Electronic properties of a class of one-dimensional quasiperiodic systems

Electronic properties of a class of one-dimensional quasiperiodic systems are studied by the extended Kohmoto-Kadanoff-Tang (KKT) renormalization-group method. The employed models are tight-binding diagonal and off-diagonal models. It is showed that the energy spectra of the quasiperiodic systems are Cantor-like, namely the spectra are self-similar and the energy gaps are every-where dense on the realE-line.     

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.     

The acoustic phonon spectrum of penrose tilings

The spectral weight function associated with the vibrational modes of a two-dimensional quasicrystal is studied numerically. It is found that plane waves corresponding to special symmetry points in reciprocal space are at least very nearly eigenstates of the system. Near periodicities in lineshape parameters plotted as a function of wavevector are found to occur, and the first Brillouin zone edge is identified with lattice parameters. The contribution of these modes to the specific heat is found to obey a two-dimensional Debye Law.     

Statistical mechanics of a quasiperiodic one-dimensional magnetic chain

In this paper we study the thermodynamic properties of the Ising model on a linear chain in which the sites are generated according to the Fibonacci sequence. We calculate the partition function, the specific heat and the q-dependent magnetic susceptibility.     

The one phonon Raman spectrum in microcrystalline silicon

The red shift and the broadening of the Raman signal from microcrystalline silicon films is described in terms of a relaxation in the q-vector selection rule for the excitation of the Raman active optical phonons. The relationship between width and shift calculated from the known dispersion relation in c-Si is in good agreement with available data. An increase in the decay rate of the optical phonons predicted on the basis of the same model is confirmed experimentally.     

Statistical properties of one-dimensional binary sequences with power-law power spectrum

By the Fourier filtering method, we generate one-dimensional binary sequences from coarse-grained continuous sequences with preset exponents α₀. Using the spectrum analysis, we find that the corresponding binary sequences have pure 1/f^α power spectrum and spectrum exponents α∈[0.0,2.0], where f is the frequency. We evaluate numerically the relation between α and α₀. Using the autocorrelation function analysis, the detrended fluctuation analysis, the duration time analysis and the entropy analysis, we investigate extensively the statistical properties of such binary sequences. We find that the statistical properties are basically different for α<1 and α>1, and binary sequences become more and more ordered as α increases.     

On phonon localization in nearly one-dimensional solids

The condition for experimental observation of effects of phonon localization in nearly one-dimensional dielectric solids are investigated. While there seems to be no observable effect in thin wires, phonon localization can lead to a minimum in the thermal diffusivity curve D_T(T) of solids with a chain-like structure and weak inter-chain molecular forces.     

The spectrum of a one-dimensional hierarchical model

The spectrum of a discrete Schrödinger operator with a hierarchically distributed potential is studied both by a renormalization group technique and by numerical analysis. A suitable choice of the potential makes it possible to reduce the original problem to a two-dimensional map. Scaling laws for the band-edge energyE _be and for the integrated density of states are predicted together with the global properties of the spectrum. Different scaling regimes are obtained depending on a hierarchy positive parameterR: for R<1/2 the usual scaling laws for the periodic case are obtained, while forR>1/2 the scaling behavior depends explicitly onR.     

Transmission gaps in one-dimensional Fibonacci quasiperiodic structure containing epsilon-negative materials

We investigate the transmission properties of one-dimensional Fibonacci quasiperiodic structure consisting of dispersive and lossless epsilon-negative (ENG) materials. It is found that for both TE and TM polarizations with normal and oblique incidences, there exist transmission gaps which are invariant with a change of scale and sensitive to incident angles. Analytical methods based on transfer matrices and effective medium theory have been used to explain the properties of transmission gaps.     

Anharmonic phonon lifetimes in carbon nanotubes: evidence for a one-dimensional phonon decay bottleneck

High-resolution Raman spectroscopy is applied to suspended single-walled carbon nanotubes (SWNTs) to elucidate the puzzling differences in the lifetime of the radial breathing mode (RBM) obtained from different experimental techniques. Whereas recent tunneling experiments suggest a room temperature RBM lifetime as long as 10 ns, previous Raman experiments yield lifetimes shorter than 2 ps. The lifetimes obtained in this study are longer than 5 ps-a significant step in the direction of the tunneling results. We argue that the remaining discrepancy is due to the existence of phonon decay bottlenecks caused by the one-dimensional nature of nanotubes. Numerical simulations of the RBM decay show that it is possible to reconcile the short lifetimes measured spectroscopically with the long lifetimes obtained in tunneling experiments.     

Photonic properties of metallic-mean quasiperiodic chains

The light propagation through a stack of two media with different refractive indices, which are aligned according to different quasiperiodic sequences determined by metallic means, is studied using the transfer matrix method. The focus lies on the investigation of the influence of the underlying quasiperiodic sequence as well as the dependence of the transmission on the frequency, the incidence angle of the light wave and different ratios of the refractive indices. In contrast to a periodically aligned stack we find complete transmission for the quasiperiodic systems for a wide range of different refractive indices for small incidence angles. Additional bands of moderate transmission occur for frequencies in the range of the photonic band gaps of the periodic system. Further, for fixed indices of refraction we find a range of almost perfect transmission for angles close to the angle of total reflection, which is caused by the bending of photonic transmission bands towards higher frequencies for increasing incidence angles. Comparing with the results of a periodic stack the quasiperiodicity seems to have only an influence in the region around the midgap frequency of a periodic stack.     

Optical phonon spectrum of germanium quantum dots

We have observed additional lines, shifted in both directions relative to the frequency of the bulk phonon of Ge, in the Raman scattering spectra from optical phonons in germanium quantum dots. The observed phonon modes are shown to be due to the straining of the quantum dots as a result of the lattice mismatch of the Ge and Si matrices. The observed frequency shifts, with allowance for optical-phonon localization effects, make it possible to determine the sizes of the regions with different strain states in the quantum dots. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 279–283 (25 August 1999)     

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with nonHermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.