Conducting Surface States Research Articles

Effect of the hexagonal warping on the dynamical conductivity of surface states in a topological insulator

We report on the effect of hexagonal warping on the dynamical conductivity of the surface states of a topological insulator in the presence of nonmagnetic impurities. It is found that the photon energy dependent conductivities are determined by a polarization-function-liked term, Π2 (q,ω), which contains a velocity term corresponding to the difference of group velocities between the two states due to an electron-impurity scattering. This is different from the conductivity of 2-dimentional electron systems where the conductivity depends on the inverse imaginary part of the dielectric function Im [1/κ(q,ω)]. We present both the real part and imaginary part of the polarization function with different warping strength. It is found that the warping strength can both enhance single particle excitations (SPEs) and suppress the screening effect of electrons. As a result the inverse scattering time is enhanced by up to about two orders of magnitudes. The real part of the longitudinal conductivity of the intra-band process is analog to the case with a conductivity of σ ~ μδ(ω). The broadening of the spectrum in the low energy is not only determined by chemical potential, but also dependent on the warping strength. At higher frequency, the real part of conductivity shows a jump at the threshold photon energy of μ, where the inter-band contribution takes over.

Flat electronic bands in long sequences of rhombohedral-stacked graphene

The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic properties. It has been predicted that a rhombohedral (ABC) stacking displays a conducting surface state with flat electronic dispersion. In such a flat band, the role of electron-electron correlation is enhanced, possibly resulting in high ${T}_{\mathrm{c}}$ superconductivity, charge-density wave, or magnetic orders. Clean experimental band-structure measurements of ABC-stacked specimens are missing because the samples are usually too small in size. Here, we directly image the band structure of large multilayer graphene flakes containing approximately 14 consecutive ABC layers. Angle-resolved photoemission spectroscopy experiments reveal the flat electronic bands near the $K$ point extends by $0.13\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$ at the Fermi level at liquid nitrogen temperature. First-principles calculations identify the electronic ground state as an antiferromagnetic state with a band gap of about 40 meV.

Higher-order topological insulators.

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk but conducting surface states that are topologically protected by time-reversal (or spatial) symmetries. We extend the notion of three-dimensional topological insulators to systems that host no gapless surface states but exhibit topologically protected gapless hinge states. Their topological character is protected by spatiotemporal symmetries of which we present two cases: (i) Chiral higher-order topological insulators protected by the combination of time-reversal and a fourfold rotation symmetry. Their hinge states are chiral modes, and the bulk topology is -classified. (ii) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs, and the bulk topology is -classified. We provide the topological invariants for both cases. Furthermore, we show that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.

Quantum materials for thermoelectricity

Abstract

Manifestations of Surface States in the Longitudinal Magnetoresistance of an Array of Bi Nanowires

The longitudinal magnetoresistance of the array of parallel-oriented bismuth nanowires each 100 nm in diameter grown by electrochemical deposition in nanopores of an Al2O3 membrane has been studied in magnetic fields up to 14 T and at temperatures down to 0.3 K. The resistance increases with the field and reaches a broad maximum in fields about 10 T. An anomalous increase in the resistance in weak fields is qualitatively consistent with the suppression of the antilocalization correction to the resistance, and the maximum is qualitatively associated with the classical size effect. Near the maximum at temperatures below 0.8 K, manifestations of reproducible magneto-oscillations of the resistance, which are periodic in field, have been detected. The period of these oscillations is close to a value corresponding to the passage of the flux quantum hc/e through the section of a nanowire. The Fourier analysis also confirms that the oscillations are periodic. This result is similar to the manifestation the Aharonov–Bohm effect caused by conducting surface states of Dirac fermions occupying L-valleys of bismuth.

Large Enhancement of Thermal Conductivity and Lorenz Number in Topological Insulator Thin Films.

Topological insulators (TI) have attracted extensive research effort due to their insulating bulk states but conducting surface states. However, investigation and understanding of thermal transport in topological insulators, particularly the effect of surface states, are lacking. In this work, we studied thickness-dependent in-plane thermal and electrical conductivity of Bi2Te2Se TI thin films. A large enhancement in both thermal and electrical conductivity was observed for films with thicknesses below 20 nm, which is attributed to the surface states and bulk-insulating nature of these films. Moreover, a surface Lorenz number much larger than the Sommerfeld value was found. Systematic transport measurements indicated that the Fermi surface is located near the charge neutrality point (CNP) when the film thickness is below 20 nm. Possible reasons for the large Lorenz number include electrical and thermal current decoupling in the surface state Dirac fluid, and bipolar diffusion transport. A simple computational model indicates that the surface states and bipolar diffusion indeed can lead to enhanced electrical and thermal transport and a large Lorenz number.

Observation of Volkov-Pankratov states in topological HgTe heterojunctions using high-frequency compressibility

It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. In this article we report on a set of experimental observations indicating the existence of massive surface states. These states are confined at the interface and dominate equilibrium and transport properties at high energy and/or high electric field. By monitoring the AC admittance of HgTe topological insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energy and electric fields. The Dirac surface states are characterized by a compressibility minimum, a linear energy dependence and a high mobility persisting up to energies much larger than the transport bandgap of the bulk. New features are revealed at high energies with signatures such as conductance peaks, compressibility bumps, a strong charge metastability and a Hall resistance anomaly. These features point to the existence of excited massive surface states, responsible for a strong intersubband scattering with the Dirac states and the nucleation of metastable bulk carriers. The spectrum of excited states agrees with predictions of a phenomenological model of the topological-trivial semiconductor interface. The model accounts for the finite interface depth and the effect of electric fields. The existence of excited topological states is essential for the understanding of topological phases and opens a route for engineering and exploiting topological resources in quantum technology.

Bulk vs. Surface Structure of 3d Metal Impurities in Topological Insulator Bi2Te3

Topological insulators have become one of the most prominent research topics in materials science in recent years. Specifically, Bi2Te3 is one of the most promising for technological applications due to its conductive surface states and insulating bulk properties. Herein, we contrast the bulk and surface structural environments of dopant ions Cr, Mn, Fe, Co, Ni, and Cu in Bi2Te3 thin films in order to further elucidate this compound. Our measurements show the preferred oxidation state and surrounding crystal environment of each 3d-metal atomic species, and how they are incorporated into Bi2Te3. We show that in each case there is a unique interplay between structural environments, and that it is highly dependant on the dopant atom. Mn impurities in Bi2Te3 purely substitute into Bi sites in a 2+ oxidation state. Cr atoms seem only to reside on the surface and are effectively not able to be absorbed into the bulk. Whereas for Co and Ni, an array of substitutional, interstitial, and metallic configurations occur. Considering the relatively heavy Cu atoms, metallic clusters are highly favourable. The situation with Fe is even more complex, displaying a mix of oxidation states that differ greatly between the surface and bulk environments.

Chalcogenide-based van der Waals epitaxy: Interface conductivity of tellurium on Si(111)

We present a combined experimental and theoretical analysis of a Te rich interface layer which represents a template for chalcogenide-based van der Waals epitaxy on Si(111). On a clean Si(111)-$(1\ifmmode\times\else\texttimes\fi{}1)$ surface, we find Te to form a Te/Si(111)-$(1\ifmmode\times\else\texttimes\fi{}1)$ reconstruction to saturate the substrate bonds. A problem arising is that such an interface layer can potentially be highly conductive, undermining the applicability of the on-top grown films in electric devices. We perform here a detailed structural analysis of the pristine Te termination and present direct measurements of its electrical conductivity by in situ distance-dependent four-probe measurements. The experimental results are analyzed with respect to density functional theory calculations and the implications of the interface termination with respect to the electrical conductivity of chalcogenide-based topological insulator thin films are discussed. In detail, we find a Te/Si(111)-$(1\ifmmode\times\else\texttimes\fi{}1)$ interface conductivity of ${\ensuremath{\sigma}}_{2\mathrm{D}}^{\mathrm{Te}}=2.6(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.28em}{0ex}}\mathrm{S}/\ensuremath{\square}$, which is small compared to the typical conductivity of topological surface states.

Manipulating topological-insulator properties using quantum confinement

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron–hole asymmetry are disentangled and their respective physical consequences elucidated.

Type-II Dirac surface states in topological crystalline insulators

We study the properties of a family of anti-pervoskite materials, which are topological crystalline insulators with an insulating bulk but a conducting surface. Using ab-initio DFT calculations, we investigate the bulk and surface topology and show that these materials exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. While type-I Dirac states give rise to closed circular Fermi surfaces, type-II Dirac surface states are characterized by open electron and hole pockets that touch each other. We find that the type-II Dirac states exhibit characteristic van-Hove singularities in their dispersion, which can serve as an experimental fingerprint. In addition, we study the response of the surface states to magnetic fields.

Ambipolar surface state transport in nonmetallic stoichiometric Bi2Se3 crystals

Achieving true bulk insulating behavior in Bi$_2$Se$_3$, the archetypal topological insulator with a simplistic one-band electronic structure and sizable band gap, has been prohibited by a well-known self-doping effect caused by selenium vacancies, whose extra electrons shift the chemical potential into the bulk conduction band. We report a new synthesis method for achieving stoichiometric Bi$_2$Se$_3$ crystals that exhibit nonmetallic behavior in electrical transport down to low temperatures. Hall effect measurements indicate the presence of both electron- and hole-like carriers, with the latter identified with surface state conduction and the achievement of ambipolar transport in bulk Bi$_2$Se$_3$ crystals without gating techniques. With carrier mobilities surpassing the highest values yet reported for topological surface states in this material, the achievement of ambipolar transport via upward band bending is found to provide a key method to advancing the potential of this material for future study and applications.

Compositional effects on the low-temperature transport properties of non-stoichiometric Bi2TexSey-based crystals

We grew a series of non-stoichiometric crystals of the ternary alloy Bi2TexSey via a direct solidification route. The temperature-dependent electrical and thermal transport properties, such as electrical resistivity (ρ), Seebeck coefficient (S), Hall coefficient (RH), and thermal conductivity (κ), of six selected crystals of Bi2TexSey with x + y ~ 3 were studied. We found that the physical properties of the Bi2TexSey-based crystals varied significantly with the Te/Se (x/y) content. This is essentially due to the modification of the electronic band structure of the crystals with the change in sample composition, which ultimately leads to the formation of a p-type material (Bi2Te2.10Se0.66) from an n-type Bi2Te1.89Se0.98. Most importantly, the feature associated with surface-state conduction at low temperatures was also observed in some of these crystals, including Bi2Te1.89Se0.98, Bi2Te2.16Se0.71, and Bi2Te2.10Se0.66. In particular, two highly resistive compounds, Bi2Te2.16Se0.71 and Bi2Te2.10Se0.66 with low carrier densities were identified as potential materials for topological applications. The observed complex transport behavior was realized in connection with the formation of impurity bands (multiband effects) in the Bi2TexSey-based systems. Analysis of the lattice thermal conductivity of the Bi2TexSey-based crystals indicates that the sample composition has a major effect on low-temperature heat conduction via phonon-boundary and phonon-point-defect scattering. Finally, the highest room temperature thermoelectric figure of merit, a ZT of about 0.46, was achieved for n-type Bi2Te1.63Se1.23.

Characterization And Synthesis Of Bi2Se3 Topological Insulator Thin Film Using Thermal Evaporation

Topological insulators are the new phase of matter with bulk insulating and conducting surface states. Among the known three dimensional topological insulators, bismuth selenide (Bi2Se3) is one of the most promising materials for studying topological insulating properties. Bi2Se3 thin films are grown using thermal evaporation technique and atomically smooth films are obtained by post annealing treatment. Pure phase of Bi2Se3 is confirmed using x-ray diffraction; Raman spectroscopy shows a strong intensity of A 1 1g, E 2 g and A 2 1g modes in Bi2Se3 thin films. The surface studies on these films are carried out using scanning electron microscopy and atomic force microscopy. X-ray photoelectron spectroscopy (XPS) is used for elemental analyses in Bi2Se3 thin film. The surface quality of the film is improved with plasma etching (i.e. argon etching) in XPS. High quality Bi2Se3 thin films can be used further for investigation on transport properties of topological insulators. Copyright © 2016 VBRI Press.

Magnetic and nonmagnetic doping dependence of the conducting surface states inSmB6

Kondo insulator $\mathrm{Sm}{\mathrm{B}}_{6}$ has attracted attention because it can realize new topological phenomena driven by the interplay between strong correlation effect and topology. However, its topological nature is still under debate. To examine the topological aspect, we demonstrate the nonmagnetic La and magnetic Ce doping dependence of the resistance of $\mathrm{Sm}{\mathrm{B}}_{6}$. Moreover, the resistance ratios of different thicknesses are analyzed to confirm the surface contribution. Lightly doped La samples show a purely conducting surface region at low temperature, whereas the lightly doped Ce samples do not have any conducting region at low temperature. Furthermore, based on the analysis of the electrical transport data of $\mathrm{S}{\mathrm{m}}_{1\ensuremath{-}x}\mathrm{L}{\mathrm{a}}_{x}{\mathrm{B}}_{6}$ $(0.0\ensuremath{\le}x\ensuremath{\le}1.0)$, an electronic phase diagram was found, composed of four regions: region I $(0.0\ensuremath{\le}x\ensuremath{\le}0.06)$, II $(0.1\ensuremath{\le}x\ensuremath{\le}0.15)$, III $(x\ensuremath{\approx}0.2)$, and IV $(0.25\ensuremath{\le}x\ensuremath{\le}1.0)$. Region I is characterized by the presence of conducting surface states, region II is characterized by the insulating phase due to the $d\ensuremath{-}f$ hybridization gap without the conducting surface state, region III is characterized by the disappearance of the $d\ensuremath{-}f$ hybridization gap and the existence of valence fluctuation, and region IV is a typical metallic state.

Surface state conductivity in epitaxially grown Bi1−xSbx(111) films

Topologically non-trivial surface states were reported first on Sbx bulk crystals. In this study we present transport measurements performed on thin Sbx-films (up to 24 nm thickness) grown epitaxially on Si(111) with various Sb-concentrations (up to x = 0.22). The analysis of the temperature dependency allowed us to distinguish between different transport channels originating from surface and bulk bands as well as impurity states. At temperatures below 30 K the transport is mediated by surface states while at higher temperatures activated transport via bulk channels sets in. The surface state conductivity and bulk band gaps can be tuned by the Sb-concentration and film thickness, respectively. For films as thin as 4 nm the surface state transport is strongly suppressed in contrast to Bi(111) films grown under identical conditions. The impurity channel is of intrinsic origin due to the growth and alloy formation process and turns out to be located at the buried interface.

Low-temperature conducting state in two candidate topological Kondo insulators:SmB6andCe3Bi4Pt3

The authors have studied SmB${}_{6}$ and Ce${}_{3}$Bi${}_{4}$Pt${}_{3}$. Both of these Kondo insulators show a saturation of the increasing resistivity at low temperature that suggests an additional conduction channel and is consistent with the theoretical prediction that these systems should host robust surface states due to their nontrivial topology. While previous work has shown that the resistance saturation in SmB${}_{6}$ is due to conducting surface states, this work demonstrates that the origin of the resistance saturation in Ce${}_{3}$Bi${}_{4}$Pt${}_{3}$ is through the bulk of the material and not the surface. The contrasting behavior of the two materials when the surface is disordered with ion-irradiation supports this conclusion, and also demonstrates the sensitivity of the resistance of the surface state in SmB${}_{6}$ to small levels of disorder. Finally, the low-temperature specific heat of SmB${}_{6}$ shows a residual linear term, and the origin of this term has been highly debated recently. Through measurements of single crystals and powders, it is shown that this term dominantly arises from the bulk and not the surface state.

Gate‐Tunable Transport Properties of In Situ Capped Bi2Te3 Topological Insulator Thin Films

Combining of the ability to prepare high‐quality, intrinsic Bi2Te3 topological insulator thin films of low carrier density with in situ protective capping, a pronounced, gate‐tunable change in transport properties of Bi2Te3 thin films is demonstrated. Using a back gate, the carrier density is tuned by a factor of ≈7 in an Al2O3 capped Bi2Te3 sample and by a factor of ≈2 in Te capped Bi2Te3 films. Full depletion of bulk carriers is achieved, which allows access to the topological transport regime dominated by surface state conduction. When the Fermi level is placed in the bulk band gap, the presence of two coherent conduction channels associated with the two decoupled surfaces is observed. The magnetotransport results show that the combination of capping layers and electrostatic tuning of the Fermi level provide a technological platform to investigate the topological properties of surface states in transport experiments and pave the way toward the implementation of a variety of topological quantum devices.

Impurity effect on surface states of Bi (111) ultrathin films**Project supported by the National Basic Research Program of China (Grants Nos. 2015CB921400 and 2011CB921802) and the National Natural Science Foundation of China (Grants Nos. 11374057, 11434003, and 11421404).

The surface impurity effect on the surface-state conductivity and weak antilocalization (WAL) effect has been investigated in epitaxial Bi (111) films by magnetotransport measurements at low temperatures. The surface-state conductivity is significantly reduced by the surface impurities of Cu, Fe, and Co. The magnetotransport data demonstrate that the observed WAL is robust against deposition of nonmagnetic impurities, but it is quenched by the deposition of magnetic impurities which break the time reversal symmetry. Our results help to shed light on the effect of surface impurities on the electron and spin transport properties of a 2D surface electron systems.

A partially protected surface state

Physics A signature feature of topological insulators is conductive surface states that are immune to certain types of disorder. This “topological protection” appears to be at work in compounds such as Bi2Se3, in which electrons interact with one another only weakly. Whether these protected surface states exist in SmB6, a material whose insulating bulk is caused by strong electronic correlations, is still a subject of debate. Park et al. used a tunneling technique to find states on the surface of SmB6 that appeared to have the same linear dispersion as those in Bi2Se3 but were only partially protected. The loss of protection was caused by the interaction of the surface states with the magnetic excitations of the bulk. Proc. Natl. Acad. Sci. U.S.A. 10.1073/pnas.1606042113 (2016).