Colloquium : Topological band theory Bansil, A.; Lin, Hsin; Das, Tanmoy
Reviews of modern physics,
06/2016, Letnik:
88, Številka:
2
Journal Article
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The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient ...characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. This review begins by discussing underpinnings of the topological band theory, which involve a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder and interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary, and quaternary compounds, transition metal and functionof-electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites, and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultrathin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. This Colloquium concludes by giving a perspective on research directions where further work will broadly benefit the topological materials field.
A topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction-driven band inversion. The topological phase in the Bi1-x Sbx system is due to an odd number of band ...inversions. A related spin-orbit system, the Pb1-x Snx 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 Pb1-x Snx 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 Bi1-x Sbx . Our observation of the spin-polarized Dirac surface states in the inverted Pb1-x Snx 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.
The Kondo insulator SmB6 has long been known to exhibit low-temperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the ...anomalous transport regime by combining state-of-the-art laser and synchrotron-based angle-resolved photoemission techniques. We observe clear in-gap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB6.
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— δ Se δ )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.
Silicene is a one-atom-thick two-dimensional crystal of silicon with a hexagonal lattice structure that is related to that of graphene but with atomic bonds that are buckled rather than flat. This ...buckling confers advantages on silicene over graphene, because it should, in principle, generate both a band gap and polarized spin-states that can be controlled with a perpendicular electric field. Here we use first-principles calculations to show that field-gated silicene possesses two gapped Dirac cones exhibiting nearly 100% spin-polarization, situated at the corners of the Brillouin zone. Using this fact, we propose a design for a silicene-based spin-filter that should enable the spin-polarization of an output current to be switched electrically, without switching external magnetic fields. Our quantum transport calculations indicate that the proposed designs will be highly efficient (nearly 100% spin-polarization) and robust against weak disorder and edge imperfections. We also propose a Y-shaped spin/valley separator that produces spin-polarized current at two output terminals with opposite spins.
We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of 'beyond graphene' compounds, including films of transition-metal dichalcogenides ...(TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.
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 300 K. 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.
Recent experiments and theories have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, ...which can show macroscopic quantum-entanglement effects. Such systems feature two-dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe interacting quarks. It has been proposed that a topological insulator with a single Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study that reveals the first observation of such a topological state of matter featuring a single surface Dirac cone realized in the naturally occurring Bi2Se3 class of materials. Our results, supported by our theoretical calculations, demonstrate that undoped Bi2Se3 can serve as the parent matrix compound for the long-sought topological device where in-plane carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.
We review the intermediate coupling model for treating electronic correlations in the cuprates. Spectral signatures of the intermediate coupling scenario are identified and used to adduce that the ...cuprates fall in the intermediate rather than the weak or the strong coupling limits. A robust, 'beyond local-density approximation' framework for obtaining wide-ranging properties of the cuprates via a GW-approximation based self-consistent self-energy correction for incorporating correlation effects is delineated. In this way, doping- and temperature-dependent spectra, from the undoped insulator to the overdoped metal, in the normal as well as the superconducting state, with features of both weak and strong coupling can be modeled in a material-specific manner with very few parameters. Efficacy of the model is shown by considering available spectroscopic data on electron- and hole-doped cuprates from angle-resolved photoemission, scanning tunneling microscopy/spectroscopy, neutron scattering, inelastic light scattering, optical and other experiments. Generalizations to treat systems with multiple correlated bands such as the heavy-fermions, the ruthenates and the actinides are discussed.
We study interference patterns of a magnetically doped topological insulator Bi(2-x)Fe(x)Te(3+d) by using Fourier transform scanning tunneling spectroscopy and observe several new scattering ...channels. A comparison with angle-resolved photoemission spectroscopy allows us to unambiguously ascertain the momentum-space origin of distinct dispersing channels along high-symmetry directions and identify those originating from time-reversal symmetry breaking. Our analysis also reveals that the surface state survives far above the energy where angle-resolved photoemission spectroscopy finds the onset of continuum bulk bands.
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