一维晶格振动声子谱的全量子理论和"不变量本征算符"方法

建立一维晶格振动声子谱的全量子理论,其哈密顿量是自动包含了Born-von-Karmann边界条件的环链量子哈密顿量,然后用不变本征算符方法简捷地求出其声子谱.     

Optical vibration modes and electron－phonon interaction in ternary mixed crystals of polar semiconductors

Optical vibrations of the lattice and the electron－phonon interaction in polar ternary mixed crystals are studied in the framework of the continuum model of Born and Huang and the random-element-isodisplacement model. A normal-coordinate system to describe the optical vibration in ternary mixed crystals is correctly adopted to derive a new Fr?hlich-like Hamiltonian for the electron－phonon interaction including the unit-cell volume variation influence. The numerical results for the phonon modes, the electron－phonon coupling constants and the polaronic energies for several typical materials are obtained. It is verified that the nonlinearity of the electron－phonon coupling effects with the composition is essential and the unit-cell volume effects cannot be neglected for most ternary mixed crystals.     

On the stability of ferromagnetism in intermediate valence systems

It is known that the deformations of the electronic charge density induced by lattice displacements play an important role in lattice dynamics. The multipole expansion of these deformations around the positions of both the cation and the anion leads to a rather general type of deformable shell model. This cluster deformation model can be applied not only to ionic crystals but also to a large variety of other materials like mixed-valence compounds. Taking TiN as an example, it is shown that the model is able to describe the very pronounced phonon anomalies in superconducting transitionmetal compounds and to reproduce the measured phonon dispersion curves within the experimental errors.     

纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

非简谐性离子晶格在光场中的能谱动态斯塔克效应

以文献（５）在偶极近似与旋转波近似下导出的哈密顿算符（Ｈａｍｉｌｔｏｎｉｎａｎ）为基础,并以单模光频支声子与单模光场的共振耦合系统为简化模型,取得该耦合系统相互作用能谱的比较严格的解析解,同时还发现一种起源于声子－声子耦合的真空（能级）平移效应,可以预期,本文所研究的能谱将是有关晶体物质结构的又一种信息源。     

Decoherence in superconducting quantum bits by phonon radiation

We discuss a fundamental limitation for the coherent operation of superconducting quantum bits originating from phonon radiation generated in the Josephson junctions of the device. The time dependent superconducting phase across the junction produces an electric field that couples to the underlying crystal lattice via the piezoelectric effect. We determine the radiation resistance of the junction due to phonon emission and derive substantial decoherence rates for the quantum bits, which are compatible with quality factors measured in recent experiments.     

On the self-trapping of an electron due to lattice interaction

The problem of the sharpness of the polaron self-trapping transition for a single electron placed in the conduction band of an insulator and interacting with the phonons of the underlying lattice is investigated within the Fröhlich Hamiltonian. It is shown that this phenomenon depends sensitively on the lattice dimensionality, the nature of the electron-phonon coupling, the nature of the phonon dispersion; and on the discrete or the continuum nature of the applicable Hamiltonian.     

Superconductivity mediated by the lattice fluctuations in the polaron system

The coupling between the charge transfer and the lattice fluctuations is proposed as a possible mechanism of the superconductivity in the polaron system near the cross-over from the quasi-localized to the delocalized regime. The corresponding self-energy matrix is deduced using the Holstein Hamiltonian and the equations for the off-diagonal order are formulated. The lower bound on the superconducting critical temperature is estimated and the possible relevance of the proposed mechanism for the superconducting copper oxides is discussed.     

The rôle of one- and few-phonon processes in the quantum diffusion of light particles in superconductors

The hopping motion of charged light particles in superconducting metals is discussed within the framework of a two-state model. In addition to the coupling to the superconducting electrons, the influence of phonons is investigated. It is shown that sufficiently far below the critical temperature the hopping rate is dominated by one-phonon processes if the static energy shifts between the particle ground states (so-called energy asymmetries) are finite but smaller than twice the BCS energy gap. The rôle of special two-phonon processes (named diphonon processes) resulting from non-linear coupling to the lattice is investigated. In the limit of energy asymmetries larger than twice the BCS energy gap phonon coupling does not crucially influence the jump rates.This article was processed using Springer-Verlag T_EX Z. Physik B macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

A model Hamiltonian for MgB $\mathsf{_{2}}$ which takes into account its unusual phononic features

Taking as a starting point the results of LDA calculations, which show that in the phonons have a strong quartic anharmonicity and that the bond-stretching electron-phonon interaction (EPI) has both a linear and a large quadratic component, we propose a model Hamiltonian which successfully matches a number of experimental evidences. We relate the single critical temperature for both superconducting gaps to a phonon-induced inter-band coupling whose amplitude increases with temperature. We also obtain phonon frequencies and linewidths depending on the band filling, as well as band energies and hybridization amplitudes depending on the phonon number.Received: 12 May 2003, Published online: 22 September 2003PACS: 74.20.-z Theories and models of superconducting state - 74.70.-b Superconducting materials     

Splitting of the zone-center phonon in MnO and NiO

We develop a model based on the superexchange interaction and the Heisenberg Hamiltonian to understand the zone-center transverse optical (TO) phonon splittings in the late transition-metal oxides with type-II antiferromagnetic ordering. Even for a cubic rocksalt lattice, the anisotropic magnetic coupling due to the non-cubic distribution of the spin density can produce a splitting of the TO phonon energies. To calculate these splittings for MnO and NiO, we apply a recently implemented LSDA+U method based on a pseudopotential plane-wave formalism and obtain results for both MnO and NiO which are consistent with our model predictions. The calculated splitting for MnO is in excellent agreement with a recent experiment, while the result for NiO appears to be inconsistent with current experimental results and entails further investigation.     

Possible relevance of lattice effects in high-T c superconductors

The relevance of the lattice-mediated superconducting pairing in a system of quasilocalized polarons dressed by local lattice deformations is considered. The spin correlations are taken into account using thet-J model expressed in terms of holon and spin operators. The Holstein-like Hamiltonian for holons with the transport term depending on spin correlations is transformed by the generalized Lang-Firsov transformation which implies the spread of the charge and the deformations to the nearest neighbours. The analytical formula for the superconducting transition temperatureT _c is deduced using the assumption of an extremely narrow polaron band. The hole-concentration dependence ofT _c and the isotope exponent are discussed using the classical approximation for incommensurate spiral spin correlations. This work was supported by the Grant Agency of the Czech Republic, project No. 202/96/0864.     

Real structure influence on the electron–phonon coupling properties of niobium

We performed density functional theory calculations using niobium (Nb) as a model system of a conventional superconductor, to correlate the distortion of twin defects with the electron–phonon coupling properties. Calculations using different settings of the Nb elementary cell (relaxed, distorted, super cell with zig‐zag twin defect) showed that only by including real structure elements into the setting, the Eliashberg spectral function representing the electron–phonon coupling properties was derived convincingly. Based on these density functional theory calculations of the electron–phonon cou‐ pling properties of Nb, we suggest a model for a combined superconducting/charge density wave ground state which uses a lattice distortion induced into the crystal by two‐dimensional defects as modulated background potential of the charge density wave phase. The coexistence of both phases is hereby necessary for a fine‐tuning of the Fermi surface within the small local domain of the defect to match the wavelength of the lattice distortion and the Fermi wavelength by pairing fermions to bosons. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Influence of acoustic phonons on dephasing of free excitons in quantum wells

A theory of the dephasing rate of quasi-2D free excitons due to acoustic phonon interaction at low exciton densities is presented. Both deformation potential and piezoelectric couplings are considered for the exciton–phonon interaction in quantum wells. Using the derived interaction Hamiltonian obtained recently by us, exciton linewidth and dephasing rate are calculated as a function of the exciton density, exciton temperature, exciton momentum and lattice temperature.     

离子晶格非简谐振动引起的光学非线性与增强吸收型光双稳

处理了光场（电磁场）与离子晶体的非简谐性振动之间的相互作用问题。导出了用简正坐标即声子模式所表达的非线性晶格动力学和非线性宏观极化。在旋转波近似下，得到在入射光驱动下光子－声子耦合体系的总的相干性哈密顿算符。通过相应的静态方程证明该耦合系统会出现增强吸收型光学双稳性，这也就证明了光场与各种玻色子型固体元激发，如光频支声子和半导体中激子的非线性耦合可以作为增强吸收型光双稳的机制。     

Phenomenological theory of the interaction of electrons with polar phonons in anisotropic crystals

The generalized phenomenological lattice equations of Huang are used to derive the Hamiltonian of the coupled electron phonon system in an anisotropic crystal. The dependence of the coupling constant on the angle formed by the phonon wave vector and the axis of an uniaxial crystal is given explicitely. A significant dependence of the coupling constant on this angle persists even in the case of dominant mechanical or electrostatic forces.     

Electron-phonon interaction in hemispherical quantum dot

Within the framework of the dielectric continuum (DC) model, the optical phonon modes and electron-optical-phonon interaction in hemispherical quantum dot are investigated. The proper eigenfunctions for longitudinal optical (LO) and interface optical (IO) phonon modes are constructed. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron-phonon interaction. The dispersion relation of IO phonon modes is size independent. The potential applications of these results are also discussed.     

Lattice vibrations of armchair carbon nanotubes: phonons,soliton deformations and lattice discreteness effects

Small and large-amplitude elastic deformations of the armchair structure of single-walled carbon nanotubes are investigated with emphasis on the cylindrical geometry. As starting model, we consider a discrete one-dimensional lattice of atoms interacting via a Lennard-Jones type two-body potential. In an expansion scheme using cylindrical coordinates where radial displacements are assumed negligible compared to the angular motions, a sine-lattice Hamiltonian is derived. In the limit of small-amplitude angular displacements, the dispersion spectrum of acoustic phonons is derived and the associate characteristic frequency is given as a function of parameters of the model. In the large-amplitude regime, lattice vibrations give rise to kink-type deformations which move undergoing lattice dispersion and lattice discreteness effects. The dispersion law of the kink motion is obtained and shown to lower the effect of lattice discreteness, giving rise to a vanishing Peierls stress for kink sizes of the order of a few lattice spacings. Implications of the coupling of two armchair structures on the stability of vibrational modes of an individual armchair nanotube are also discussed. A gap of forbidden modes is predicted in the phonon spectrum while the energy needed to create a kink deformation in individual nanotubes is shifted in the presence of a wall-to-wall interaction.Received: 2 August 2004, Published online: 14 December 2004PACS: 81.07.De Nanotubes - 62.30. + d Mechanical and elastic waves-vibrations - 63.22. + m Phonons in low-dimensional nanoscale materials - 63.20.Ry Anharmonic lattices modes     

Phonon dispersion and electron-phonon coupling in MgB2 and AlB2.

We present a first principles investigation of the lattice dynamics and electron-phonon coupling of the superconductor MgB2 and the isostructural AlB2 within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. Complete phonon dispersion curves and Eliashberg functions alpha2F are calculated for both systems. The main differences are related to high frequency in-plane boron vibrations, which are strongly softened in MgB2 and exhibit an exceptionally strong electron-phonon coupling. We also report on Raman measurements, which support the theoretical findings. Implications for the superconducting transition temperature are briefly discussed.     

Electron–phonon interaction in fan-shaped quantum dot and quantum wire

The optical phonon modes and electron–optical-phonon interaction in fan-shaped quantum dot and quantum wire are studied with the dielectric continuum (DC) model and separation of variables. The explicit expressions for the longitudinal optical (LO) and interface optical (IO) phonon eigenmodes are deduced. It is found that there exist two types of IO phonon modes: top interface optical (TIO) phonon mode and arc interface optical (AIO) phonon mode, in a fan-shaped quantum dot. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron–phonon interaction. The potential applications of these results are also discussed.