Disorder induced localized States in graphene

We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results also have relevance for the problem of disorder in d-wave superconductors.     

Two interacting electrons in a disorder potential: localization properties

Two electrons move in a quasi one-dimensional wire under the influence of a short-range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete analytical solution to this problem. The two-body interaction affects the density of states and, thereby, the localization length. We derive a criterion for the onset of changes of the localization length due to the two-body interaction.     

Impurities in a biased graphene bilayer

We study the problem of impurities and midgap states in a biased graphene bilayer. We show that the properties of the bound states, such as localization lengths and binding energies, can be controlled externally by an electric field effect. Moreover, the band gap is renormalized and impurity bands are created at finite impurity concentrations. Using the coherent potential approximation, we calculate the electronic density of states and its dependence on the applied bias voltage.     

New probe of the electronic structure of amorphous materials

Here we show that electrochemical equilibrium voltage curves of amorphous WO3 and TiO2 coatings exhibit fine structure in striking agreement with the density of states in the conduction bands, as obtained by ab initio calculations for the crystalline counterparts. We suggest that localization of the band states is essential for observing the electronic structure. Our highly sensitive electrochemical method opens new vistas for studying the electronic structure of nonmetallic disordered materials that can be intercalated with an ionic species.     

Fibonacci链的电子结构特性

对由递推关系S_m+1={S_m|S_m-1}生成的Fibonacci链,从Anderson紧束缚模型出发,用负本征值理论及三对角高阶厄米矩阵本征值理论,对电子的态密度和能级结构进行数值研究,直观简洁地论证其三分叉的能带结构.用重整化群方法,结合散射理论,研究链中电子的局域长度和输运系数,发现具有不同局域属性的能态.一些特定的能量区间值存在扩展态,其相应的输运系数接近1.绝大部分能量对应的电子具有很小或几乎为零的局域长度,说明链中存在相当数量的局域态.定性得出电子输运系数随Fibonacci链参数变化的规律.     

Electronic localization in disordered systems

A brief review is given of the current understanding of the electronic structure, transport properties and the nature of the electronic states in disordered systems. A simple explanation for the observed exponential behaviour in the density of states (Urbach tails) based on short-range Gaussian fluctuations is presented. The theory of Anderson localization in a disordered system is reviewed. Basic concepts, and the physics underlying the effects of weak localization, are discussed. The scaling as well as the self-consistent theory of localization are briefly reviewed. It is then argued that the problem of localization in a random potential within the so-called ladder approximation is formally equivalent to the problem of finding a bound state in a shallow potential well. Therefore all states are exponentially localized in d=1 and d=2. The fractal nature of the states is also discussed. Scaling properties in highly anisotropic systems are also discussed. A brief presentation of the recently observed metal-to-insulator transition in dequals;2 is given and, finally, a few remarks about interaction effects in disordered systems are presented.     

Delta-Davidson method for interior eigenproblem in many-spin systems

Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.     

Anderson localization for Bernoulli and other singular potentials

We prove exponential localization in the Anderson model under very weak assumptions on the potential distribution. In one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment. In particular this solves the longstanding problem of localization for Bernoulli potentials (i.e., potentials that take only two values). In dimensions greater than one we prove localization at high disorder for potentials with Hölder continuous distributions and for bounded potentials whose distribution is a convex combination of a Hölder continuous distribution with high disorder and an arbitrary distribution. These include potentials with singular distributions.We also show that for certain Bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component.Partially supported by NSF grant DMS 85-03695Partially supported by NSF grant DMS 83-01889Partially supported by G.N.F.M. C.N.R.     

Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.     

Geometrical Structure Effect on Localization Length of Carbon Nanotubes

The localization length and density of states of carbon nanotubes are evaluated within the tight-binding approximation. By comparison with the corresponding results for the square lattice tubes, it is found that the hexagonal structure affects strongly the behaviour of the density of states and localization lengths of carbon nanotubes.     

Anderson localization in 1D systems with correlated disorder

Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the localization length and the density of states and compare our numerical results with analytical predictions. Specifically, we find two distinct characteristic behaviors in the vicinity of the band center and at the unperturbed band edge, respectively. Furthermore we address the effect of the intrinsic short-range correlations.     

Infinite chain of different deltas: A simple model for a quantum wire

We present the exact diagonalization of the Schr?dinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced. Received 24 June 2002 Published online 29 November 2002     

Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential

We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm.     

Symmetries of multifractal spectra and field theories of Anderson localization

We uncover the field-theoretical origin of symmetry relations for multifractal spectra at Anderson transitions and at critical points of other disordered systems. We show that such relations follow from the conformal invariance of the critical theory, which implies their general character. We also demonstrate that for the Anderson localization problem the entire probability distribution for the local density of states possesses a symmetry arising from the invariance of correlation functions of the underlying nonlinear σ model with respect to the Weyl group of the target space of the model.     

DNA分子链电子结构特性研究

在单电子紧束缚近似下，建立了一维无序二元DNA分子链模型，计算了链长为2×10⁴个碱基对的DNA分子链的电子态密度、局域化特性，并探讨了碱基对的不同组分、格点能量无序度对电子局域态的影响.结果表明：由于DNA分子链中格点能量无序及碱基对的不同组分的存在，其电子波函数呈现出局域化的特性，而局域长度作为衡量电子局域化程度的一个尺度，受碱基对的组分及格点能量无序度的影响. 关键词： DNA分子链 电子结构 电子局域态 局域长度     

Study of density of interface states in MOS structure with ultrathin NAOS oxide

The quality of the interface region in a semiconductor device and the density of interface states (DOS) play important roles and become critical for the quality of the whole device containing ultrathin oxide films. In the present study the metal-oxide-semiconductor (MOS) structures with ultrathin SiO₂ layer were prepared on Si(100) substrates by using a low temperature nitric acid oxidation of silicon (NAOS) method. Carrier confinement in the structure produces the space quantization effect important for localization of carriers in the structure and determination of the capacitance. We determined the DOS by using the theoretical capacitance of the MOS structure computed by the quantum mechanical approach. The development of the density of SiO₂/Si interface states was analyzed by theoretical modeling of the C-V curves, based on the superposition of theoretical capacitance without interface states and additional capacitance corresponding to the charges trapped by the interface states. The development of the DOS distribution with the passivation procedures can be determined by this method.     

Lifshitz Tails for a Class of Schrödinger Operators with Random Breather-Type Potential

We derive bounds on the integrated density of states for a class of Schrödinger operators with a random potential. The potential depends on a sequence of random variables, not necessarily in a linear way. An example of such a random Schrödinger operator is the breather model, as introduced by Combes, Hislop and Mourre. For these models, we show that the integrated density of states near the bottom of the spectrum behaves according to the so called Lifshitz asymptotics. This result can be used to prove Anderson localization in certain energy/disorder regimes.     

The electronic structure of liquid silver chalcogenides: a tight-binding approach

We present a computational study of the electronic structure of the stoichiometric liquid zero-gap semiconductors [Formula: see text], [Formula: see text] and [Formula: see text]. The geometry of the fluids is described by the primitive model of charged hard spheres; the electronic structure is modelled using a tight-binding Hamiltonian. The density of states is computed considering the Madelung potential fluctuations and the topological disorder characteristic of an ionic fluid. Only the introduction of nonzero tight-binding hopping matrix elements - equivalent to the formation of chemical bonds - induces a pseudogap between the chalcogenide conduction band and the silver valence band. The Fermi level can be located in a region of a small density of states; eigenstates at [Formula: see text] are likely to exhibit disorder-induced localization.     

Error analysis of free probability approximations to the density of States of disordered systems

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with perturbation theory and isotropic entanglement theory.     

Non-locally correlated disorder and delocalization in one dimension (II). Localization length

We study the delocalization transition in a one-dimensional Dirac fermion system with randomly varying mass by using supersymmetric (SUSY) methods. In a previous paper, we calculated density of states and found that (quasi-) extended states near the band center are enhanced by non-local correlation of the random Dirac mass. Numerical studies support this conclusion. In this paper, we calculate the localization length as a function of the correlation length of the disorder. The result shows that the localization length is an increasing function of the correlation of the random mass.