Localized phonon states at the edge of the continuous spectrum

An analysis is made of the influence of defects on the averaged Green’s function of optical phonons whose imaginary part is proportional to the cross section for Raman one-phonon light scattering, which depends on the frequency transfer. A variant of the “cross” technique which can take into account the localized states at defects is used. The defects are assumed to be two-dimensional (of the dislocation type) at which localized states exist near the edge of the continuous spectrum interacting weakly with the defect. As a result of this interaction, which depends on the defect concentration, the states of the continuous spectrum are shifted and broadened, the inhomogeneous broadening depending strongly on the frequency transfer (phonon density of states effect), which leads to asymmetry of the Raman line. The defect concentration also influences the localized states which interact mainly via band states.     

Electrons in disordered systems. Scaling near the mobility edge

Renormalization group arguments are applied to an ensemble of disordered electronic systems (without electron-electron interaction). The renormalization group procedure consists of a sequence of transformations of the length and the energy scales, and of orthogonal transformations of the electronic states. Homogeneity and power laws are obtained for various one and two-particle correlations and for the low-temperature conductivity in the vicinity of the mobility edge. Two types of fixed point ensembles are proposed, a homogeneous ensemble which is roughly approximated by a cell model, and an inhomogeneous ensemble.     

Delocalization in one-dimensional tight-binding models with fractal disorder II: existence of mobility edge

In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at the band center (E = 0) in the one-dimensional tight-binding model with fractal disorder [H.S. Yamada, Eur. Phys. J. B 88, 264 (2015)]. In the present work, we study the energy (E ≠ 0) dependence of the normalized localization length (NLL) and the delocalization of the wavefunction at different energy in the same system. The mobility edges in the LDT arise when the fractal dimension of the potential landscape is larger than the critical value depending on the disorder strength, which is consistent with the previous result. In addition, we present the distribution of individual NLL and Lyapunov exponents in the system with LDT.     

Experimental investigation of the edge states structure at fractional filling factors

We experimentally study the electron transport between edge states in the fractional quantum Hall effect regime. We find an anomalous increase of the transport across the 2/3 incompressible fractional stripe in comparison with the theoretical predictions for the smooth edge potential profile. We interpret our results as a first experimental demonstration of the intrinsic structure of the incompressible stripes arising at the sample edge in the fractional quantum Hall effect regime.     

具有p波超流的一维非公度晶格中迁移率边研究

研究了具有p波超流的一维非公度晶格中迁移率边的性质. 发现适当的p波超流可以增加体系中的迁移率边的数目, 并且通过多分形分析确定了迁移率边所在的位置.     

Ginzburg-Landau functional in the vicinity of the mobility edge

The Ginzburg-Landau functional for BCS-type impure superconductors is expressed in terms of a nonlinear -model. It is shown that Anderson localization effects result in the reduction of the rigidity coefficient attached the gradient term in the Ginzburg-Landau functional. However, the rigidity coefficient remains finite at the mobility edge, where the diffusion coefficient for normal excitations vanishes.     

Probing the Ba 5d states in BaTiO3 and BaSO4: A resonant x-ray emission study at the Ba-L3 edge

We have directly probed the Ba 5d states in the ferroelectric barium titanate BaTiO₃ using two bulk-sensitive spectroscopic probes, resonant x-ray emission spectroscopy (RXES) and x-ray absorption spectroscopy in the partial fluorescence mode (PFY-XAS) at the Ba-L₃ edge. The results are compared with those of the non-ferroelectric barium sulfate BaSO₄. While the RXES spectra point to a localized character for the Ba 5d states in both compounds, the main peak of the PFY-XAS spectrum, corresponding to the dipolar transitions from 2p to 5d, is found to be significantly broader for BaTiO₃ than for BaSO₄. On the basis of band structure calculations, this broadening is ascribed to strong hybridization between the unoccupied Ba 5d and O 2p states in the ferroelectric. This suggests that the hybridization between the conduction states of the Ba²⁺ and O^2? ions, and not only Ti⁴⁺ and O^2?, plays a central role in determining the electronic structure of BaTiO₃, and is therefore likely to be indirectly correlated with the occurrence of ferroelectricity in this material.     

Spin-Peierls and incommensurate states in layered S=1/2 system TiOCl

We demonstrate that TiOCl is a good model inorganic system to investigate spin-Peierls state. Our ³⁵Cl and ^47,49Ti NMR data show that a pseudo spin-gap behavior below T*=135 K precedes successive phase transitions at T_c=94 K and into a singlet spin-Peierls ground state with a large energy gap E_g/k_B=430 K.     

The emergence of bound states in a superconducting gap at the topological insulator edge

We consider the edge of a superconducting topological insulator with the impurity in the presence of the Zeeman field. We analytically prove that in the trivial phase two Andreev bound states (ABSs) arise with energies moving from the superconducting gap edges to zero forming two Majorana-like bound states, as the impurity strength varies from 0 to ±2. When the Zeeman field is locally perturbed, ABSs arise both in the trivial and topological phases, but in the topological phase ABSs with energy near the gap edges cannot transform into Majorana bound states and vice versa.     

Fractal characteristics of critical and localized states in incommensurate quantum systems

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.     

Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge

Recently, an interesting family of quasiperiodic models with exact mobility edges(MEs) has been proposed(Phys.Rev. Lett. 114 146601(2015)). It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended(localized) states in the real space to localized(extended) ones in the Fourier space. Therefore,it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively.Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.     

Improvement of mobility edge model by using new density of states with exponential tail for organic diode

The mobility edge(ME) model with single Gaussian density of states(DOS) is simplified based on the recent experimental results about the Einstein relationship. The free holes are treated as being non-degenerate, and the trapped holes are dealt with as being degenerate. This enables the integral for the trapped holes to be easily realized in a program. The J–V curves are obtained through solving drift-diffusion equations. When this model is applied to four organic diodes, an obvious deviation between theoretical curves and experimental data is observed. In order to solve this problem, a new DOS with exponential tail is proposed. The results show that the consistence between J–V curves and experimental data based on a new DOS is far better than that based on the Gaussian DOS. The variation of extracted mobility with temperature can be well described by the Arrhenius relationship.