Electronic properties of one-dimensional quasiperiodic lattices: Green's function renormalization group approach

Using the inflation-deflation symmetry, we have developed a new real-space decimation approach to study the electronic properties of one-dimensional quasiperiodic lattices. The key result is the construction of a compact renormalization group that allows simple calculation of the average Green's function and the average density of states to any degree. The Fibonacci and the generalized Fibonacci lattices are used to demonstrate the method. Numerical results for the average density of states of these lattices show a good agreement with the results obtained by other methods. This confirms the validity and the efficiency of the approach.     

一族一维准晶的局部电子性质

本文利用推广的实空间重整化群方法,研究按膨胀规则(A,B)→(AⁿB,A)构造的一族一维泛Fibonacci准晶系(A_n序列)的局部电子性质。所引入的2n²+1种基本变换可计算该族一维准晶中任一A_n序列在任意格点的局部格林函数和局部态密度。结果表明,该方法是有效的,A_n链的电子局部态密度象Fibonacci准晶一样,呈现临界性。 关键词：     

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 CFC 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.     

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.     

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.     

聚二乙炔电子特性研究

将聚二乙炔主链简化为有限的一维复式碳原子链,利用紧束缚近似,在周期性和非周期性边界条件下,考虑π电子在最近邻的跳跃,计算和分析了不同数目聚二乙炔单体聚合而成的有限一维原子链的能谱和态密度,揭示了聚二乙炔电子结构的基本特点.     

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.     

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.     

Dynamical properties of three component Fibonacci quasicrystal

We present a real space renormalization group (RSRG) method to study the lattice dynamics of a three component Fibonacci (3CF) quasicrystal. Phonon dispersion relations corresponding to different models of this lattice are obtained. Some features of the phonon dispersion curves are compared with experiments on real quasicrystal. It is observed that the positions of the strongest Bragg peaks calculated analytically are in perfect agreement with our RSRG calculations. Received 23 October 2000 and Received in final form 11 January 2001     

Electronic density of states in sequence dependent DNA molecules

We report in this work a numerical study of the electronic density of states (DOS) in π-stacked arrays of DNA single-strand segments made up from the nucleotides guanine G, adenine A, cytosine C and thymine T, forming a Rudin-Shapiro (RS) as well as a Fibonacci (FB) polyGC quasiperiodic sequences. Both structures are constructed starting from a G nucleotide as seed and following their respective inflation rules. Our theoretical method uses Dyson’s equation together with a transfer-matrix treatment, within an electronic tight-binding Hamiltonian model, suitable to describe the DNA segments modelled by the quasiperiodic chains. We compared the DOS spectra found for the quasiperiodic structure to those using a sequence of natural DNA, as part of the human chromosome Ch22, with a remarkable concordance, as far as the RS structure is concerned. The electronic spectrum shows several peaks, corresponding to localized states, as well as a striking self-similar aspect.     

Specific heat spectra for quasiperiodic ladder sequences

We performed a theoretical study of the specific heat C(T) as a function of the temperature for double-strand quasiperiodic sequences. To mimic DNA molecules, the sequences are made up from the nucleotides guanine G, adenine A, cytosine C and thymine T, arranged according to the Fibonacci and Rudin-Shapiro quasiperiodic sequences. The energy spectra are calculated using the two-dimensional Schr?dinger equation, in a tight-binding approximation, with the on-site energy exhibiting long-range disorder and non-random hopping amplitudes. We compare the specific heat features of these quasiperiodic artificial sequences to the spectra considering a segment of the first sequenced human chromosome 22 (Ch22), a real genomic DNA sequence.     

Flux modulated flat band engineering in square-kagomé ladder network

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagomé ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical boundary created by the site with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.     

Electronic transport in double-strand poly(dG)-poly(dC) DNA segments

We study the electronic properties of a double-strand quasiperiodic DNA molecule modeled by a one-dimensional effective Hamiltonian, which includes contributions from the nucleobasis system as well as the sugar-phosphate backbone. Our theoretical approach makes use of Dyson's equation together with a transfer-matrix treatment, considering an electronic tight-binding Hamiltonian model to investigate the electronic density of states (DOS) and the electronic transmissivity of sequences of DNA finite segments. To mimic the DNA segments, we consider the finite quasiperiodic sequences of Fibonacci's type, in a poly(dG)-poly(dC) configuration, whose building blocks are the bases guanine G and cytosine C. We compared the electronic transport found for the quasiperiodic structure to those using a sequence of natural DNA, as part of the human chromosome Ch22.     

A renormalization approach to describe charge transport in quasiperiodic dangling backbone ladder (DBL)-DNA molecules

We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.     

一维准周期体系中的电子延展态

本文采用动力学映象方法,研究了作为泛Fibonacci序列一个子集的一系列一维准周期体系的电子性质,该一维准周期体系S_∞由递推公式S_l+1=S_l^2j-1S_l-1²ⁱ构造,其中l≥1,i,j为正整数,初始条件为S₀和S₁,结果表明,该一维准周期体系无论是对角模型和非对角模型,都存在电子延展态。 关键词：     

Quantum hyperdiffusion in one-dimensional tight-binding lattices

Transient quantum hyperdiffusion, namely, faster-than-ballistic wave packet spreading for a certain time scale, is found to be a typical feature in tight-binding lattices if a sublattice with on-site potential is embedded in a uniform lattice without on-site potential. The strength of the sublattice on-site potential, which can be periodic, disordered, or quasiperiodic, must be below certain threshold values for quantum hyperdiffusion to occur. This is explained by an energy band mismatch between the sublattice and the rest uniform lattice and by the structure of the underlying eigenstates. Cases with a quasiperiodic sublattice can yield remarkable hyperdiffusion exponents that are beyond three. A phenomenological explanation of hyperdiffusion exponents is also discussed.     

广义Fibonacci准周期链能谱性质

本文研究一种广义Fibonacci准周期链(孪生子模型)的电子及声子谱。重整化群分析表明,电子能谱具有3分支的自相似结构,但每一层中的中间子带又类似于周期系统。数值计算结果证明这种分析的正确性。对于声子谱,则显示出与Fibonacci链相同的性质。 关键词：     

Symmetry-breaking in local Lyapunov exponents

Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time Lyapunov exponents are nonzero, but owing to a symmetry, their global averages vanish. When the system becomes nonintegrable, this symmetry is broken. A parallel to this phenomenon occurs in mappings which derive from quasiperiodic Schr?dinger problems in 1-dimension. For values of the energy such that the eigenstate is extended, the Lyapunov exponent is zero, while if the eigenstate is localized, the Lyapunov exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local Lyapunov exponents, and corresponds to a breaking of a symmetry of the wavefunction in extended and critical states. Received 25 October 2001 / Received in final form 8 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: r.ramaswamy@mail.jnu.ac.in     

Generalized inverse participation numbers in metallic-mean quasiperiodic systems

From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers Z_q ~ N - ^{D_q (q - 1)}Z_q \sim N - ^{D_q (q - 1)} with the system size N. In particular, we investigate d-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation D _q ^dd = dD _q ^1d holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.