Observation of Fermi-energy dependent unitary impurity resonances in a strong topological insulator Bi_2Se_3 with scanning tunneling spectroscopy

Scanning tunneling spectroscopic studies of Bi_2Se_3 epitaxial films on Si (111) substrates reveal highly localized unitary impurity resonances associated with non-magnetic quantum impurities. The strength of the resonances depends on the energy difference between the Fermi level (E_F) and the Dirac point (E_D) and diverges as E_F approaches E_D. The Dirac-cone surface state of the host recovers within ~ 2Å spatial distance from impurities, suggesting robust topological protection of the surface state of topological insulators against high-density impurities that preserve time reversal symmetry

A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations

A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late

Finite-dimensional integrable systems associated with Davey-Stewartson I equation

For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained and their functional independence is proved. Therefore, the Hamiltonian systems are completely integrable in Liouville sense. A periodic solution of the Davey-Stewartson I equation is obtained by solving these classical Hamiltonian systems as an example.Comment: 18 pages, LaTe

Scanning Tunnelling Spectroscopic Studies of Dirac Fermions in Graphene and Topological Insulators

We report novel properties derived from scanning tunnelling spectroscopic (STS) studies of Dirac fermions in graphene and the surface state (SS) of a strong topological insulator (STI), Bi_2Se_3. For mono-layer graphene grown on Cu by chemical vapour deposition (CVD), strain-induced scalar and gauge potentials are manifested by the charging effects and the tunnelling conductance peaks at quantized energies, respectively. Additionally, spontaneous time-reversal symmetry breaking is evidenced by the alternating anti-localization and localization spectra associated with the zero-mode of two sublattices while global time-reversal symmetry is preserved under the presence of pseudo-magnetic fields. For Bi_2Se_3 epitaxial films grown on Si(111) by molecular beam epitaxy (MBE), spatially localized unitary impurity resonances with sensitive dependence on the energy difference between the Fermi level and the Dirac point are observed for samples thicker than 6 quintuple layers (QL). These findings are characteristic of the SS of a STI and are direct manifestation of strong topological protection against impurities. For samples thinner than 6-QL, STS studies reveal the openup of an energy gap in the SS due to overlaps of wave functions between the surface and interface layers. Additionally, spin-preserving quasiparticle interference wave-vectors are observed, which are consistent with the Rashba-like spin-orbit splitting

Extension of Hereditary Symmetry Operators

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary symmetry operators are carefully analyzed on the base of the resulting general conditions and several corresponding nonlinear systems are explicitly given out as illustrative examples.Comment: 13 pages, LaTe

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Observation of Fermi-energy dependent unitary impurity resonances in a strong topological insulator Bi2Se3 with scanning tunneling spectroscopy

Scanning tunneling spectroscopic studies of Bi2Se3 epitaxial films on Si (111) substrates reveal highly localized unitary impurity resonances associated with non-magnetic quantum impurities. The strength of the resonances depends on the energy difference between the Fermi level ({E_F}) and the Dirac point ({E_D}) and diverges as {E_F} approaches {E_D}. The Dirac-cone surface state of the host recovers within ~ 2{\AA} spatial distance from impurities, suggesting robust topological protection of the surface state of topological insulators against high-density impurities that preserve time reversal symmetry.Comment: 6 pages, 6 figures. Accepted for fast-track publication in Solid State Communications (2012

P-type ZnO by Sb doping for PN-junction photodetectors

ABSTRACT Sb-doped p-type ZnO films were grown on n-Si (100) by electron cyclotron resonance (ECR)-assisted molecular-beam epitaxy (MBE). Room temperature Hall effect measurements reveal that a heavily Sb-doped ZnO sample exhibits a low resistivity of 0.2 cm, high hole concentration of 1.7×10 18 cm -3 , and high mobility of 20.0 cm 2 /V s. Low-temperature photoluminescence (PL) measurements show an Sb-associated acceptor-bound exciton (AºX) emission exists at 3.358 eV at 8.5 K. The acceptor energy level of the Sb dopant is estimated to be 0.14 eV above the valence band. Based on these electrical and optical properties, p-n hetero-and homojunction photodetectors employing Sb-doped p-type ZnO films were designed and fabricated. The heterojunction photodiode consists of Sb-doped p-type ZnO grown on n-Si (100) substrate. An Sb-doped p-type ZnO layer with an n-type Ga-doped ZnO layer was grown on a p-Si (111) substrate to form the homojunction. Current-Voltage (I-V) characterizations reveal rectifying characteristics. Good photoresponse to UV light has been demonstrated for both hetero and homojunction photodetectors

Ultra-low carrier concentration and surface dominant transport in Sb-doped Bi2Se3 topological insulator nanoribbons

A topological insulator is a new state of matter, possessing gapless spin-locking surface states across the bulk band gap which has created new opportunities from novel electronics to energy conversion. However, the large concentration of bulk residual carriers has been a major challenge for revealing the property of the topological surface state via electron transport measurement. Here we report surface state dominated transport in Sb-doped Bi2Se3 nanoribbons with very low bulk electron concentrations. In the nanoribbons with sub-10nm thickness protected by a ZnO layer, we demonstrate complete control of their top and bottom surfaces near the Dirac point, achieving the lowest carrier concentration of 2x10^11/cm2 reported in three-dimensional (3D) topological insulators. The Sb-doped Bi2Se3 nanostructures provide an attractive materials platform to study fundamental physics in topological insulators, as well as future applications.Comment: 5 pages, 4 figures, 1 tabl