Topological insulators (TIs) are exciting materials, which exhibit unprecedented properties, such as helical spin-momentum locking, which leads to large torques for magnetic switching and highly efficient spin current detection. Here we explore the compound YPtBi, an example from the class of half-Heusler materials, for which the typical band inversion of topological insulators was predicted. We prepared this material as thin films by conventional cosputtering from elementary targets. By in situ time-of-flight momentum microscopy, a Dirac conelike surface state with a Dirac point $\ensuremath{\simeq}300$ meV below the Fermi energy was observed, in agreement with electronic structure-photoemission calculations. Only little additional spectral weight due to other states was observed at ${E}_{F}$, which corroborates the identification of the topologically protected surface state and is highly relevant for spintronics applications.

Hybrid Weyl semimetal

We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed "hybrid Weyl semimetal", in which one Weyl node is of type-I while the other is of type-II. For the hybrid Weyl semimetal, we further demonstrate the bulk Fermi surfaces and the topologically protected surface states, analyze the unique Landau level structure and quantum oscillation, and discuss the material realization.

Coupled-layer description of topological crystalline insulators

We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.

Quantum Transport and Nano Angle-resolved Photoemission Spectroscopy on the Topological Surface States of Single Sb2Te3 Nanowires.

We report on low-temperature transport and electronic band structure of p-type Sb2Te3 nanowires, grown by chemical vapor deposition. Magnetoresistance measurements unravel quantum interference phenomena, which depend on the cross-sectional dimensions of the nanowires. The observation of periodic Aharonov-Bohm-type oscillations is attributed to transport in topologically protected surface states in the Sb2Te3 nanowires. The study of universal conductance fluctuations demonstrates coherent transport along the Aharonov-Bohm paths encircling the rectangular cross-section of the nanowires. We use nanoscale angle-resolved photoemission spectroscopy on single nanowires (nano-ARPES) to provide direct experimental evidence on the nontrivial topological character of those surface states. The compiled study of the bandstructure and the magnetotransport response unambiguosly points out the presence of topologically protected surface states in the nanowires and their substantial contribution to the quantum transport effects, as well as the hole doping and Fermi velocity among other key issues. The results are consistent with the theoretical description of quantum transport in intrinsically doped quasi-one-dimensional topological insulator nanowires.

Classification of topological quantum matter with symmetries

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks of topological materials is the existence of protected gapless surface states, which arise due to a nontrivial topology of the bulk wave functions. This review provides a pedagogical introduction into the field of topological quantum matter with an emphasis on classification schemes. We consider both fully gapped and gapless topological materials and their classification in terms of nonspatial symmetries, such as time-reversal, as well as spatial symmetries, such as reflection. Furthermore, we survey the classification of gapless modes localized on topological defects. The classification of these systems is discussed by use of homotopy groups, Clifford algebras, K-theory, and non-linear sigma models describing the Anderson (de-)localization at the surface or inside a defect of the material. Theoretical model systems and their topological invariants are reviewed together with recent experimental results in order to provide a unified and comprehensive perspective of the field. While the bulk of this article is concerned with the topological properties of noninteracting or mean-field Hamiltonians, we also provide a brief overview of recent results and open questions concerning the topological classifications of interacting systems.

Raman scattering in correlated thin films as a probe of chargeless surface states

Several powerful techniques exist to detect topologically protected surface states of weakly-interacting electronic systems. In contrast, surface modes of strongly interacting systems which do not carry electric charge are much harder to detect. We propose resonant light scattering as a means of probing the chargeless surface modes of interacting quantum spin systems, and illustrate its efficacy by a concrete calculation for the 3D hyperhoneycomb Kitaev quantum spin liquid phase. We show that resonant scattering is required to efficiently couple to this model's sublattice polarized surface modes, comprised of emergent Majorana fermions that result from spin fractionalization. We demonstrate that the low-energy response is dominated by the surface contribution for thin films, allowing identification and characterization of emergent topological band structures.

Single-electron induced surface plasmons on a topological nanoparticle.

It is rarely the case that a single electron affects the behaviour of several hundred thousands of atoms. Here we demonstrate a phenomenon where this happens. The key role is played by topological insulators—materials that have surface states protected by time-reversal symmetry. Such states are delocalized over the surface and are immune to its imperfections in contrast to ordinary insulators. For topological insulators, the effects of these surface states will be more strongly pronounced in the case of nanoparticles. Here we show that under the influence of light a single electron in a topologically protected surface state creates a surface charge density similar to a plasmon in a metallic nanoparticle. Such an electron can act as a screening layer, which suppresses absorption inside the particle. In addition, it can couple phonons and light, giving rise to a previously unreported topological particle polariton mode. These effects may be useful in the areas of plasmonics, cavity electrodynamics and quantum information.

Helicity‐Dependent Photovoltaic Effect in Bi2Se3 Under Normal Incident Light

Topological insulators (TIs) form a new class of materials with an insulating bulk and conducting surfaces ensured by topologically protected surface states (TPSS). The impact of the helicity of a normally incident laser beam on the photovoltaic effect in the TI Bi2Se3 is investigated. The observation of a helicity‐dependent photovoltaic effect for normally incident light indicates the presence of out‐of‐plane spin components for some TPSSs due to the hexagonal warping. In addition, fluctuations in the electrostatic potential at the surface locally break the rotational symmetry of the film allowing the helicity‐dependent photovoltaic effect. Our result suggests that engineering local electrostatic potentials in Bi2Se3 would allow the control of optically generated spin currents, which may be useful for applications in spin‐optoelectronics.

Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2.

The dispersion of charge carriers in a metal is distinctly different from that of free electrons owing to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics, and they can twist the quantum phase of electrons into topologically non-trivial knots-producing protected surface states with anomalous electromagnetic properties. These effects intertwine in materials known as Weyl semimetals, and in their crystal-symmetry-protected analogues, Dirac semimetals. The latter show a linear electronic dispersion in three dimensions described by two copies of the Weyl equation (a theoretical description of massless relativistic fermions). At the surface of a crystal, the broken translational symmetry creates topological surface states, so-called Fermi arcs, which have no counterparts in high-energy physics or conventional condensed matter systems. Here we present Shubnikov-de Haas oscillations in focused-ion-beam-prepared microstructures of Cd3As2 that are consistent with the theoretically predicted 'Weyl orbits', a kind of cyclotron motion that weaves together Fermi-arc and chiral bulk states. In contrast to conventional cyclotron orbits, this motion is driven by the transfer of chirality from one Weyl node to another, rather than momentum transfer of the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application.