Topologically-protected Surface States Research Articles

From classical to quantum regime of topological surface states via defect engineering

Since the notion of topological insulator (TI) was envisioned in late 2000s, topology has become a new paradigm in condensed matter physics. Realization of topology as a generic property of materials has led to numerous predictions of topological effects. Although most of the classical topological effects, directly resulting from the presence of the spin-momentum-locked topological surface states (TSS), were experimentally confirmed soon after the theoretical prediction of TIs, many topological quantum effects remained elusive for a long while. It turns out that native defects, particularly interfacial defects, have been the main culprit behind this impasse. Even after quantum regime is achieved for the bulk states, TSS still tends to remain in the classical regime due to high density of interfacial defects, which frequently donate mobile carriers due to the very nature of the topologically-protected surface states. However, with several defect engineering schemes that suppress these effects, a series of topological quantum effects have emerged including quantum anomalous Hall effect, quantum Hall effect, quantized Faraday/Kerr rotations, topological quantum phase transitions, axion insulating state, zeroth-Landau level state, etc. Here, we review how these defect engineering schemes have allowed topological surface states to pull out of the murky classical regime and reveal their elusive quantum signatures, over the past decade.

Superior peroxidase mimetic activity induced by topological surface states of Weyl semimetal WTe2

Nanozymes, as promising alternatives that integrate the advantage of natural enzymes and nanomaterials are attracted enormous interest due to their low cost, environmental tolerance, high stability, as well as significant catalytic activity. Two-dimensional materials, transition metal dichalcogenides (TMDs) harbor the potential as peroxidase mimic which is attributed to the active edge sites and surface electron transfer capability. However, a challenge faced in peroxidase mimetic of TMDs is the low catalytic activity which originates from the inert structures. Here, we, for the first time, report that the typical Weyl semimetal WTe2 possesses the superior peroxidase-like performance toward H2O2, which derives from the two-step electron-pathway. We demonstrate a novel functionality of the Weyl semimetal through introducing topologically protected surface states (TSSs) for regulating the electron transfer processes. The underlying mechanism for TSSs promoting enzyme mimetic catalysis is attributed to the effective electron bath provided by the robust TSSs. Experiments and the first-principles calculations show that TSSs of WTe2 which serve as effective electron baths are directly involved in the two-step electron transfer process. In the first step, TSSs accept the electrons donated by the substrate which further enhances the substrate’s absorption. Upon H2O2 adsorption, the electrons are transferred out of TSSs and injected into the absorbed H2O2 orbitals. These findings offer a new linkage between the topological matters with TSSs and nanomaterials for enzyme mimicking.

Few-layer antimonene electrical properties

Antimonene -a single layer of antimony atoms- and its few layer forms are among the latest additions to the 2D mono-elemental materials family. Numerous predictions and experimental evidence of its remarkable properties including (opto)electronic, energetic or biomedical, among others, together with its robustness under ambient conditions, have attracted the attention of the scientific community. However, experimental evidence of its electrical properties is still lacking. Here, we characterized the electronic properties of mechanically exfoliated flakes of few-layer (FL) antimonene of different thicknesses (∼ 2–40 nm) through photoemission electron microscopy, kelvin probe force microscopy and transport measurements, which allows us to estimate a sheet resistance of ∼ 1200 Ω sq−1 and a mobility of ∼ 150 cm2V−1s−1 in ambient conditions, independent of the flake thickness. Alternatively, our theoretical calculations indicate that topologically protected surface states (TPSS) should play a key role in the electronic properties of FL antimonene, which supports our experimental findings. We anticipate our work will trigger further experimental studies on TPSS in FL antimonene thanks to its simple structure and significant stability in ambient environments.

Van der Waals heterostructures based on three-dimensional topological insulators

Three-dimensional (3D) topological insulators (TIs) have generated tremendous research interest over the past decade due to their topologically-protected surface states with linear dispersion and helical spin texture. The topological surface states offer an important platform to realize topological phase transitions, topological magnetoelectric effects and topological superconductivity via 3D TI-based heterostructures. In this review, we summarize the key findings of magneto and quantum transport properties in 3D TIs and their related heterostructures with normal insulators, ferromagnets and superconductors. For intrinsic 3D TIs, the experimental evidences of the topological surface states and their coupling effects are reviewed. Whereas for 3D TI related heterostructures, we focus on some important phenomenological magnetotransport activities and provide explanations for the proximity-induced topological and quantum effects.

Parasitic conduction channels in topological insulator thin films

Thin films of topological insulators (TI) usually exhibit multiple parallel conduction channels for the transport of electrical current. Beside the topologically protected surface states (TSS), parallel channels may exist, namely the interior of the not-ideally insulating TI film, the interface layer to the substrate, and the substrate itself. To be able to take advantage of the auspicious transport properties of the TSS, the influence of the parasitic parallel channels on the total current transport has to be minimized. Because the conductivity of the interior (bulk) of the thin TI film is difficult to access by measurements, we propose here an approach for calculating the mobile charge carrier concentration in the TI film. To this end, we calculate the near-surface band bending using parameters obtained experimentally from surface-sensitive measurements, namely (gate-dependent) four-point resistance measurements and angle-resolved photoelectron spectroscopy (ARPES). While in most cases another parameter in the calculations, i.e. the concentration of unintentional dopants inside the thin TI film, is unknown, it turns out that in the thin-film limit the band bending is largely independent of the dopant concentration in the film. Thus, a well-founded estimate of the total mobile charge carrier concentration and the conductivity of the interior of the thin TI film proves possible. Since the interface and substrate conductivities can be measured by a four-probe conductance measurement prior to the deposition of the TI film, the total contribution of all parasitic channels, and therefore also the contribution of the vitally important TSS, can be determined reliably.

Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance.

Spectroscopy of discrete Landau levels (LLs) in bulk-insulating three-dimensional topological insulators (3D TIs) in perpendicular magnetic field characterizes the Dirac nature of their surface states. Despite a number of studies demonstrating the quantum Hall effect (QHE) of topological surface states, quantitative evaluation of the LL energies, which serve as fundamental electronic quantities for study of the quantum states, is still limited. In this work, we explore the density of states of LLs by measuring quantum capacitance (CQ) in a truly bulk insulating 3D TI via a van der Waals heterostructure configuration. By applying dual-gate voltages, we access the individual surface states' LLs and extract their chemical potentials to quantify the LL spacings of each surface. We evaluate the LLs' energies at two distinguished QH states, namely, dissipationless (ν = ±1) and dissipative (ν = 0) states in the 3D TI.

Nanoscale Near-Field Tomography of Surface States on (Bi0.5Sb0.5)2Te3.

Three-dimensional topological insulators (TIs) have attracted tremendous interest for their possibility to host massless Dirac Fermions in topologically protected surface states (TSSs), which may enable new kinds of high-speed electronics. However, recent reports have outlined the importance of band bending effects within these materials, which results in an additional two-dimensional electron gas (2DEG) with finite mass at the surface. TI surfaces are also known to be highly inhomogeneous on the nanoscale, which is masked in conventional far-field studies. Here, we use near-field microscopy in the mid-infrared spectral range to probe the local surface properties of custom-tailored (Bi0.5Sb0.5)2Te3 structures with nanometer precision in all three spatial dimensions. Applying nanotomography and nanospectroscopy, we reveal a few-nanometer-thick layer of high surface conductivity and retrieve its local dielectric function without assuming any model for the spectral response. This allows us to directly distinguish between different types of surface states. An intersubband transition within the massive 2DEG formed by quantum confinement in the bent conduction band manifests itself as a sharp, surface-bound, Lorentzian-shaped resonance. An additional broadband background in the imaginary part of the dielectric function may be caused by the TSS. Tracing the intersubband resonance with nanometer spatial precision, we observe changes of its frequency, likely originating from local variations of doping or/and the mixing ratio between Bi and Sb. Our results highlight the importance of studying the surfaces of these novel materials on the nanoscale to directly access the local optical and electronic properties via the dielectric function.

Physical properties of noncentrosymmetric tungsten and molybdenum aluminides

A lack of spatial inversion symmetry gives rise to a variety of unconventional physics, from noncollinear order and Skyrmion lattice phases in magnetic materials to topologically-protected surface states in certain band insulators, to mixed-parity pairing states in superconductors. The search for exotic physics in such materials is largely limited by a lack of candidate materials, and often by difficulty in obtaining crystals. Here, we report the single crystal growth and physical properties of the noncentrosymmetric tungsten aluminide cage compounds Al$_4$W and Al$_5$W, alongside related molybdenum aluminides in which spin-orbit coupling should be significantly weaker. All compounds are nonmagnetic metals. Their high conductivities suggest the opportunity to find superconductivity at lower temperatures, while the limits we can place on their transition temperatures suggest that any superconductivity may be expected to exhibit significant parity mixing.

Unusual magnetoresistance oscillations in preferentially oriented p -type polycrystalline ZrTe5

Recently, Wang et al. (arXiv:1704.00995) reported quantum oscillation in magnetoresistance with the periodicity in the logarithm of a magnetic field (B) for $p$-type $\mathrm{ZrT}{\mathrm{e}}_{5}$. They have ascribed this type of behavior to the discrete scale invariance resulting from Efimov bound states. We have prepared high-quality stoichiometric ($p$-type) $\mathrm{ZrT}{\mathrm{e}}_{5}$ polycrystals and observed magnetoresistance oscillations, which are periodic in B. These oscillations are in contrast to usual SdH oscillations or log B dependent oscillations as observed for tellurium-deficient and stoichiometric $\mathrm{ZrT}{\mathrm{e}}_{5}$, respectively. We obtained small cyclotron effective mass (${m}^{*}\ensuremath{\sim}0.05{m}_{e}$), very high mobility of $\ensuremath{\sim}2.2\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{Vs}$, and the signature of topological protected surface states in the compound. The magnetic data show zero cusp paramagnetic susceptibility, which supports the existence of topological surface states in $\mathrm{ZrT}{\mathrm{e}}_{5}$.

Size and host-medium effects on topologically protected surface states in bianisotropic three-dimensional optical waveguides

We study the optical properties of bi-anisotropic optical waveguides with nontrivial topological structure in wavevector space, placed in an ordinary dielectric matrix. We derive an exact analytical description of the eigenmodes of the systems with arbitrary parameters that allows us to investigate topologically protected surface states (TPSS) in details. In particular, we find that the TPSS on the waveguides would disappear (1) if their radius is smaller than a critical radius due to the dimensional quantization of azimuthal wavenumber, and also (2) if the permittivity of the host-medium exceeds a critical value. Interestingly, we also find that the TPSS in the waveguides have negative refraction for some geometries. We have found a TPSS phase diagram that will pave the way for development of the topological waveguides for optical interconnects and devices.

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.

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.

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.

Disorder-driven topological phase transition inBi2Se3films

Topological insulators (TI) are a phase of matter that host unusual metallic states on their surfaces. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photo-emission spectroscopy and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI Bi2Se3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically-protected surface states, and will provoke new studies as to the fundamental nature of topological phase of matter in the presence of disorder.

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.

High-temperature stability of electron transport in semiconductors with strong spin-orbital interaction

Experimental results of the magnetotransport measurements (longitudinal magnetoresistance ${R}_{xx}$ and the Hall resistance ${R}_{xy}$) are presented over a wide interval of temperatures for several samples of ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ ($x\ensuremath{\approx}0.13--0.15$) grown by MBE---thin layers (thickness about 100 nm) strained and not strained and thick ones with thickness about $1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. 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) behavior of the Hall resistance is registered in the same temperature interval. These peculiarities of the ${R}_{xx}$ and ${R}_{xy}$ for strained thin layers are interpreted using quantum Hall conductivity (QHC) on topologically protected surface states (TPSS) [C. Br\une et al., Phys. Rev. Lett. 106, 126803 (2011)]. In the case of not strained layers it is assumed that the QHC on the TPSS (or on the resonant interface states) contributes also to the conductance of the bulk samples.

Ultra-broadband and high-responsive photodetectors based on bismuth film at room temperature.

Bismuth (Bi) has undergone researches for dozens of years on account of its abundant physics including the remarkably high mobility, exceptional large positive magnetoresistance and the coexistence of an insulating interior as well as metallic surfaces. Very recently, two-dimensional topologically-protected surface states immune to nonmagnetic perturbation such as surface oxidation and impurity scattering were experimentally demonstrated through systematic magnetotransport measurements, e.g. weak antilocalization effect and angular dependent Shubnikov-de Haas oscillations. Such robust metallic surface states, which are efficient in carrier transportation, along with its small bulk gap (14 meV) make Bi favored for high-responsive broadband photodetection. Here, we for the first time demonstrate the stable ultra-broadband photoresponse from 370 nm to 1550 nm with good reproducibility at room temperature based on a Bi photodetector. The fabricated device’s responsivity approaches 250 mA/W, accompanied with a rise time of 0.9 s and a decay time of 1.9 s. The photocurrent is linear dependent on the voltage and incident power, offering good tunability for multi-purpose applications. Thickness-dependent conductance and photocurrent reveal that the bulk is the optically active layer while the surface channel is responsible for carrier transportation. These findings pave an avenue to develop ultra-broadband Bi photodetectors for the next-generation multifunctional optoelectronic devices.

Inducing magnetism onto the surface of a topological crystalline insulator

Inducing magnetism onto a topological crystalline insulator (TCI) has been predicted to result in several novel quantum electromagnetic effects. This is a consequence of the highly strain-sensitive band topology of such symmetry-protected systems. We thus show that placing the TCI surface of SnTe in proximity to EuS, a ferromagnetic insulator, induces magnetism at the interface between SnTe and EuS and thus breaks time-reversal-symmetry in the TCI. Magnetotransport experiments on SnTe-EuS-SnTe trilayer devices reveal a hysteretic lowering of the resistance at the TCI surface that coincides with an increase in the density of magnetic domain walls. This additional conduction could be a signature of topologically-protected surface states within domain walls. Additionally, a hysteretic anomalous Hall effect reveals that the usual in-plane magnetic moment of the EuS layer is canted towards a perpendicular direction at the interface. These results are evidence of induced magnetism at the SnTe-EuS interfaces resulting in broken time-reversal symmetry in the TCI.

Self-consistentk·pcalculations for gated thin layers of three-dimensional topological insulators

Topological protected surface states are one of the hallmarks of three-dimensional topological insulators. In this work we theoretically analyze the gate-voltage-effects on a quasi-3D layer of HgTe. We find that while the gapless surface states dominate the transport, as an external gate voltage is applied, the existence of bulk charge carriers is likely to occur. We also find that due to screening effects, physical properties that arise from the bottom surface are gate-voltage independent. Finally, we point out the experimental signatures that characterize these effects.

Topological nodal semimetals

We present a study of "nodal semimetal" phases, in which non-degenerate conduction and valence bands touch at points (the "Weyl semimetal") or lines (the "line node semimetal") in three-dimensional momentum space. We discuss a general approach to such states by perturbation of the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time reversal (TR) or inversion symmetry. We give an explicit model realization of both types of states in a NI--TI superlattice structure with broken TR symmetry. Both the Weyl and the line-node semimetals are characterized by topologically-protected surface states, although in the line-node case some additional symmetries must be imposed to retain this topological protection. The edge states have the form of "Fermi arcs" in the case of the Weyl semimetal: these are chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. The chiral character of the edge states leads to a finite Hall conductivity. In contrast, the edge states of the line-node semimetal are "flat bands": these states are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone, given by the projection of the line node onto the plane of the edge. We discuss unusual transport properties of the nodal semimetals, and in particular point out quantum critical-like scaling of the DC and optical conductivity of the Weyl semimetal, and similarities to the conductivity of graphene in the line node case.