三聚化非厄密晶格中具有趋肤效应的拓扑边缘态

近年来,探索新的拓扑量子结构、深入分析各种多聚化拓扑晶格中的新奇物理性质已经成为热点.并且,多聚化拓扑模型在量子光学等领域的研究也愈发深入,拥有广阔的发展前景.本文聚焦于研究三聚化非厄密晶格中的新奇拓扑特性.首先,若晶胞内最近邻正反向耦合不相等,三聚化模型中的体态和边缘态出现趋肤效应.其中,随着最近邻耦合正反系数差的增大,拓扑保护的边缘态的宽度和简并度均可被调制,边缘态数量也会减少.其次,当在考虑次近邻耦合的影响时,随着次近邻耦合系数在适当范围内变化,系统本征能谱的上下能隙及其中具有趋肤效应的边缘态也会发生不对称的变化.此外,当适当改变两种耦合系数,三聚化非厄密模型的体态和边缘态的局域程度也会随之发生变化.     

Boundary Hamiltonian Theory for Gapped Topological Orders

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces,with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by(bi-) modules over Frobenius algebras.     

Finite size effects on the helical edge states on the Lieb lattice

For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit(ISO)coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall(QSH) effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.     

Total and surface density of states on the Bethe lattice

A novel approach for calculating the density of surface states in a disordered system is presented. It is shown that the node counting method for calculating the energy spectrum of a system holds for the Bethe lattice. An exact method for calculating the total density of states of a disordered Bethe system terminating on a closed surface, as well as the contribution of the bulk and surface states to it is then developed and applied to the cases of Lorentzian and Gaussian randomness. The results are discussed in connection to relevant material from the literature.     

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

A spectral classification of general one‐dimensional binary aperiodic crystals (BACs) based on both their diffraction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth‐order energy spectrum main features for BACs belonging to different spectral classes, including Fibonacci‐class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed‐type Hamiltonians which include both diagonal and off‐diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation effects present in the underlying lattice is introduced. Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which defines the basic anatomy of the zeroth‐order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci‐class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for specific particular choices of the corresponding model parameters only. The transmission coefficient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.     

On the lattice spectrum contribution to the free energy of defect solids

The energy functional of lattice vibrations of a defect solid is derived. Using the ζ-function method the contribution of the lattice spectrum on defect states of solids to the free energy is then calculated perturbatively by means of differential geometric methods.     

Invisible surface defects in a tight-binding lattice

Surface Tamm states arise in one-dimensional lattices from some defects at the lattice edge and their energy generally falls in a gap of the crystal. The defects at the surface change rather generally the phase of propagative Bloch waves scattered off at the lattice edge, so that an observer, far from the surface, can detect the existence of edge defects from e.g. time-of-flight measurements as a delay or an advancement of a Bloch wave packet. Here we show that a special class of defects can sustain surface Tamm states which are invisible, in a sense that reflected waves acquire the same phase as in a fully homogeneous lattice with no surface state. Surface states have an energy embedded into the tight-binding lattice band and show a lower than exponential (algebraic) localization. Like most of bound states in the continuum of von Neumann-Wigner type, such states are fragile and decay into resonance surface states in presence of perturbations or lattice disorder. The impact of structural lattice imperfections and disorder on the invisibility of the defects is investigated by numerical simulations.     

Structural, electronic and optical properties of orthorhombic distorted perovskite TbMnO3

This paper calculates the structural parameters, electronic and optical properties of orthorhombic distorted perovskite-type TbMnO3 by first principles using density functional theory within the generalised gradient approximation. The calculated equilibrium lattice constants are in a reasonable agreement with theoretical and experimental data. The energy band structure, density of states and partial density of states of elements are obtained. Band structures show that TbMnO3 is an indirect band gap between the O 2p states and Mn 3d states, and the band gap is of 0.48 eV agreeing with experimental result. Furthermore, the optical properties, including the dielectric function, absorption coefficient, optical reflectivity, refractive index and energy loss spectrum are calculated and analysed, showing that the TbMnO3 is a promising dielectric material.     

The electronic properties of graphene and graphene ribbons under simple shear strain

A tight-binding model is used to study the energy band of graphene and graphene ribbon under simple shear strain. The ribbon consists of lines of carbon atoms in an armchair or zigzag orientation where a simple shear strain is applied in the x-direction keeping the atomic distances in the y-direction unchanged. Such modification in the lattice gives an energy band that differs in several aspects from the one without any shear and with pure shear. The changes in the spectrum depend on the line displacement of the ribbon, and also on the modified hopping parameter. It is also shown that this simple shear strain tunes the electronic properties of both graphene and graphene ribbon, opening and closing energy gaps for different displacements of the system. The modified density of states is also shown.     

Non-abelian quantum Hall effect in topological flat bands

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.     

A possible new electron state above liquid helium

Excited states of helium atoms have been observed in the bulk liquid. We discuss the properties of such states if created at the surface. For low quantum numbers the surface is a weak perturbation compared to the atomic excitation energy. At high quantum numbers (weakly bound states) the electron wave function is forced out of the interior of the fluid and the energy spectrum is Rydberg-like.     

Electronic properties of a Penrose tiling lattice in a magnetic field

The one-electron energy spectrum of a two-dimensional Penrose tiling lattice in a uniform magnetic field is calculated as a function of magnetic fields with a tight-binding Hamiltonian. The calculated results show the following remarkable features characteristic of the Penrose lattice. (1) The density of states in a magnetic field has a central peak with zero width at the zero energy. It is shown that the zero-energy states correspond to the ring states in which the wavefunction has a non-vanishing amplitudes only at the sites on a ring-like region around the origin. (2) The energy levels coalesce into Landau type levels and the boundary states due to the finite size effects based on a fixed boundary condition appear in the gap region between Landau levels. (3) The magnetic field dependence of the energy spectrum has a repeated pattern of self-similarity with the golden mean ratio of two successive periods.     

Adsorption on graphene with vacancy-type defects: A model approach

The influence of graphene lattice defects on the adsorption properties of graphene has been considered. The adsorption properties have been investigated in the framework of the Anderson model. The disorder of the graphene crystal lattice has been analyzed using the T-matrix approximation. It has been found that the characteristic energy levels of defects are located near the Dirac point (±1 eV), because the most significant distortions of the spectrum due to the presence of defects in the graphene crystal lattice are observed in the vicinity of this point. Analytical expressions for the density of states of disordered graphene and atoms adsorbed on it have been obtained. A numerical calculation of the charge transfer in the considered system has been carried out. The obtained values of the charge transfer are in good agreement with the results of other studies, where the charge transfer was calculated using the experimental data and the density functional theory method. In the absence of defects, the presented results are well consistent with the results obtained within the M-model of adsorption (Davydov model). An approximation for the density of states of disordered graphene and the shift function of an adsorbed atom has been proposed. This approximation allows one to obtain analytical expressions for the charge transfer, energy of adsorption, and dipole moment.     

Surface photovoltage spectroscopy study of CdS thin films

The method of surface photovoltage spectroscopy has been applied to the study of the surface properties of thin CdS films deposited by vacuum evaporation. The energy spectrum of the surface states is obtained and their kinetic parameters are calculated. A comparison is made of the results obtained in air and in vacuum for non-recrystallized and recrystallized samples. The results for thin films are compared with the data on monocrystal CdS in the literature. It is assumed that the surface states established in the films are of a donor-like type.     

The topological quantum phase transitions in Lieb lattice driven by the Rashba SOC and exchange field

The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieblattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) anduniform exchange field. The Lieb lattice has a simple cubic symmetry, which ischaracterized by the single Dirac-cone per Brillouin zone and the middle flat band in theband structure. The intrinsic SOC is essentially needed to open the full energy gap in thebulk. The QSH effect could survive even in the presence of the exchange field. In terms ofthe first Chern number and the spin Chern number, we study the topological nature and thetopological phase transition from the time-reversal symmetry broken QSH effect to the QAHeffect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributionsare obtained numerically, where the helical edge states and the chiral edge states revealthe non-trivial topological QSH and QAH properties, respectively.     

Anregung von Kristallgitterschwingungen durch Elektronenstrahlen

The interaction of electrons with lattice vibrations in thin films of LiF, NaF, MgO, and Al₂O₃ has been studied by means of high resolution electron energy spectroscopy. Just above the excitation energy of the transversal optical modes small bands in the energy loss spectrum are observed. According to the dielectric theory of an unbounded medium only longitudinal optical modes should be excited. The observed energy loss spectrum may be explained by the excitation of surface lattice vibrations. A theoretical energy loss spectrum of LiF has been computed taking into account the surface effects. It is in excellent agreement with the experimental spectrum. Apart from electrons with energy loss also electrons with energy gain were observed. The intensity distribution of the energy gain spectrum is equivalent to the energy loss spectrum. Energy loss and gain spectra of fast electrons by excitation of lattice vibration are corresponding to the Stokes- and Antistokes lines of spectroscopy of light optics.     

Insight into lattice thermal impedance via equilibrium molecular dynamics: case study on Al

Using results of equilibrium molecular dynamics simulation in conjunction with the Green–Kubo formalism, we present a general treatment of thermal impedance of a crystal lattice with a monatomic unit cell. The treatment is based on an analytical expression for the heat current autocorrelation function which reveals, in a monatomic lattice, an energy gap between the origin of the phonon states and the beginning of the energy spectrum of the so-called acoustic short-range phonon modes. Although, we consider here the f.c.c. Al model as a case example, the analytical expression is shown to be consistent for different models of elemental f.c.c. crystals over a wide temperature range. Furthermore, we predict a frequency ‘window’ where the thermal waves can be generated in a monatomic lattice by an external periodic temperature perturbation.     

Spin fluctuation spectrum of electron-doped high-Tc superconductors

The magnetic excitation spectrum of electron-doped copper oxide superconductors is calculated using the Hubbard model on a square lattice. First, the on-site repulsion is treated with the random phase approximation. The spectrum of electron-doped systems in the superconducting state is compared with that of hole-doped systems, and the relationship between the frequency at which a peak grows in the spectrum and the superconducting energy gap at a hot spot (an intersection of the Fermi surface and the magnetic Brillouin zone boundary) is investigated. As compared with the hole-doped systems, the resonance condition is difficult to be satisfied in the electron-doped systems because of the small density of states around the hot spot. Moreover, the correlation effect in the Hubbard model is treated by the fluctuation-exchange approximation (FLEX), and the spin fluctuation spectra in the superconducting state in a wide region of the wave vector and frequency are calculated. We have found that the intensity of the magnetic spectrum at incommensurate wave vectors obtained with the FLEX is considerably weaker than that obtained with the RPA. The validity of the Fermi-liquid approach is also discussed.