New Geometric Algorithms for Fully Connected Staged Self-Assembly

We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et al. showed that a relatively small number of tile types suffices to produce arbitrary shapes in this model. However, these constructions were only based on a spanning tree of the geometric shape, so they did not produce full connectivity of the underlying grid graph in the case of shapes with holes; designing fully connected assemblies with a polylogarithmic number of stages was left as a major open problem. We resolve this challenge by presenting new systems for staged assembly that produce fully connected polyominoes in O(log^2 n) stages, for various scale factors and temperature {\tau} = 2 as well as {\tau} = 1. Our constructions work even for shapes with holes and uses only a constant number of glues and tiles. Moreover, the underlying approach is more geometric in nature, implying that it promised to be more feasible for shapes with compact geometric description.Comment: 21 pages, 14 figures; full version of conference paper in DNA2

SU(5) Heterotic Standard Model Bundles

We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and give three generations of Standard Model fermions after symmetry breaking by Wilson lines of the intermediate SU(5) GUT-group to the Standard Model gauge group. Among the solutions we find some which can be perturbed to solutions of the Strominger system. Thus these solutions provide a step toward the construction of phenomenologically realistic heterotic flux compactifications via non-Kahler deformations of Calabi-Yau geometries with bundles. This particular class of solutions involves a rank two hidden sector bundle and does not require background fivebranes for anomaly cancellation.Comment: 17 page

Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3

Topological insulators are a recently discovered class of materials with fascinating properties: While the inside of the solid is insulating, fundamental symmetry considerations require the surfaces to be metallic. The metallic surface states show an unconventional spin texture, electron dynamics and stability. Recently, surfaces with only a single Dirac cone dispersion have received particular attention. These are predicted to play host to a number of novel physical phenomena such as Majorana fermions, magnetic monopoles and unconventional superconductivity. Such effects will mostly occur when the topological surface state lies in close proximity to a magnetic or electric field, a (superconducting) metal, or if the material is in a confined geometry. Here we show that a band bending near to the surface of the topological insulator Bi$_2$Se$_3$ gives rise to the formation of a two-dimensional electron gas (2DEG). The 2DEG, renowned from semiconductor surfaces and interfaces where it forms the basis of the integer and fractional quantum Hall effects, two-dimensional superconductivity, and a plethora of practical applications, coexists with the topological surface state in Bi$_2$Se$_3$. This leads to the unique situation where a topological and a non-topological, easily tunable and potentially superconducting, metallic state are confined to the same region of space.Comment: 12 pages, 3 figure

The space group classification of topological band insulators

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.Comment: Accepted in Nature Physic

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

Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface

Recent theories and experiments 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 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 strongly interacting particles. It has been proposed that a topological insulator with a single spin-textured 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 and first-principle theoretical calculation-predictions that reveal the first observation of such a topological state of matter featuring a single-surface-Dirac-cone realized in the naturally occurring Bi$_2$Se$_3$ class of materials. Our results, supported by our theoretical predictions and calculations, demonstrate that undoped compound of this class of materials can serve as the parent matrix compound for the long-sought topological device where in-plane surface 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.Comment: 3 Figures, 18 pages, Submitted to NATURE PHYSICS in December 200

Topological Crystalline Insulators in the SnTe Material Class

Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe, by identifying its nonzero topological index. We predict that as a manifestation of this nontrivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust against disorder and topologically protected by reflection symmetry of the crystal with respect to {110} mirror plane. Breaking this mirror symmetry via elastic strain engineering or applying an in-plane magnetic field can open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectrics, infrared detection, and tunable electronics. Closely related semiconductors PbTe and PbSe also become topological crystalline insulators after band inversion by pressure, strain and alloying.Comment: submitted on Feb. 10, 2012; to appear in Nature Communications; 5 pages, 4 figure

Gate-tuned normal and superconducting transport at the surface of a topological insulator

Three-dimensional topological insulators are characterized by the presence of a bandgap in their bulk and gapless Dirac fermions at their surfaces. New physical phenomena originating from the presence of the Dirac fermions are predicted to occur, and to be experimentally accessible via transport measurements in suitably designed electronic devices. Here we study transport through superconducting junctions fabricated on thin Bi2Se3 single crystals, equipped with a gate electrode. In the presence of perpendicular magnetic field B, sweeping the gate voltage enables us to observe the filling of the Dirac fermion Landau levels, whose character evolves continuously from electron- to hole-like. When B=0, a supercurrent appears, whose magnitude can be gate tuned, and is minimum at the charge neutrality point determined from the Landau level filling. Our results demonstrate how gated nano-electronic devices give control over normal and superconducting transport of Dirac fermions at an individual surface of a three-dimensional topological insulator.Comment: 28 pages, 5 figure

Band structure engineering in (Bi1-xSbx)2Te3 ternary topological insulators

Three-dimensional (3D) topological insulators (TI) are novel quantum materials with insulating bulk and topologically protected metallic surfaces with Dirac-like band structure. The spin-helical Dirac surface states are expected to host exotic topological quantum effects and find applications in spintronics and quantum computation. The experimental realization of these ideas requires fabrication of versatile devices based on bulk-insulating TIs with tunable surface states. The main challenge facing the current TI materials exemplified by Bi2Se3 and Bi2Te3 is the significant bulk conduction, which remains unsolved despite extensive efforts involving nanostructuring, chemical doping and electrical gating. Here we report a novel approach for engineering the band structure of TIs by molecular beam epitaxy (MBE) growth of (Bi1-xSbx)2Te3 ternary compounds. Angle-resolved photoemission spectroscopy (ARPES) and transport measurements show that the topological surface states exist over the entire composition range of (Bi1-xSbx)2Te3 (x = 0 to 1), indicating the robustness of bulk Z2 topology. Most remarkably, the systematic band engineering leads to ideal TIs with truly insulating bulk and tunable surface state across the Dirac point that behave like one quarter of graphene. This work demonstrates a new route to achieving intrinsic quantum transport of the topological surface states and designing conceptually new TI devices with well-established semiconductor technology.Comment: Minor changes in title, text and figures. Supplementary information adde

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