Program - Symposium MM: Topological Insulators

Two-dimensional (2D) topological insulators provide a wealth of fascinating properties caused by their protected edge-states. Several theoretical proposals for suitable materials have been made, however, most in an idealized state that is difficult to realize experimentally. Relaxations and reconstructions at the edges can modify the localization of the states or alter the number of conductive channels. Interaction of a nanoribbon with a substrate leads to doping and a changed spectrum. Although these influences will, in general, complicate the situation, they also offer the possibility to tune the materials properties, e.g., enhance spin-orbit coupling effects by proximity to the substrate. I will discuss these concepts mainly on the example of Bi bilayers and graphene ribbons, showing results of density-functional theory calculations together with experimental evidence, where available.

Three-dimensional topological insulators (3D TIs) recently emerge as a new state of quantum matter, which can be classified with Z₂ topological invariants [1]. It possesses a massless Dirac Fermion in a bulk energy gap whose spin orientations are locked with electron momentum, resulting in a helical spin texture. A number of 3D TIs have been intensively studied, among which Bi₂Se₃ has been regarded as one of the most promising candidates for potential applications in ultra-low power consumption quantum devices that can work stably at room temperature due to a sufficiently large bulk energy gap [2]. Therefore, a significant effort has been made towards spintronic applications using quantum topological transport, but the surface contribution to conduction was hardly observed even at low carrier density. Recently, the scanning tunneling microscopy has demonstrated that a strong surface state – bulk continuum scattering occurs near the Dirac node energy, which might limit the surface electron conduction in Bi₂Se₃ [3]. This observation stimulates us to search for new 3D TIs possessing more ideal Dirac Fermions sufficiently isolated from the bulk continuum as actually predicted in several ternary compounds [4]. Here we have studied the surface Dirac cones of several ternary chalcogenides including TlBiSe₂ and PbBi₂Te₄ by high-resolution angle resolved photoemission spectroscopy using synchrotron radiation at Hiroshima Synchrotron Radiation Center (HiSOR). The single topological surface state is confirmed to be present at the surface Brillouin zone (SBZ) center for TlBiSe₂. The Dirac cone is practically ideal especially near the Dirac point and its velocity is larger than for Bi₂Se₃. There are no bulk continuum states that energetically overlap with the DP, which means that the scattering channel from the topological surface state to the bulk continuum is suppressed. [5]. We have also clarified that PbBi₂Te₄ is the 3D TI, accompanying a single Dirac cone at the SBZ center. The size of the Fermi surface contours are significantly large in the bulk energy gap region. Besides, this material is found to have a Z₂ topological invariant 1; (111). These novel findings pave an effective way for controlling the group velocity with sufficiently large spin current density by tuning the chemical potential in the topological quantum transport region. References [1] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007). [2] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010). [3] S. Kim et al., Phys. Rev. Lett. 107, 056803 (2011). [4] B. Yan et al., Euro Phys. Lett. 90, 37002 (2010)./ S. V. Eremeev et al., JETP Lett. 92, 161 (2010)./ T. V. Menshchikova et al., JETP Letters 93, 15 (2011). [5] K. Kuroda et al., Phys. Rev. Lett. 105, 146801 (2010).

Intercalation of metal atoms into topological insulator materials can result in many profound effects such as superconductivity as demonstrated in Cu-intercalated Bi₂Se₃. We have recently developed a simple, wet-chemical method to intercalate high densities of zero-valent metal atoms into vapor-liquid-solid grown and hydrothermally synthesized chalcogenide Bi₂Se₃ nanoribbons. The zero-valent nature of the intercalant atoms allows super-stoichiometric amounts to be intercalated. Intercalated metallic atoms form essentially two-dimensional, atomically thin metal sheets possessing long-range atomic order. The reduced dimensionality results in many unexpected and surprising behaviors. We offer this as a new method towards accessing new and exciting physics in topological insulator nanomaterials.

Three-dimensional (3D) topological insulators (TIs) are a new state of quantum matter with a bulk gap generated by the spin orbit interaction and odd number of relativistic Dirac fermions on the surface. The robust surface states of TIs can be the host for many striking quantum phenomena, such as an image magnetic monopole induced by an electric charge and Majorana fermions induced by the proximity effect from a superconductor. Recently, several classes of materials were theoretically predicted to be the simplest 3D TIs whose surface states consist of a single Dirac cone. By investigating the surface state of these materials with angle-resolved photoemission spectroscopy (ARPES), we demonstrate that the surface state consists of a single Dirac cone; and with appropriate hole doping, the Fermi level (EF) can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Furthermore, by simultaneously introducing magnetic and charge doping into Bi2Se3 to break the time reversal symmetry and tune the EF, we observed a gap formation at the Dirac point and successfully realized the insulating massive Dirac fermion state. Our results not only confirm that a single surface Dirac cone exist in 3D materials, but also pave the way for promising applications.

Topological insulators (TIs) with interior bulk gap and gapless edge or surface states open new physical states of material, showing unique quantum mechanical phenomenon such as quantum spin Hall effect. To date, various TIs including HgTe, Bi1-xSbx, Bi2Te3, and Bi2Se3 are theoretically predicted and existence of the conducting surface states are confirmed experimentally. Recently, the possibility of TI with anisotropic Dirac cone in Ag2Te is predicted. However, despite extensive transport and magnetic properties on the Ag2Te since 1950s, so far experimental observation has not probed the sensitivity of TI nature. Here we report TI’s properties of single crystalline Ag2Te nanowires and nanoplates. Ag2Te nanowires exhibit clear Aharanov-Bohm (AB) oscillation with period fitted to h/e value. Angle and temperature dependences of AB oscillation confirm the existence of the conducting surface states in the Ag2Te nanowire. Ag2Te nanoplates show pronounced Shubnikov-de Haas (SdH) oscillation. The high carrier mobility exceeding 22,000 cm2/Vs and clear SdH oscillation are indebted to high crystallinity and low impurity of chemically synthesized Ag2Te nanostructures. All the experimental results support TI nature of Ag2Te and can lead new applications in nanoelectronics and spin-based transistor as well as understanding of intrinsic physics of topological insulator with highly anisotropic Dirac cone.

A key feature of the metallic surface states on topological insulators is the spin-momentum locking: the states are non-degenerate and the direction of the electron spin is defined for each momentum. Spin and angle-resolved photoemission spectroscopy can provide direct access to both these quantities and thus to the full details of the spin structure in momentum space. In collaboration with Hsieh, Hasan et al., we have successfully applied this technique to unambiguously verify that BiSb alloys [1] and Bi2Te3 and Bi2Se3 crystals [2] have a non-trivial topology. Due to our full vectorial measurement of the spin polarization, the coupling of the topological state to the crystal structure can be observed by the appearance of an out-of-plane spin component. In the limit of ultra-thin films the topological states from the top and bottom surface will hybridize, which leads to the formation of an energy gap and a spin mixing between the two boundaries. By using spin-resolved measurements at several photon energies on Bi2Se3 films of few quintuple-layer thickness we elucidate the evolution of the spin-structure with film thickness. Topological states generally appear at the boundary between topological and trivial matter, where the latter may be the vacuum. When the surface of a topological material is structurally disrupted enough, it may become trivial. In the topological insulator PbBi4Te7, which consists of alternating quintuple and septuple layers, there are indications that the topological state survives on a strongly perturbed surface simply by moving into the subsurface, to the new boundary between topological and trivial matter. [1] D. Hsieh et al. Science 323, 919 (2009). [2] D. Hsieh et al. Nature 460, 1101 (2009).

The electronic structure of the topological insulator Bi₂Se₃ was probed using angle-resolved photoemission spectroscopy (ARPES). The electronic properties of clean and adsorbate-covered samples were studied for a combination of different bulk dopings and adsorbates. Due to contamination on the surface, the Dirac point of the topological surface states moves to higher binding energies, indicating an increasingly strong downward bending of the bands near the surface. This time-dependent band bending can be accelerated by intentionally exposing the surface to carbon monoxide, alkali atoms and other species. For a sufficiently strong band bending, new spectral features in the energy region of both the valence band and the conduction band are found. These changes are explained by a confinement of the states and the formation of quantum well states. This interpretation is supported by simple calculations of the band bending effects and by photon energy-dependent ARPES measurement that show how the band dispersion in the direction perpendicular to the surface is lost and non-dispersing, sharp states appear within the energy regions of the projected bulk bands. For a strong band bending, the conduction band quantum well states are strongly Rashba split.

Topological surface states (TSS) are protected by time reversal symmetry (TRS) [1]. If we remove this protection by violating the TRS we expect drastic changes in the electronic structure as was shown in transport measurements in the 2D topological insulator case of HgTe quantum wells [2]. For three-dimensional topological insulators, much more efficient than an external magnetic field is the use of ferromagnetic impurities. Besides, many proposals already exist that suggest interesting effects connected to interfaces of ferromagnets and topological insulators. Our angle resolved photoemission studies are focussed on the in situ surface doping of three-dimensional topological insulators Bi2Te3 and Bi2Se3 with Fe. We give direct evidence that the TSS can withstand magnetic impurities. In contrast to a recent study [3], where a gap of 100 meV was reported, we show that the TSS remains intact and no gap opens even for Fe coverages in the monolayer regime. Moreover, we show that Fe can increase or decrease the Dirac point's binding energy depending on the temperature during deposition. Our findings are assisted by scanning tunneling microscopy and core level spectroscopy and suggest the possibility of interfacing topological insulators with ferromagnets for future device applications. We also report on a strong circular dichroism effect in angle-resolved photoemission of Bi2Te3 [4]. Our measurements reveal a strong variation of the strength and the sign of the effect, depending on the photon energy. By comparing the results with spin resolved measurements and with one-step-photoemission calculations we want to answer the question whether or not the strong spin momentum locking in topological insulators allows a spin detection without spin sensitive equipment. [1] Kane and Mele, Phy. Rev. Lett 95, 146802 (2005); Liang Fu, Kane and Mele, Phys. Rev. Lett. 98, 106803 (2007). [2] König et al., Science 318, 5851 (2007) [3] Wray et al., Nature Physics 7 (1), 32-37 (2010) [4] Scholz et al. arXiv:1108.1053v1

Topological insulators are characterized by their particular electronic structure which enables metallic like charge conduction at surfaces of an otherwise insulating material. Angular resolved photoemission spectroscopy (ARPES) is the obvious choice for studying the electronic structure of surfaces, and technological developments in the field of electron spectrometers and laboratory light sources have led to new possibilities in electronic structure determination. We have investigated thin films of the topological insulator Bi₂Se₃ in an ARPES experiment, where a laser is used for photo excitation and photoelectrons are detected with an angular resolving time-of-flight spectrometer. The laser system used in this study is operated at repetition rates between 200 kHz and 1 MHz and generates 10 ps photon pulses with a photon energy of 10.5 eV. This photon energy is high enough to enable one to cover a significant part of the Brillouin zone of many materials of current interest. On the other hand, it is low enough so that a significant part of the photo excited electrons come from the bulk or buried interfaces. The photoelectrons are detected with an angle resolving time-of-flight spectrometer, which can cover angle and energy windows of up to 30° and up to 70 eV, respectively. A maximum in-plane k vector 1.21 â„« can be reached. With this setup 3 dimensional momentum-momentum energy band dispersions can be recorded with high momentum and energy resolution. ARPES measurements have been performed on in-situ grown Bi₂Se₃ films grown on Bi-terminated Si(111). The thickness of the films varied between 6 QL (quintuple layer) and 12 QL. Thanks to the bulk sensitivity of laser ARPES the Dirac states located at the Bi₂Se₃-Si interface are clearly observed for the thinner films in addition to the vacuum interface states and quantum well states. The location of the Dirac point at the Si and vacuum interfaces as well as their evolution with time and thickness are discussed in the context of surface doping and band bending.

Known theoretically for decades, Majorana fermions have never been observed as fundamental particles. But there is growing excitement among condensed matter physicists that Majorana fermions could be observed as quasiparticles in the solid state. This excitement is fueled by their remarkable properties: They are their own antiparticle and obey an exotic (and yet unobserved) form of quantum statistics called non-Abelian statistics. These properties make Majorana fermions the simplest candidate for realizing topological quantum information processing which could go a long way towards alleviating the problem of decoherence in conventional quantum computation. Among the systems predicted to support Majorana fermions are exotic fractional quantum Hall states as well as hybrid structures of topological insulators, semimentals, or semiconductors with conventional superconductors. Realizations based on semiconductor quantum wires in proximity to conventional superconductors are perhaps particularly promising since they allow for relatively detailed scenarios of how to manipulate Majorana fermions. In this talk, I will discuss this proposal including recent developments.

Three dimensional topological insulators (TIs), a new quantum state of matter, have recently become a fertile farmland in which plenty of exotic quantum physical phenomena can grow. By introducing superconducting states into a TI via superconducting proximity effect, namely Cooper pairs tunneling into TI at TI/SC interface, the interplay between TI and SC can lead to the Majorana Fermions (MFs). MFs in solids obey highly unusual non-Abelian quantum statistics, are considered as the most promising candidate for fault-tolerant quantum computation. Here we report scanning tunneling microscopy (STM) observation of superconductivity in Bi2Se3 thin films grown on BCS type s-wave superconductor NbSe2 by molecular beam epitaxy (MBE) technique. Our data show that the Cooper pairs formation persists in the thickness regime from one quintuple layer (QL) up to seven QLs of Bi2Se3 at which topological order forms. This observation lays the groundwork for experimentally realizing MFs in condensed matter physics. In cooperation with Mei-Xiao Wang, Canhua Liu, Jin-Peng Xu, Fang Yang, Lin Miao, Meng-Yu Yao, C. L. Gao, Chenyi Shen, Xucun Ma, X. Chen, Zhu-An Xu, Ying Liu, Shou-Cheng Zhang, Dong Qian and Qi-Kun Xue

The long-sought yet elusive Majorana fermion is predicted to arise from a combination of a superconductor and a topological insulator. An essential step in the hunt for this emergent particle is the unequivocal observation of supercurrent in a topological phase. Here, we present direct evidence for a Josephson supercurrent in superconductor (Nb) - topological insulator (Bi2Te3) - superconductor e-beam fabricated junctions by the observation of clear Shapiro steps under microwave irradiation, and a Fraunhofer-type dependence of the critical current on magnetic field. The dependence of the critical current on temperature and electrode spacing shows that the junctions are in the ballistic limit. Shubnikov-de Haas oscillations in magnetic fields up to 30 T reveal a topologically non-trivial two-dimensional surface state. We argue that the ballistic Josephson current is hosted by this surface state despite the fact that the normal state transport is dominated by diffusive bulk conductivity. The lateral Nb-Bi2Te3-Nb junctions hence provide prospects for the realization of devices supporting Majorana fermions.