Lifshitz Tails on the Bethe Lattice: A Combinatorial Approach

The density of states of disordered hopping models generically exhibits an essential singularity around the edges of its support, known as a Lifshitz tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size limit of random regular graphs, converging locally to the infinite regular tree, for both diagonal and off-diagonal disorder. The exponential growth of the volume and surface of balls on these lattices is an obstacle for the techniques used to characterize the Lifshitz tails in the finite-dimensional case. We circumvent this difficulty by computing bounds on the moments of the density of states, and by deriving their implications on the behavior of the integrated density of states.     

无序系统中电子局域态分布

本文应用一种计算无序系统中电子本征态的方法,求得了含有2000个粒子的无序系统中电子局域态的分布,并结合态密度、计算误差进行了分析讨论。所得结果表明,在不同的能量范围内局域态的分布不同,分布可遍及整个系统,且与无序度有关。 关键词：     

Effective surface potential method for calculating surface states

A novel formalism (the effective surface potential method) is developed for calculating surface states. Like the Green function method of Kalkstein and Soven and the transfer matrix method of Falicov and Yndurain, the technique is exact for simple tight binding Hamiltonians. As well as offering an alternative viewpoint, the present method provides a simple analytic expression describing the surface states. At each point k_s in the surface Brillouin zone the semi-infinite solid is viewed as an effective linear chain where each element of the chain is a planar layer. The solution to the linear chain problem can be expressed in terms of an effective potential h(k_s,E) at each energy E. A number of examples are presented in detail; “sp^d” Hamiltonians for a linear chain (d = 1), the honeycomb lattice (d = 2), the 111 surface of silicon (d = 3), and a dissected Bethe lattice. Various exact results are given, e.g. the extremities of surface state bands and the surface density of states of p-like (delta function) bands. The results of Kalkstein and Soven for the 100 surface of a simple cubic solid with a perturbation on the surface layer are rederived.     

Local density of states of a finite-sized rectangular-lattice photonic crystal with separable profile of permittivity

A different approach in the calculation of two-dimensional local density of states has been presented for a two-dimensional finite rectangular-lattice photonic crystal with a separable profile of permittivity. Approximate staircase structures are already shown to be useful for their ability to reproduce actual properties of practical square lattice photonic crystals. Using the effective resonance approach in a Fabry–Perot resonator and transfer matrix method an analytical expression for calculating a two-dimensional local density of states can be derived for both polarisations in the structure. It is shown that for this geometry one can resolve the modes as a product of two separate functions each being a function of x- and y-coordinates. The results have been investigated for the two-dimensional local density of states in the ordered finite structure and in the disordered structure. The main advantage of this method in calculating the local density of states is its extremely efficient numerical evaluations. As an application we introduce a cavity-like defect in the vicinity of a waveguide-like defect and examine the variation of local density of states in the plane of the structure at band gap frequency.     

A self-consistent model calculation of the electronic structure of ordered,disordered and hydrogenated Pd3Fe

We study, within the Bethe lattice approximation, the electronic structure of the ordered, disordered and hydrogenated intermetallic Pd₃Fe. We employ a simple one-orbital per site model hamiltonian, which includes a Hubbard-like Coulomb interaction term. This is treated in the Hartree-Fock approximation. We present results for the number of electrons, magnetic moments, and density of states at the Fermi level. Good agreement with available experimental data is obtained.     

An analytic study of the friedel criterion in disordered magnetic states in transition metals in the presence ofS-D hybridisation,using the cluster bethe lattice approach

In this paper we present a new theory for including both short range order and long range order simultaneously in the well known cluster Bethe lattice method for binary alloys. We have used this theory for obtaining the Friedel criterion for the appearance of magnetic moments in disordered states using the single band Hubbard model. This is followed by a study of this criterion in a two-bands-d hybridised Hubbard model, which is considered as a simulation of real transition metals. A new technique for solving this problem in the Bethe lattice network is presented, which yields an analytic solution for the critical correlation strength in the presence of hybridisation and short range order. It is found that in all cases hybridisation tends to diminish the tendency for magnetisation, which is in accord with physical expectations.     

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous X X X Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.     

Theory of electronic structure of non-dilute transition metal alloys : Ni-Cu

The density of states for the Ni-Cu alloy system has been calculated as a function of concentration by the supercell method. This method takes into account inter-site interactions in contrast with current effective medium or single site theories. We show that the method is practical for the study of disordered systems. Comparison is made with previous work as well as with photoemission data.     

Effect of the d-f correlation on the electronic structure of intermediate valence systems

The electronic structure of an intermediate valence system is calculated by means of a real space renormalization technique on a Bethe lattice. The d-f Coulomb repulsion G is treated into the alloy analogy approximation. The valence and the densities of states are calculated as a function of G. We find that the hybridization gap decreases when G increases, and that the density of states at the Fermi level exhibits a peak as a function of G.     

Theory of electronic structure of non-dilute transition metal alloys : NiCu

The density of states for the NiCu alloys system has been calculated as a function of concentration by the supercell method. This method takes into account inter-site interactions in contrast with current effective medium or single site theories. We show that the method is practical for the study of disordered systems. Comparison is made with previous work as well as with photoemission data.     

THE RESEARCH OF ELECTRONIC PROPERTIES OF HYDROGENATED а-Si

We first used Bethe lattice method and coherent potential approximation method to calculate the densities of bulk and surface states for a-Si,a-Si:H. The ideal vacancies were also studied.The results agree with experiments and other works.Dihedral disorder contributes to the submerging of a peak and sp peak of the valence band.In hydrogenated case,extra structure appears in the spectrum of densities of surface states.Doped hydrogen affects the densities of bulk states in the gap in principle,but hydrogen is not important for densities of surface states in the gap.Finally,we obtained self-energies which are in good.agreement with the empirical results from experiments and other methods^[1].     

Atomic approximation for alloys and their surfaces

We report a simple, ab initio method for calculating the electronic structure of compositionally disordered alloys. Results are shown for Cu/Ni and Ag/Pd bulk systems, and the first calculations are reported for the surface electronic structure of random alloys, exemplified by {111} surface states of Cu/Ni and Cu/Al alloys.     

A Cluster-Bethe-Lattice approach to spin-waves in dilute ferromagnets

We study the spin-wave spectra of a dilute ferromagnet within the cluster-Bethe-lattice approximation. Short range order effects for the alloy are included. A study of finite size clusters connected at their edges to Bethe lattices of the same coordination number allows us to determine: (i) the stability condition for the magnetic system; (ii) the continuum spin-wave local density of states; and (iii) the existence of localized states below and above the continuum states.     

Chiral metal as a ferromagnetic super spin chain

The electrons on the surface of a disordered multi-layer integer quantum Hall system constitute an unusual chiral metal with ballistic motion transverse to the field, and diffusive motion parallel to it. We present a non-perturbative analytic treatment of an appropriate model, consisting of disordered chiral fermions in two dimensions. A supersymmetric generating functional is set up for the correlation functions of this system. The strong disorder limit is mapped into a supersymmetric spin chain, with ferromagnetic exchange coupling, reflecting the electron's chiral motion. The ferromagnetic ground state and the spin wave excitations, corresponding to the diffusion modes of the chiral metal, are found exactly. The parametric density of states correlator in the ergodic limit is computed from a Boltzmann-weighted sum over low-energy spin states. The result is of a universal form and coincides with that for a hermitian random matrix.     

Bethe ansatz results for the 4f-electron spectra of a degenerate Anderson model

We show that the density of states for localized 4f electrons coupled to a conduction band calculated in the framework of Bethe ansatz solution for the degenerate Anderson model qualitatively disagree with the well-known results obtained for the same model but using a variational approach. The scales of parameters used in our Bethe ansatz calculations to fit the experiments disagree with the commonly accepted values from other studies. This implies narrower conduction bands hybridized with 4f orbitals or questions the applicability of the Bethe ansatz for a degenerate Anderson model for the high-energy characteristics of some rare-earth systems.     

A self-consistent TB-LMTO-augmented space recursion method for disordered binary alloys

We developed a complete self-consistent TB-LMTO-Augmented space recursion (ASR) method for calculating configurational average properties of substitutionally disordered binary alloys. We applied our method to fcc based Cu-Ni, Ag-Pd for different concentrations of constituent elements and body-centered cubic based ferromagnetic Fe-V (50-50) alloy. For this systems we investigated the convergence of total energy and l-dependent potential parameters, charges, magnetic moment, energy moments of density of states with the number of iterations. Our results show good agreement with the existing calculations and also with the experimental results where it is available. The Madelung energy correction due to the charge transfer has also been included by the method developed by Ruban et al.     

Electronic density of states of group-IV semiconductors: A cluster-Bethe lattice approach for realistic Hamiltonians

We have extended the cluster-Bethe lattice method to study realistic tight-binding Hamiltonians. The numerical solution of the transfer matrix in the Bethe lattice is very stable and requires about 50 steps of our iterative procedure to reach convergency. We apply this method to study the density of states of group-IV semiconductors (C, Si, Ge) using a five-parameter sp³ Hamiltonian, which takes into account all possible interactions between sp³ hybrids in nearest-neighbor atoms. Our results show clearly that the main features of the density of states are due to short-range order. Clusters of about 30 atoms reproduce very well the crystalline density of states. Based on our results we propose a model for the density of states in the gap region of an amorphous semiconductor.     

Spatio-temporal conjecture for diffusion

We present here a conjecture about the equivalence between the noise density of states of a system governed by a generalized Langevin equation and the fluctuation in the energy density of states in a Hamiltonian system. We present evidence of this for a disordered Heisenberg system.     

A new theory for including short range order in the cluster Bethe lattice method: Application to the Hubbard model

A new theory for incorporating short range order (SRO) in the cluster Bethe lattice method (CBLM) for disordered binary alloys is proposed. It is applied to determine the condition for the appearance of moments in the disordered phase of a narrow-band metal for general values of concentration and SRO parameter. The final result (i) yields all the known limiting conditions exactly and (ii) displays in a transparant form the SRO dependence, indicating the merit of the present approach.     

一维纳米固体的电子结构

本文通过计算一维纳米固体模型的电子态密度,针对颗粒大小、颗粒界面无序度等物理量,讨论了一维纳米固体的电子结构。结果表明颗粒大小对电子能态结构影响较大,而颗粒界面无序度主要引起能带宽度和态密度大小的变化。 关键词：