Noncompact atomic insulators

We study the conditions for Bloch bands to be spanned by symmetric and strictly compact Wannier states that have zero overlap with all lattice sites beyond a certain range. Similar to the characterization of topological insulators in terms of an algebraic (rather than exponential) localization of Wannier states, we find that there may be impediments to the compact localization even of topologically “trivial” obstructed atomic insulators. These insulators admit exponentially localized Wannier states centered at unoccupied orbitals of the crystalline lattice. First, we establish a sufficient condition for an insulator to have a compact representative. Second, for C 2 rotational symmetry, we prove that the complement of fragile topological bands cannot be compact, even if it is an atomic insulator. Third, for C 4 symmetry, our findings imply that there exist fragile bands with zero correlation length. Fourth, for a C 3 -symmetric atomic insulator, we explicitly derive that there are no compact Wannier states overlapping with less than 18 lattice sites. We conjecture that this obstruction generalizes to all finite Wannier sizes. Our results can be regarded as the stepping stone to a generalized theory of Wannier states beyond dipole or quadrupole polarization

Exact quantum scars in the chiral nonlinear Luttinger liquid

While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit for an analytic solution. In this work, we find a subextensive number of exact eigenstates for a large family of density-density interaction terms. These states are embedded in a continuum of strongly correlated excited states. The real-space entanglement entropy of some exact states scales logarithmically with system size while that of others has volume-law scaling. We introduce momentum-space entanglement as an unambiguous differentiator between these exact states and the remaining excited states. With regard to momentum space, the exact states behave as bona fide quantum many-body scars: they exhibit identically zero momentum-space entanglement, while typical eigenstates behave thermally. We corroborate this finding by a level statistics analysis. Furthermore, we detail the general formalism for systematically finding all interaction terms and associated exact states, and present a number of infinite exact state sequences extending to arbitrarily high energies. Unlike many previous examples of quantum many-body scars, the exact states uncovered here do not lie at equidistant energies and do not follow from a special operator algebra. Instead, they are uniquely enabled by the interplay of Fermi statistics and chirality

Tunable Multifunctional Topological Insulators in Ternary Heusler Compounds

Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude of spin-orbit coupling (by the atomic charge). Based on the first-principle calculations we demonstrate that around fifty Heusler compounds show the band inversion similar to HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare earth element Ln which can realize additional properties ranging from superconductivity (e. g. LaPtBi[12]) to magnetism (e. g. GdPtBi[13]) and heavy-fermion behavior (e. g. YbPtBi[14]). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.Comment: 20 pages, 5 figure

Topological Surface States Protected From Backscattering by Chiral Spin Texture

Topological insulators are a new class of insulators in which a bulk gap for electronic excitations is generated by strong spin orbit coupling. These novel materials are distinguished from ordinary insulators by the presence of gapless metallic boundary states, akin to the chiral edge modes in quantum Hall systems, but with unconventional spin textures. Recently, experiments and theoretical efforts have provided strong evidence for both two- and three-dimensional topological insulators and their novel edge and surface states in semiconductor quantum well structures and several Bi-based compounds. A key characteristic of these spin-textured boundary states is their insensitivity to spin-independent scattering, which protects them from backscattering and localization. These chiral states are potentially useful for spin-based electronics, in which long spin coherence is critical, and also for quantum computing applications, where topological protection can enable fault-tolerant information processing. Here we use a scanning tunneling microscope (STM) to visualize the gapless surface states of the three-dimensional topological insulator BiSb and to examine their scattering behavior from disorder caused by random alloying in this compound. Combining STM and angle-resolved photoemission spectroscopy, we show that despite strong atomic scale disorder, backscattering between states of opposite momentum and opposite spin is absent. Our observation of spin-selective scattering demonstrates that the chiral nature of these states protects the spin of the carriers; they therefore have the potential to be used for coherent spin transport in spintronic devices.Comment: to be appear in Nature on August 9, 200

Aharonov-Bohm interference in topological insulator nanoribbons

Topological insulators represent novel phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport measurements. Recently, Bi2Se3 and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface and verified by angle-resolved photoemission spectroscopy experiments. Here, we show unambiguous transport evidence of topological surface states through periodic quantum interference effects in layered single-crystalline Bi2Se3 nanoribbons. Pronounced Aharonov-Bohm oscillations in the magnetoresistance clearly demonstrate the coverage of two-dimensional electrons on the entire surface, as expected from the topological nature of the surface states. The dominance of the primary h/e oscillation and its temperature dependence demonstrate the robustness of these electronic states. Our results suggest that topological insulator nanoribbons afford novel promising materials for future spintronic devices at room temperature.Comment: 5 pages, 4 figures, RevTex forma

One-dimensional Topological Edge States of Bismuth Bilayers

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance as well as edge-dominated current flow. However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) and there have been recent experimental indications of possible topological boundary states at their edges. However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that are consistent with strong suppression of backscattering as predicted for the propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia

A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect \cite{Klitzing,Tsui} dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the extreme quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic field. Bulk Bi$_{1-x}$Sb$_x$ single crystals are expected to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher dimensional analogues of the edge states that characterize a spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi$_{1-x}$Sb$_x$ is predicted to exhibit three-dimensional Dirac particles, another topic of heightened current interest. Here, using incident-photon-energy-modulated (IPEM-ARPES), we report the first direct observation of massive Dirac particles in the bulk of Bi$_{0.9}$Sb$_{0.1}$, locate the Kramers' points at the sample's boundary and provide a comprehensive mapping of the topological Dirac insulator's gapless surface modes. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the much sought exotic "topological metal". They also suggest that this material has potential application in developing next-generation quantum computing devices.Comment: 16 pages, 3 Figures. Submitted to NATURE on 25th November(2007

Spin-related tunneling through a nanostructured electric-magnetic barrier on the surface of a topological insulator

We investigate quantum tunneling through a single electric and/or magnetic barrier on the surface of a three-dimensional topological insulator. We found that (1) the propagating behavior of electrons in such system exhibits a strong dependence on the direction of the incident electron wavevector and incident energy, giving the possibility to construct a wave vector and/or energy filter; (2) the spin orientation can be tuned by changing the magnetic barrier structure as well as the incident angles and energies

Fractional quantum Hall effect in the absence of Landau levels

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the FQHE in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically nontrivial flat band model on the checkerboard lattice \cite{sun}. In the presence of nearest-neighboring repulsion ($U$), we find that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5 filling, however, a next-nearest-neighboring repulsion is needed for the occurrence of the 1/5 FQHE when $U$ is not too strong. We demonstrate the characteristic features of these novel states and determine the phase diagram correspondingly.Comment: 6 pages and 4 figure