Surface States Of Dirac Fermions Research Articles

Topological Thermoelectric Materials Based on Bismuth Telluride

The main directions of experimental studies of topological insulators based on bismuth and antimony chalcogenides, which are related to the possibility of using the properties of the surface states of Dirac fermions in thermoelectricity, have been considered. The results of studies of the Van der Waals interlayer surface (0001) in single-crystal layered films of solid solutions of n- and p-type conductivity with substitutions of atoms in Bi and Te sublattices performed by micro-Raman spectroscopy, scanning tunneling microscopy, and scanning tunneling spectroscopy have been discussed. The oscillations of galvanomagnetic effects in strong magnetic fields and thermoelectric properties measured under normal conditions and at high pressures have been analyzed. The compositions of solid solutions in which the contribution of the surface states of Dirac fermions increases because of an increase in the surface concentration of fermions and the Fermi velocity depending on the energy of the Dirac point, the value of the Seebeck coefficient, and the power parameter have been determined.

Дифференциальная туннельная проводимость в многокомпонентных твердых растворах Bi-=SUB=-2-x-=/SUB=-Sb-=SUB=-x-=/SUB=-Te-=SUB=-3-y-z-=/SUB=-Se-=SUB=-y-=/SUB=-S-=SUB=-z-=/SUB=-

Differential tunnel conductance of the interlayer van der Waals surface (0001) was investigated in n-Bi2-xSbxTe3-y-zSeySz multicomponent solid solutions at x = 0.2, y = z = 0.09, optimized for near room temperatures with a high power factor, and at x = 0.4, y = 0, z = 0.06 with optimal thermoelectric properties for low temperatures and a high Seebek coefficient. It is shown that the intensity of the fluctuations of the Dirac point energy, a shift the top of the valence band and presence of surface levels in the energy gap formed by impurity defects is determined with composition and thermoelectric properties of solid solutions. The contribution of the surface states of Dirac fermions increases in n-Bi1.8Sb0.2Te2.82Se0.09S0.09 solid solution with a high power factor due to significant decrease of the surface concentration near the charge neutrality point and the growth of fermion mobility.

Гальваномагнитные свойства в анизотропных слоистых пленках на основе халькогенидов висмута

In anisotropic layered films of a multicomponent n-Bi1.92In0.02Te2.85Se0.15 solid solution in strong magnetic fields from 2 to 14 T at low temperatures, quantum oscillations of magnetoresistance associated with surface states of electrons in 3D topological insulators were studied. From the analysis of the spectral distribution of the amplitudes of quantum oscillations of magnetoresistance, the main parameters of the Dirac fermion surface states are determined. A comparison of the results with the data obtained by the method of scanning tunnel spectroscopy was carried out. It is shown that a high surface concentration determines the contribution of the Dirac fermion surface states to the thermoelectric properties of n-Bi1.92In0.02Te2.85Se0.15.

STM and STS studies of topological n-type (Bi, In)2(Te, Se, S)3 thermoelectrics

In topological n-type thermoelectrics based on Bi2Te3 with atomic substitutions Bi → In, Te → Se, S, the morphology and the surface states of Dirac fermions on the interlayer (0001) surface of van der Waals were studied by scanning tunneling microscopy and spectroscopy (STM/STS) techniques. By the STM method, the dark and light spots on the surface were found, which intensities depend on the composition and thermoelectric properties of solid solutions such as the Seebeck coefficient and thermoelectric power factor. The observed surface morphology features in the solid solutions are explained by distortions of surface electronic states originated from atomic substitutions, the influence of doping impurity, and formation mainly of substitutional impurity defects in thermoelectrics. The dips associated with substitutional impurities and antisite defects were found from the analysis of the height profiles obtained on the (0001) surface. Fast Fourier transform of the morphology STM images of the (0001) surface were used to obtain the interference patterns of the quasiparticles excitation caused by surface electrons scattering by defects. The Dirac point energy and its fluctuations, peak energies of surface defects, the positions of the valence and conduction band edges, and the energy gap were determined from an analysis of tunneling spectra. A correlation between the parameters of surface states of Dirac fermions and thermoelectric properties was found. Thus, a contribution of the fermions surface states increases with rise of the surface concentration in solid solutions with high power factor, and the largest concentration value was observed in the Bi1.98In0.02Te2.85Se0.15 composition. The dependences of Fermi energy on the wave vector for different solid solutions are described by a set of Dirac cone sections located within the limits of the fluctuations of the Dirac point energy that explained by weak changes of the Fermi velocity for studied atomic substitutions in sublattices of bismuth telluride.

Topological Surface States of Multicomponent Thermoelectrics Based on Bismuth Telluride

The surface states of Dirac fermions in p-Bi2Te3, p-Bi2 –xSbxTe3 –ySey, and p-Bi2 –x–ySnxGeyTe3 thermoelectrics were studied and its topological characteristics were obtained by scanning tunneling techniques in dependence on compositions. It was shown that the thermoelectric power factor and the material parameter enhance with the shift of the Dirac point to the top of the valence band with the increasing of atomic substitution in these thermoelectrics. A growth contribution of the surface states is determined by an increase of the Fermi velocity for large atomic substitutions of Bi at x > 1.5 and small substitutions in the Te sublattice (y = 0.06). In compositions with smaller substitutions at x = 1–1.3 and y = 0.06–0.09, similar effect of the surface states is determined due to raising the surface concentration of charge carriers.

Tuning Insulator-Semimetal Transitions in 3D Topological Insulator thin Films by Intersurface Hybridization and In-Plane Magnetic Fields.

A pair of Dirac points (analogous to a vortex-antivortex pair) associated with opposite topological numbers (with ±π Berry phases) can be merged together through parameter tuning and annihilated to gap the Dirac spectrum, offering a canonical example of a topological phase transition. Here, we report transport studies on thin films of BiSbTeSe_{2}, which is a 3D topological insulator that hosts spin-helical gapless (semimetallic) Dirac fermion surface states for sufficiently thick samples, with an observed resistivity close to h/4e^{2} at the charge neutral point. When the sample thickness is reduced to below ∼10 nm thick, we observe a transition from metallic to insulating behavior, consistent with the expectation that the Dirac cones from the top and bottom surfaces hybridize (analogous to a "merging" in the real space) to give a trivial gapped insulator. Furthermore, we observe that an in-plane magnetic field can drive the system again towards a metallic behavior, with a prominent negative magnetoresistance (up to ∼-95%) and a temperature-insensitive resistivity close to h/2e^{2} at the charge neutral point. The observation is consistent with a predicted effect of an in-plane magnetic field to reduce the hybridization gap (which, if small enough, may be smeared by disorder and give rise to a metallic behavior). A sufficiently strong magnetic field is predicted to restore and split again the Dirac points in the momentum space, inducing a distinct 2D topological semimetal phase with two single-fold Dirac cones of opposite spin-momentum windings.

Topological Surface States of Dirac Fermions in n-Bi2Te3 –ySey Thermoelectrics

In n-Bi2Te3 and n-Bi2Te3 –ySey thermoelectrics, the surface states of Dirac fermions of the interlayer Van der Waals surface (0001) are studied by scanning tunneling microscopy and spectroscopy. The surface morphology and modulated line profiles of the tunneling microscopy images are determined by local distortions of the surface density of electronic states and depend on the composition. The Dirac point ED in the studied compositions is localized in the band gap and shifts to the top of the valence band with increasing Se content in n-Bi2Te3 –ySey alloys. The dependence between the parameters of the surface states of Dirac fermions (Dirac-point position, Fermi velocity, surface fermion concentration) and thermoelectric properties (Seebeck coefficient and power parameter) in the thermoelectrics under study is determined.

Thermoelectric and Galvanomagnetic Properties of Layered n-Bi2 –xSbxTe3 –ySey Films

The thermoelectric properties in the temperature range 4.2–300 K and magnetoresistance oscillations in strong magnetic fields at low temperatures are studied in nanostructured layered films of topological thermoelectric materials n-Bi2 –xSbxTe3 –ySey. It is shown that the thermoelectric figure of merit in layered n-Bi2 –xSbxTe3 –ySey films is larger than that in the bulk material due both to an increase in the Seebeck coefficient below room temperature and to a decrease in the thermal conductivity and its weaker temperature dependence. Analysis of the magnetoresistance oscillations is used to determine the parameters of the topological surface states of Dirac fermions and estimate their influence on the thermoelectric properties.

Топологические поверхностные состояния фермионов Дирака в термоэлектриках n-Bi-=SUB=-2-=/SUB=-Te-=SUB=-3-y-=/SUB=-Se-=SUB=-y-=/SUB=-

Topological surface states of Dirac fermions in n-Bi2Te3−ySey thermoelectrics L.N. Lukyanova, I.V. Makarenko, O.A. Usov, P.A. Dementev Ioffe Institute, 194021 St. Petersburg, Russia Abstract In n-Bi2Te3 and n-Bi2Te3−ySey thermoelectrics, the surface states of Dirac fermions of the interlayer van der Waals plane (0001) were studied by scanning tunneling microscopy (STM) and spectroscopy. The surface morphology and modulated line profiles of the images in tunneling microscopy is determined by local distortions of the surface electron states density and depend on the composition. The Dirac point ED of the studied compositions is localized in the energy gap, and it shifts to the top of the valence band with increase of Se content in the solid solutions. The dependence between Dirac surface state parameters (the Dirac point position, the Fermi velocity, the fermion surface concentration) and thermoelectric properties (Seebeck coefficient and the power factor) is established for the thermoelectrics studied.

Термоэлектрические и гальваномагнитные свойства слоистых пленок n-Bi-=SUB=-2-x-=/SUB=-Sb-=SUB=-x-=/SUB=-Te-=SUB=-3-y-=/SUB=-Se-=SUB=-y-=/SUB=-

n nanostructured layered films of topological thermoelectrics n-Bi2−xSbxTe3−y Sey , thermoelectric properties in the temperature range of 4.2−300K and magnetoresistance oscillations in strong magnetic fields at low temperatures were studied. It is shown that thermoelectric efficiency in the layered n-Bi2−xSbxTe3−y Sey films increases as compared with bulk material due to both an increase in the Seebeck coefficient at the temperatures below room one, and a decrease in thermal conductivity and weakening of its temperature dependence. From the analysis of magnetoresistance oscillations, the parameters of topological surface states of Dirac fermions were determined and their influence on thermoelectric properties was estimated.

Scanning tunneling spectroscopy of the surface states of Dirac fermions in thermoelectrics based on bismuth telluride

The morphology of the interlayer van der Waals surface and differential tunneling conductance in p-Bi2−xSbxTe3−ySey solid solutions were studied by scanning tunneling microscopy and spectroscopy in dependence on compositions. The topological characteristics of the Dirac fermion surface states were determined. It was shown that the thermoelectric power factor and the material parameter enhance with the shift of the Dirac point to the top of the valence band with the increasing of atomic substitution in these thermoelectrics. A correlation between topological characteristics, power factor and material parameters was found. A growth contribution of the surface states is determined by an increase of the Fermi velocity for large atomic substitutions of Bi at x > 1.5 and small substitutions in the Te sublattice (y = 0.06). In compositions with smaller substitutions at x = (1–1.3) and y = (0.06–0.09), similar effect of the surface states is determined by raising the surface concentration of charge carriers.

Quantum confinement and heavy surface states of Dirac fermions in bismuth (111) films: An analytical approach

Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is a topologically nontrivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near the $\overline{\mathrm{M}}$ point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in the $\overline{\mathrm{\ensuremath{\Gamma}}}\text{\ensuremath{-}}\overline{\mathrm{M}}$ direction order of ten free electron masses and light effective mass in the $\overline{\mathrm{M}}\text{\ensuremath{-}}\overline{\mathrm{K}}$ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not split. In such a symmetric film with arbitrary thickness, the bottom of the lowest quantum confinement subband in the conduction band coincides with the bottom of the bulk conduction band in the $\overline{\mathrm{M}}$ point.

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.

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.

Transport properties of heteroepitaxial films based on bismuth telluride in strong magnetic fields

The temperature and magnetic-field dependences of the galvanomagnetic properties of n-Bi2Te3 heteroepitaxial films in magnetic fields to 14 T at low temperatures are studied. It is shown that steps in the magnetic-field dependences of the quantum Hall effect and the plateau in the temperature dependences of the magnetoresistance of films are caused by topological surface states of Dirac fermions.

On the density-of-states effective mass and charge-carrier mobility in heteroepitaxial films of bismuth telluride and Bi0.5Sb1.5Te3 solid solution

It is shown that the Seebeck coefficient α, the power factor α2σ, and the density-of-states effective mass m/m 0 in heteroepitaxial films of Bi0.5Sb1.5Te3 solid solution are higher than the corresponding characteristics of bulk thermoelectric materials. The elevated values and weak temperature dependences of these parameters lead to a rise in the parameter proportional to the effective mass, the charge-carrier mobility, and the figure of merit. The character of change in α, α2σ, and m/m 0 is determined by the peculiarities of the mechanism of charge-carrier scattering, the anisotropy of the constant-energy surface, and the possible influence of topological surface states of Dirac fermions in the films.

On the morphology of the interlayer surface and micro-Raman spectra of layered films in topological insulators based on bismuth telluride

Resonant micro-Raman spectra and the morphology of the interlayer Van der Waals surface are studied for layered thin films of n-Bi2Te3 and solid solutions based on Bi2Te3. It is found that the composition, thickness, surface morphology, and the method of obtaining films affect the relative intensity of Raman phonons, which are sensitive to the topological surface states of Dirac fermions.

Magnetic Dirac fermions and Chern insulator supported on pristine silicon surface

Emergence of ferromagnetism in non-magnetic semiconductors is strongly desirable, especially in topological materials thanks to the possibility to achieve quantum anomalous Hall effect. Based on first-principles calculations, we propose that for Si thin film grown on metal substrate, the pristine Si(111)-root3xroot3 surface with a spontaneous weak reconstruction has a strong tendency of ferromagnetism and nontrivial topological properties, characterized by spin polarized Dirac-fermion surface states. In contrast to conventional routes relying on introduction of alien charge carriers or specially patterned substrates, the spontaneous magnetic order and spin-orbit coupling on the pristine silicon surface together gives rise to quantized anomalous Hall effect with a finite Chern number C=-1. This work suggests exciting opportunities in silicon-based spintronics and quantum computing free from alien dopants or proximity effects.

Surface morphology and Raman spectroscopy of thin layers of antimony and bismuth chalcogenides

The phonon spectra in thin layers of bismuth telluride and solid solutions of Bi2–xSbxTe3–ySey of different composition, belonging to three-dimensional topological insulators, have been investigated by micro-Raman spectroscopy, and the morphology of an interlayer van der Waals (0001) surface in them has been studied by semicontact atomic force microscopy at room temperature. The analysis of the Raman spectra and the intensity ratio of active and inactive longitudinal optical modes depending on the composition, morphology of the interlayer surface, and thickness of the layers enabled the estimation of the effect of topological surface states of Dirac fermions, associated with the strengthening of the electron–phonon interaction as a result of resonance Raman scattering, and the identification of the compositions, in which the contribution of topological surface states becomes dominant.

Theory of interacting topological crystalline insulators

We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multi-valley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group $Z_8$. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap 8 flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of $U(1)\times Z_2$ symmetry-protected topological (SPT) phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between 3D topological phases protected by spatial symmetries and 2D topological phases protected by internal symmetries.