Extended State to Localization in Random Aperiodic Chains

The electronic states in Thus-Morse chain (TMC) and generalized Fibonacci chain (GFC) are studied by solving eigenequation and using transfer matrix method. Two model Hamiltonians are studied. One contains the nearest neighbor (n.n.) hopping terms only and the other has additionally next nearest neighbor (n.n.n.) hopping terms. Based on the transfer matrix method, a criterion of transition from the extended to the localized states is suggested for GFC and TMC. The numerical calculation shows the existence of both extended and localized states in pure aperiodic system. A random potential is introduced to the diagonal term of the Hamiltonian and then the extended states are always changed to be localized. The exponents related to the localization length as a function of randomness are calculated. For different kinds of aperiodic chain, the critical value of randomness for the transition from extended to the localized states are found to be zero, consistent with the case of ordinary one-dimensional systems.     

THERMALLY ACTIVATED HOPPING IN Dy1-xPrxBa2Cu3O7-δ SYSTEM

The temperature dependence of resistivity in Dy_1-xPr_xBa₂Cu₃O_7-δ system with x>0.6 was measured. The experimental results show that Pr substitution leads to the localization of mobile holes and such a localization is enhanced with increasing Pr concentration. The gradually enhancing of localization induces Anderson transitions one by one in this system, including the transition from the conduction by excitation of holes to the one by thermal activation hopping between localized states, the so called Anderson transition type-I, and the transition from nearest neighbor hopping (NNH) to variable range hopping (VRH), the Anderson transition type-II, and the Anderson transition type-lI from 3D to 2D.     

Unified Solutions of the Hard-Core Fermi-and Bose-Hubbard Models

A unified algebraic approach to both the hard-core Fermi- and Bose-Hubbard models is extended to boththe finite- and infinite-site with periodic condition cases. Excitation energies and the corresponding wavefunctions ofboth the models with nearest neighbor hopping are exactly derived by using a new and simple algebraic method. It isfound that spectra of both the models are determined simply by eigenvalue problem of N × N hopping matrix, where Nis the number of sites for finite system or the period of sites for infinite system.     

有限二维复式晶格电子结构的尺度效应

以二维复式晶格作为有限系统的集团模型,利用紧束缚近似,在考虑链间耦合及链端效应的情况下,计算了格点数分别为16、32、64、128时π电子在最近邻及次近邻跳跃集团的能谱和态密度.讨论了不同格点数和结构参数对态密度及带宽的影响.     

Planar spin chain with competing interactions in an external magnetic field

The 1D classical planar model with nearest neighbor (NN) and next nearest neighbor (NNN) competing interactions is studied at finite temperature in presence of an external magnetic field by the transfer matrix method. In particular we are interested into helix configurations supported by an exchange competition strong enough. The short range order (SRO) is strictly related to the zero temperature long range order (LRO). Our exact calculation makes possible the comparison with the current expectation that a discontinuous helix-fan transition occurs before the continuous fan-collinear transition takes place. This feeling is based on the extrapolation of low field-high field zero temperature expansions. We find strong evidence that this expectation is fulfilled when the turn angle of the helix is lesser than /2, whereas for turn angles greater than /2 the discontinuous transition does not take place and the helix changes continuously to a collinear configuration as the magnetic field is increased. Our conclusion is based on the analysis of the SRO at finite temperature exactly calculated by the transfer matrix method and on the zero temperature exact calculation of the minimum energy of commensurate configurations.     

Disorder and localization of electrons in bilayer graphene

We investigate localization behavior of electron states in bilayer graphene formed with the Bernal stacking in the presence of various types of disorder (site-energy, in-plane hopping and inter-plane hopping) by the use of the transfer matrix method. It is found that all the states are localized at various kinds of disorder (site-energy, in-plane hopping and inter-plane hopping) except that in the case of inter-plane-hopping disorder the states at the zero energy are critical. The implications of the results are discussed.     

A renormalization scheme for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

An iteration scheme which makes use of a numerical renormalization group approach is used to calculate the spectrum of vibronic levels. This spectrum resulted from dynamic effects occurring in certain molecules or impurities in insulators.The Hamiltonian of these systems is expressed in the matrix form, using products of suitable electron-phonon states as a basis. In applying this method to multimode electron-phonon systems, phonon modes are coupled in a chain-like fashion. Then a finite chain calculation in terms of Hubbard X-operators is explored by setting up the vibronic Hamiltonian.Calculations are based on Lanczos algorithm, in which only the nearest neighbor matrix elements along the chain need to be taken into account. The iterative scheme is then applied to a two-level electronic system coupled to phonons. A single-particle Green's function corresponding to a two-level system is applied to calculate the spectral density of states, which, coupled to single mode is carried out. The strength of lines in density of states is affected by the coupling constant as well as the temperature dependence of some measurable quantities.     

Transition curves for the variance of the nearest neighbor spacing distribution for Poisson to Gaussian orthogonal and unitary ensemble transitions

Using an appropriate 2x2 random matrix ensemble, transition curves for the variance of the nearest neighbor spacing distribution are constructed for the Poisson to Gaussian orthogonal and unitary ensemble transitions in terms of an easily identifiable transition parameter.     

The integer quantum Hall effect of a square lattice with an array of point defects

The electronic properties of a square lattice under an applied perpendicular magnetic field in the presence of impurities or vacancies are investigated by the tight-binding method including up to second nearest neighbor interactions. These imperfections result in new gaps and bands in the Hofstadter butterfly even when the second order interactions break the bipartite symmetry. In addition, the whole spectrum of the Hall conduction is obtained by the Kubo formula for the corresponding cases. The results are in accordance with the Thouless-Kohmoto-Nightingale-den Nijs integers when the Fermi energy lies in an energy gap. We find that the states due to the vacancies or impurities with small hopping constants are highly localized and do not contribute to the Hall conduction. However, the impurities with high hopping constants result in new Hall plateaus with constant conduction of σ(xy)?=±?e(2)/h, since high hopping constants increase the probability of an electron contributing to the conduction.     

Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.     

Chemical trends for localized gap states in amorphous semiconductors

The absence or presence of unpaired spin and of variable range hopping due to the localized gap states (dangling bond states) in various amorphous semiconductors is explained based on the chemical nature of constituent atoms and randomness of the glass structure. The randomness is also correlated with optical absorption data.     

Many-Body Localization Transition in the Heisenberg Ising Chain

In this paper, we use exact matrix diagonalization to explore the many-body localization (MBL) transition of the Heisenberg Ising spin-1/2 chain with nearest neighbor couplings and disordered external fields. It demonstrates that the fidelity, magnetization and spin-spin space correlation can be used to characterize the many-body localization transition in this closed spin system which is also in agreement with previous analytical and numerical results. We test the properties for the middle third many-body eigenstates. It shows that for this model with random-field, the excited-state fidelity exhibits a pronounced drop at the transition and then gradually tends to be stable in the localized phase, the critical point and the final value of averaged fidelity are all size dependent. It demonstrates that disordered external fields drive the occurrence of the MBL transition. Moreover, we investigate the magnetization and spin-spin space correlation in this model to verify the conclusion we got and further explore the properties of ergodic phase and localized phase.

     

Edge states enhanced by long-range hopping: An analytical study

We analyze the behavior of edge states in long-range(LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method(TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in oneand two-dimensional(2D) superconductors with LR hopping and pairing.     

Fluorescence and host-guest energy transfer in polymeric chains

Intrachain singlet electronic excitation energy transfer from host polyvinylcarbazole (PVCa) to guest vinylbenzocarbazole (VBCa) units has been studied through measurements of the quenching effect on PVCa fluorescence and observation of the sensitized guest VBCa emission in solutions at 293 and 77K for different intramolecular concentrations of guest VBCa units. A method of taking into account intrinsic traps of singlet excitons (excimer forming sites, EFS), ordinarily present in an impurity free polymer macromolecule, has been elaborated. The comparison of the experimental data with theory shows that the one-dimensional singlet excitation energy transfer in a polymeric chain involves motion of incoherent excitons randomly hopping to a nearest neighbor along the line under conditions when capturing occurs upon the first visit of a trap and trapping centers of different origin become indistinguishable as regards their capturing capability.     

Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be sensitive on the mutual values of the intra-strand and inter-strand tunnel hoppings, whose distribution displays a unique three-subband self-similar pattern in a parameter subspace. In addition, it is observed that special numerical correlations between the nearest and the next-nearest neighbor hopping integrals can render a substantial part of the energy spectrum absolutely continuous. Extended, Bloch like functions populate the above continuous zones, signalling a complete delocalization of single particle states even in such a non-translationally invariant system, and more importantly, a phenomenon that can be engineered by tuning the relative strengths of the hopping parameters. A commutation relation between the potential and the hopping matrices enables us to work out the precise correlation which helps to engineer the extended eigenfunctions and determine the band positions at will.     

扩展Su-Schrieffer-Heeger模型在周期性边界条件下的相变

文章计算了含有三种跃迁项(最近邻(NN)、次近邻(NNN)、次次近邻(NNNN)跃迁项)的扩展Su-Schrieffer-Heeger(SSH)模型(模型ⅰ)的热力学特性.对仅含有二种跃迁项(NN、NNN跃迁项)的扩展SSH模型(模型ⅱ)、仅含有一种跃迁项(NN跃迁项)的SSH模型(模型ⅲ)也作了类似的计算.在低温下,每个模型都有相变且跃迁项的存在会降低相变温度.由于NNN跃迁项的存在,在极低温条件下,关于热容量与温度比(HCOTR)随温度变化的单调性,模型i与其它两个模型存在差异.在低温下,模型ⅰ的HCOTR的单调性,会受NN或NNN或NNNN跃迁项的影响并且NN或NNN跃迁项会影响其相变.     

Orbital nature of ferromagnetic magnons in manganites

Magnon excitation in a ferromagnetic state of Sm(0.55)Sr(0.45)MnO(3) located on the verge of the metal-insulator transition has been studied in terms of the neutron scattering experiment. The anomalous magnon dispersion with the zone-boundary softening is well described by the Heisenberg model with extended exchange coupling constants J(s). In particular the fourth neighbor coupling J(4) is as large as 0.6 times the nearest neighbor one J(1). Theoretical analysis based on the local density approximation + Hubbard U band calculation reveals that this one-dimensional exchange path is due to the (3z(2)-r(2))-type orbital correlation, in sharp contrast to previous proposals.