Hsin Lin

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface

Y. Xia, 2 D. Qian, 3 D. Hsieh, 2 L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan 2 Department of Physics, Princeton University, Princeton, NJ 08544, USA Princeton Center for Complex Materials, Princeton University, Princeton, NJ 08544, USA Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China Department of Physics, Northeastern University, Boston, MA 02115, USA Department of Chemistry, Princeton University, Princeton, NJ 08544, USA (Dated: Submitted for publication in December 2008)

A tunable topological insulator in the spin helical Dirac transport regime

Helical Dirac fermions—charge carriers that behave as massless relativistic particles with an intrinsic angular momentum (spin) locked to its translational momentum—are proposed to be the key to realizing fundamentally new phenomena in condensed matter physics. Prominent examples include the anomalous quantization of magneto-electric coupling, half-fermion states that are their own antiparticle, and charge fractionalization in a Bose–Einstein condensate, all of which are not possible with conventional Dirac fermions of the graphene variety. Helical Dirac fermions have so far remained elusive owing to the lack of necessary spin-sensitive measurements and because such fermions are forbidden to exist in conventional materials harbouring relativistic electrons, such as graphene or bismuth. It has recently been proposed that helical Dirac fermions may exist at the edges of certain types of topologically ordered insulators—materials with a bulk insulating gap of spin–orbit origin and surface states protected against scattering by time-reversal symmetry—and that their peculiar properties may be accessed provided the insulator is tuned into the so-called topological transport regime. However, helical Dirac fermions have not been observed in existing topological insulators. Here we report the realization and characterization of a tunable topological insulator in a bismuth-based class of material by combining spin-imaging and momentum-resolved spectroscopies, bulk charge compensation, Hall transport measurements and surface quantum control. Our results reveal a spin-momentum locked Dirac cone carrying a non-trivial Berry’s phase that is nearly 100 per cent spin-polarized, which exhibits a tunable topological fermion density in the vicinity of the Kramers point and can be driven to the long-sought topological spin transport regime. The observed topological nodal state is shown to be protected even up to 300u2009K. Our demonstration of room-temperature topological order and non-trivial spin-texture in stoichiometric Bi2Se3.Mx (Mx indicates surface doping or gating control) paves the way for future graphene-like studies of topological insulators, and applications of the observed spin-polarized edge channels in spintronic and computing technologies possibly at room temperature.Princeton University, Princeton, NJ 08544, USA Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China Swiss Light Source, Paul Scherrer Institute, CH-5232, Villigen, Switzerland Physik-Institut, Universität Zürich-Irchel, 8057 Zürich, Switzerland Advanced Light Source, Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA Department of Physics, Northeastern University, Boston, MA 02115, USA Department of Chemistry, Princeton University, Princeton, NJ 08544, USA Princeton Center for Complex Materials, Princeton University, Princeton NJ 08544, USA

Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2

Quantum systems in confined geometries are host to novel physical phenomena. Examples include quantum Hall systems in semiconductors and Dirac electrons in graphene. Interest in such systems has also been intensified by the recent discovery of a large enhancement in photoluminescence quantum efficiency and a potential route to valleytronics in atomically thin layers of transition metal dichalcogenides, MX2 (M = Mo, W; X = S, Se, Te), which are closely related to the indirect-to-direct bandgap transition in monolayers. Here, we report the first direct observation of the transition from indirect to direct bandgap in monolayer samples by using angle-resolved photoemission spectroscopy on high-quality thin films of MoSe2 with variable thickness, grown by molecular beam epitaxy. The band structure measured experimentally indicates a stronger tendency of monolayer MoSe2 towards a direct bandgap, as well as a larger gap size, than theoretically predicted. Moreover, our finding of a significant spin-splitting of ∼ 180 meV at the valence band maximum of a monolayer MoSe2 film could expand its possible application to spintronic devices.

Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena

Topological insulators (TI) realize a novel state of quantum matter that are distinguished by topological invariants of bulk band structure rather than spontaneously broken symmetries. A number of exotic quantum phenomena have been predicted to exist in multiply-connected geometries which require an enormous amount of materials flexibility. We have extended our previous search for TI materials from binary (Bi2X3 series) to the thermoelectric ternary compounds. We discover that the distorted LuPtSb is the first ternary compound harboring a 3D topological insulator state. We also show that the half-Heusler LuPtSb-type series is a natural platform that hosts a range of candidate compounds, alloys and artificial heterostructures (quantum-wells). We also discovered several different paradigms of trivial and non-trivial topological ordering in this class, including a metallic nontrivial topological state in YAuPb. Some of these materials are grown (results will be reported separately).Recent discovery of spin-polarized single-Dirac-cone insulators, whose variants can host magnetism and superconductivity, has generated widespread research activity in condensed-matter and materials-physics communities. Some of the most interesting topological phenomena, however, require topological insulators to be placed in multiply connected, highly constrained geometries with magnets and superconductors, all of which thus require a large number of functional variants with materials design flexibility as well as electronic, magnetic and superconducting tunability. Given the optimum materials, topological properties open up new vistas in spintronics, quantum computing and fundamental physics. We have extended the search for topological insulators from the binary Bi-based series to the ternary thermoelectric Heusler compounds. Here we show that, although a large majority of the well-known Heuslers such as TiNiSn and LuNiBi are rather topologically trivial, the distorted LnPtSb-type (such as LnPtBi or LnPdBi, Ln = f(n) lanthanides) compounds belonging to the half-Heusler subclass harbour Z(2) = -1 topological insulator parent states, where Z(2) is the band purity product index. Our results suggest that half-Heuslers provide a new platform for deriving a host of topologically exotic compounds and their nanoscale or thin-film device versions through the inherent flexibility of their lattice parameter, spin-orbit strength and magnetic moment tunability paving the way for the realization of multifunctional topological devices.

A topological insulator surface under strong Coulomb, magnetic and disorder perturbations

Topological insulators embody a state of bulk matter characterized by spin-momentum-locked surface states that span the bulk bandgap. This highly unusual surface spin environment provides a rich ground for uncovering new phenomena. Understanding the response of a topological surface to strong Coulomb perturbations represents a frontier in discovering the interacting and emergent many-body physics of topological surfaces. Here we present the first controlled study of topological insulator surfaces under Coulomb and magnetic perturbations. We have used time-resolved deposition of iron, with a large Coulomb charge and significant magnetic moment, to systematically modify the topological spin structure of the Bi_2Se_3 surface. We observe that such perturbation leads to the creation of odd multiples of Dirac fermions and that magnetic interactions break time-reversal symmetry in the presence of band hybridizations. We present a theoretical model to account for the observed electron dynamics of the topological surface. Taken collectively, these results are a critical guide in controlling electron mobility and quantum behaviour of topological surfaces, not only for device applications but also in setting the stage for creating exotic particles such as axions or imaging monopoles on the surface.

Observation of a topological crystalline insulator phase and topological phase transition in Pb 1− x Sn x Te

A topological insulator protected by time-reversal symmetry is realized via spinorbit interaction driven band inversion. The topological phase in the Bi1−xSbx system is due to an odd number of band inversions. A related spin-orbit system, the Pb1−xSnxTe, has long been known to contain an even number of inversions based on band theory. Here we experimentally investigate the possibility of a mirror symmetry protected topological crystalline insulator phase in the Pb1−xSnxTe class of materials which has been theoretically predicted to exist in its end compound SnTe. Our experimental results show that at a finite-Pb composition above the topological inversion phase transition, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order distinct from that observed in Bi1−xSbx. Our observation of the spin-polarized Dirac surface states in the inverted Pb1−xSnxTe and their absence in the non-inverted compounds related via a topological phase transition provide the experimental groundwork for opening the research on novel topological order in quantum devices.A topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction-driven band inversion. The topological phase in the Bi(1-x)Sb(x) system is due to an odd number of band inversions. A related spin-orbit system, the Pb(1-x)Sn(x)Te, has long been known to contain an even number of inversions based on band theory. Here we experimentally investigate the possibility of a mirror symmetry-protected topological crystalline insulator phase in the Pb(1-x)Sn(x)Te class of materials that has been theoretically predicted to exist in its end compound SnTe. Our experimental results show that at a finite Pb composition above the topological inversion phase transition, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order distinct from that observed in Bi(1-x)Sb(x). Our observation of the spin-polarized Dirac surface states in the inverted Pb(1-x)Sn(x)Te and their absence in the non-inverted compounds related via a topological phase transition provide the experimental groundwork for opening the research on novel topological order in quantum devices.

Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator

Two types of bulk insulator are realized in the same family of compounds through chemical doping. The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S1–δSeδ)2, in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum–locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.

Observation of topological order in a superconducting doped topological insulator

When doped with copper, the topological insulator Bi2Se3 becomes superconducting. But for new physics and applications the search is not for just any superconductor; the material must retain its topological character. And indeed that is the case with doped Bi2Se3.

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator

Half-Massless Certain materials, such as topological crystalline insulators (TCIs), host robust surface states that have a Dirac (graphene-like) dispersion associated with massless carriers; the breaking of protective symmetry within such materials should cause the carriers to acquire mass. Okada et al. (p. 1496, published online 29 August) used scanning tunneling microscopy to map out the energies of the electronic levels of the TCI Pb1-xSnxSe as a function of the strength of an external magnetic field. The massless Dirac fermions coexisted with massive ones, presumably as a consequence of a distortion of the crystalline structure affecting only one of the two mirror symmetries. Scanning tunneling spectroscopy of Pb1–xSnxSe in a magnetic field reveals two types of Dirac fermions. In topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with distinct characteristics. The breaking of crystal symmetry in TCIs is predicted to impart mass to the massless Dirac fermions. Here, we report high-resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe that reveal the coexistence of zero-mass Dirac fermions protected by crystal symmetry with massive Dirac fermions consistent with crystal symmetry breaking. In addition, we show two distinct regimes of the Fermi surface topology separated by a Van-Hove singularity at the Lifshitz transition point. Our work paves the way for engineering the Dirac band gap and realizing interaction-driven topological quantum phenomena in TCIs.

Single-Dirac-cone topological surface states in the TlBiSe(2) class of topological semiconductors.

We investigate several strong spin-orbit coupling ternary chalcogenides related to the (Pb,Sn)Te series of compounds. Our first-principles calculations predict the low-temperature rhombohedral ordered phase in TlBiTe₂, TlBiSe₂, and TlSbX₂ (X=Te, Se, S) to be topologically nontrivial. We identify the specific surface termination that realizes the single Dirac cone through first-principles surface state computations. This termination minimizes effects of dangling bonds, making it favorable for photoemission experiments. In addition, our analysis predicts that thin films of these materials could harbor novel 2D quantum spin Hall states, and support odd-parity topological superconductivity.