Session S03: Topological Phases and Their Excitations

Growth of a predicted two-dimensional topological insulator based on InBi-Si(111)-√7×√7

Using combined scanning tunneling microscopy (STM) measurements and first-principles electronic structure calculations, we extensively studied the atomic and electronic properties of a √7-InBi overlayer on Si(111). We propose and demonstrate an effective experimental process to successfully form a large well-ordered √7 surface by depositing Bi atoms on the In-Si(111)-4×1 substrate. The STM images exhibit a honeycomb pattern. After performing an exhaustive computational search, we identified the atomic structures of the surface at In and Bi coverages of 6/7 and 3/7 monolayers, respectively. We discovered a trimer model with a lower energy than the previously proposed model. The simulated STM images of trimer models confirm the presence of the honeycomb pattern in accord with our experimental STM images. Most importantly, we found that the surface is robust, preserving the topologically nontrivial phase. Our edge state calculations verify that the InBi overlayer on Si(111) is indeed a two-dimensional topological insulator (TI). Moreover, hybrid functional calculations result in band gaps up to 70 meV, which is high enough for room-temperature experiments. Our findings lay the foundation for the materials realization of 2D TIs by growing an InBi overlayer on a Si(111) substrate.   

Topological Phase Transition from a Quantum Spin Hall Insulator to a Chern Insulator

The effect of magnetic field on electronic transport in InAs/GaSb quantum spin Hall systems is investigated. As theoretical works [1-3] indicate, the system will undergo an insulator-metal-insulator phase transition at a critical magnetic field where the lowest Landau Levels (LLs) of electron and hole cross. Here we observe a distinct bulk conductance peak emerging around 12T in InAs/GaSb double layer systems. Both its temperature dependence and abruptly increasing signal fluctuation is consistent with a metallic phase arising from the topological phase transition between a QSHI phase and a Chern insulator phase. In the meanwhile the response of helical edge state is also systematically studied and the results will be presented.

[1] D. Pikulin, T. Hyart, S. Mi et al., Phy. Rev. B 89, 161403 (R) (2014)
[2] S. Zhang, Y. Zhang and S. Shen, Phy. Rev. B 90, 115305 (2014)
[3] J. Chen, J. Wang and Q. Shun, Phy. Rev. B 85, 125401 (2012)   

Shift insulators: rotation-protected two-dimensional topological crystalline insulators

We study a two-dimensional tight-binding model of a topological crystalline insulator protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g. p_± orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. We show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed on addition of appropriate atomic orbitals, which implies 'fragile' topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients.
Ref: S. Liu, A. Vishwanath, E. Khalaf, arXiv: 1809.01636.   

Scanning tunneling microscopy and spectroscopy on strong spin-orbit coupling chalcogenides

A large number of A₂B₃ type chalcogenides with strong spin-orbit coupling like Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ etc. are topological insulators (TI) whereas Sb₂Se₃ is an exception in this group. In this talk, I will show, as the TI Bi₂Se₃, Sb₂Se₃ displays generation of highly spin-polarized current by point contact Andreev reflection spectroscopy. However, unlike in Bi₂Se₃, in case of Sb₂Se₃, a prominent quasiparticle interference (QPI) pattern could be observed in STM conductance mapping which contradicts the above experiment. According to the band structure calculation, there are two trivial surface states available and among them, one shows large splitting due to Rashba type spin-orbit coupling. In addition, we observe a large negative and anisotropic magnetoresistance in Sb₂Se₃. Experimental data reveal Sb₂Se₃ to be a trivial band insulator under ambient conditions with high spin-polarization due to Rashba type spin-orbit coupling.   

A new topological crystalline insulator state in the TaAs2materials class

Crystalline symmetries drive a variety of topological crystalline insulator (TCI) phases in materials. Here, based on first-principles calculations combined with associated symmetry analysis, we identify a new rotational-symmetry protected TCI state in the TaAs₂family of compounds. The low-energy band structure consists of two bulk nodal lines in the absence of spin-orbit coupling (SOC) effects. Turning on the SOC opens a continuous band gap in the spectrum and drives the system into a C₂Tsymmetry protected TCI state. On the (010) surface, we show the presence of rotational-symmetry-protected nontrivial Dirac cone states within a local bulk energy gap of 300 meV. Our results indicate that the TaAs₂materials family provides an ideal setting for exploring unique physics associated with the rotational-symmetry protected TCIs.   

Conductance Oscillations in Gated Topological Insulator Heterostructures

Recent theoretical studies have shown that the properties of the surface state of 3D Topological Insulators (TIs) may be different from the topological interface states in a heterostructure containing TIs [1]. Directly accessing these interface states is, however, challenging. We propose that a transport measurement on a gated double junction sandwich device yields critical information about the topological interface states. We show that the conductance oscillations as a function of the gating potential can be used to extract the Fermi velocity and other parameters characterizing their dispersion. Crucially, these results are only weakly dependent on the boundary conditions at the lateral sandwich junctions. We discuss relevance of our results to proposed applications of TIs in functional devices.

[1] Mahmoud M. Asmar, Daniel E. Sheehy and Ilya Vekhter, PRB 95 241115 (2017).   

Tunable skyrmion-skyrmion interactions on the surface of a three dimensional topological insulator

The surface of a three-dimensional topological insulator is characterized by a gapless two-dimensional Dirac cone dispersion. In a magnetic topological insulator, this surface dispersion is gapped by a Zeeman term proportional to the local magnetization. Magnetic skyrmions—stable, low energy excitations in chiral planar magnetic systems—lead to sign changes in this Zeemen term and, consequently, topologically protected bound states. It has been shown previously [1] that magnetic skyrmions on the surface of a topological insulator may result in a discrete set of localized orbitals—skyrmion bound states. We study the skyrmion-skyrmion interaction mediated by the hybridization of these orbitals. In particular, we consider the effective interaction between a pair of skyrmions in the presence of their hybridized orbitals. We show that the skyrmions form a bound state for high chemical potential. For low chemical potential their interaction is strictly repulsive. For intermediate chemical potential, both the bound and the unbound configurations locally minimize the free energy. We support our phenomenological theory with numerical calculations.

[1] H. M. Hurst, D. K. Efimkin, J. Zang, and V. Galitski, Phys. Rev. B, 91, 060401 (2015)   

Strain-driven topological phase transitions and tunable topological states in the Bi2Se3 family.

Strain allows for a controlled manipulation of the topological order and Dirac states in three-dimensional Bi-chalcogenide topological insulators. Based on ab-initio density functional methods, we predict a universal phase diagram for the Bi₂Se₃ family. Under elastic strain these compounds present metallic, topological and trivial insulating phases. Furthermore, by strain engineering we built realistic topological homojunctions (THs) in Bi₂Se₃. We show how the topological interface states arising in such THs can be reversibly tuned along with their electron doping, spatial localization and mutual interaction. A TH contains the simplest topological interface, and hence constitutes the 'Hydrogen atom' of topological states of matter. Our findings show a route to tune the topological states within the field of straintronics.

[1] Strain effects in topological insulators: topological order and the emergence of switchable topological interface states in Sb₂Te₃/Bi₂Te₃ heterojunctions. H Aramberri, MC Muñoz, Phys. Rev. B 95, 205422 (2017).
[2] Strain-driven tunable topological states in Bi₂Se₃. H Aramberri, MC Muñoz, J. Phys. Mater. 1 (1), 015009 (2018).   

Closing the surface bandgap in thin Bi2Se3/graphene heterostructures

Topological insulator (TI), a band insulator with topologically protected edge states, is one of the most interesting materials in the field of condensed matter. For application, suppression of the bulk effect is crucial, but in ultrathin TI materials, with thicknesses less than 3 QL, the surface band has a finite bandgap because of the hybridization between the top and bottom surface states. Here, we studied the gapless top surface Dirac state of strained 3 QL Bi₂Se₃/graphene heterostructures. A strain caused by the graphene layer reduces the bandgap of surface states, and the band bending resulting from the charge transfer at the Bi₂Se₃-graphene interface induces localization of surface states to each top and bottom layer to suppress the overlap of the two surface states. In addition, we verified the independent transport channel of the top surface Dirac state in Bi₂Se₃/graphene heterostructures by measuring the magneto-conductance. Our findings suggest that the strain and the proximity effect in TI/non-TI heterostructures may be feasible ways to engineer the topological surface states beyond the physical and topological thickness limit.   

Surface states of topological crystalline insulators

We study topological crystalline insulator (TCI) phases hosting anomalous surface states. These include traditional surface states with two-dimensional Dirac dispersion as well as one-dimensional hinge modes characteristic of higher-order phases. Both of these can be captured by analyzing a general surface theory with multiple flavors of Dirac fermions and identifying global symmetry obstructions to achieving a fully gapped surface. This method is used to obtain a full classification of TCIs protected by time-reversal symmetry in the presence of strong spin-orbit coupling in the 230 space groups as well as TCIs protected by inversion in the ten different Altland-Zirnbauer symmetry classes. Furthermore, we establish a correspondence between the existence of surface states in a TCI and the existence of a stable (rather than fragile) obstruction to finding a basis of symmetric localized Wannier functions. Finally, we discuss possible extension of the results to magnetic space groups.   

THz spectroscopy of ultralow carrier density topological insulator thin films

Sb₂Te₃ is one of the earliest known examples of a 3D topological insulator with a single Dirac cone on the surface. Pure Sb₂Te₃ is generally p-doped with the Fermi level embedded in the bulk valence band which makes it challenging to study surface state dynamics through transport and optical measurements. Only recently, bulk insulating Sb₂Te₃ thin films have been grown using molecular beam epitaxy via chemical doping and buffer layer engineering. In addition, the carrier densities in these films are exceptionally low, nearly an order of magnitude lower than the best results obtained in Bi₂Se₃. Here we report the magneto-optical response of regular and bulk insulating (p-type and n-type) Sb₂Te₃ films at THz frequencies using time-domain polarimetry. While undoped, bulk conducting samples exhibit usual semiclassical behaviour, the bulk insulating samples show unusual optical properties and quantized response in presence of magnetic fields.   

Strong Pumping of Fragile Topology in Higher-Order Topological Insulators and Semimetals

To gain insight on their response and surface states, topological insulators (TIs) and semimetals are frequently re-expressed as periodic tuning cycles of lower-dimensional insulators with nontrivial topology or multipole moments. The recent discovery of 3D higher-order TIs (HOTIs) and semimetals, which exhibit gapless 1D hinges, poses a clear question: “what are the possible 2D insulators that may be pumped to realize higher-order topology?” We answer this question by demonstrating that 2D “fragile” TIs, which are only topologically nontrivial for small numbers of valence bands, exhibit the same anomalous 0D corner modes as 2D obstructed atomic limits. We reveal that the most general HOTIs, including the well-studied “axion insulator,” are equivalent to pumping cycles of fragile-phase corner charge, and introduce nested Wilson loop invariants to diagnose corner charges in 2D and strong pumping in 3D. We then extend discussion to more exotic examples. Finally, we show that the fragile-phase pumping formulation directly implies the crystal defect and flux responses of 3D HOTIs and weak fragile TIs.   

Boundary networks of helical or chiral edges induced by bulk topology

We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are two-dimensional second-order topological insulators and three-dimensional topological fullerenes. As a consequence of bulk-edge correspondence, these edge networks can faithfully predict properties such as the energy and fractional charge related to the bound states (edge solitons) in the aforementioned systems, including several aspects that were previously complicated or obscure.   

Seebeck effect in 3D topological insulator thin films

Growing thin films is one of the methods to investigate the intrinsic physical properties of Dirac surface state in three-dimensional Topological insulators (3D-TIs). However, the suppression of the bulk in thin films can be recognized only at low temperatures, and no systematic study has been carried out to confirm whether surface dominant transport can be realized in a wide range of temperature. Here, we report our systematic measurements of sheet resistance (R), Hall coefficient (R_H), Shubnikov-de-Haas (SdH) quantum oscillations, Seebeck coefficient (S) as a function of both thickness (d) and temperature (T) using high-quality Bi_2-xSb_xTe_3-ySe_y single crystal thin films. R and S shift systematically from the bulk/surface coexisting regime to the surface dominant one by reducing d. S of thinner films clearly shows a linear T-dependence with a negative polarity from 300 to 2K, indicating a surface dominant transport in a wide-temperature region. Quantitative arguments are made as to how the contribution of bulk carrier can be suppressed, using both R_H and SdH measurements. We propose that Seebeck coefficient can become a convenient and powerful tool to evaluate the intrinsic carrier concentration for the topological surface in 3D-TIs even in the absence of magnetic field.   

Glide-symmetric topological crystalline insulators with inversion symmetry

It is known that three-dimensional systems with glide symmetry can be characterized by a Z₂ topological invariant in class A, and it is expressed in terms of integrals of the Berry curvature. In this presentation, we consider what happens to the glide-Z₂ invariant, when the inversion symmetry is added. There are two ways to add the inversion symmetry, leading to the space group No. 13 or No. 14. In the space group 13, we find that the glide-Z₂ invariant is expressed in terms of the irreducible representations at high-symmetric points in the moment space, which constitutes the Z₂×Z₂ symmetry-based indicators for this space group, together with the Chern number modulo 2. In the space group 14, we find that the symmetry-based indicator Z₂ is given by the combination of the glide-Z₂ invariant and the Chern number. From the irreducible representations at high-symmetry points in this case, we can only know possible combinations of the glide-Z₂ invariant and the Chern number. Moreover, we show that in both cases the Z₄ strong topological invariant for inversion symmetric systems is directly related to the glide-Z₂ invariant and the Chern number. Finally, we also investigate topological invariants for glide-symmetric systems with nonprimitive lattice with and without inversion symmetry.