Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

Effects of Thermal Lattice Vibration on the Effective Potential of Weak-Coupling Bipolaron in a Quantum Dot

Based on the Huybrechts' linear-combination operator,effects of thermal lattice vibration on the effective potential of weak-coupling bipolaron in semiconductor quantum dots are studied by using the LLP variational method and quantum statistical theory.The results show that the absolute value of the induced potential of the bipolaron increases with increasing the electron-phonon coupling strength,but decreases with increasing the temperature and the distance of electrons,respectively;the absolute value of the effective potential increases with increasing the radius of the quantum dot,electron-phonon coupling strength and the distance of electrons,respectively,but decreases with increasing the temperature;the temperature and electron-phonon interaction have the important influence on the formation and state properties of the bipolaron:the bipolarons in the bound state are closer and more stable when the electron-phonon coupling strength is larger or the temperature is lower;the confinement potential and coulomb repulsive potential between electrons are unfavorable to the formation of bipolarons in the bound state.     

Coherent state and superconductivity in the free carrier-bipolaron interacting system

In this paper a model to describe the free carrier-bipolaron interacting system is proposed. Effective hopping of the bipolaron is studied in the slave-boson approach, and a characteristic temperature T¹ is obtained, below which the system enters a coherent state. The density of states in the normal state and the superconductivity of the system are discussed in a quasiparticle picture. The results show that the mixing between the free carrier and the bipolaron results in an enhancement of the effective mass of the quasiparticle and meanwhile the renormalized coupling interaction, arising from the negative correlation energy in the bipolaron region, enhances the effective superconducting coupling interaction. Under the most favourable conditions, the superconducting transition temperature T_c ∼ ω_c, where ω_c is the Debye frequency related with local electron-phonon coupling. In general we have T¹ > T_c ⪢ T_c0 (T_c0 is the superconducting transition temperature of a usual superconductor). Therefore the system will firstly enter a coherent state before becoming a high-T_c superconductor.     

Soliton-Like Bipolaron in Two-Dimensional Deformable Electron-Phonon System

Based on Emin's idea of deformation potential in deformable continuum, a bipolaron Hamiltonian is generalized to two-dimensional deformable electron-phonon system with the assumption of localized deformation potential of δ function. The dynamic properties of bipolaron are studied in the framework of Davydov's soliton theory, and a nonlinear Schrodinger equation is derived using the principle of least action. By function-series method, an exact two-dimensional (2D) soliton solution is obtained. We find that the center-of-mass motion of bipolaron is shown in a solitary wave form, and its relative motion is a harmonic one.     

Criterion for formation of the first bound state of an optical polaron

The ground state of an optical polaron has been analyzed for an arbitrary force of the electron-phonon coupling. The eigenvalue differential equation is transformed into the Fredholm integral equation. With the trace method applied to the kernel of integral equation, it is found that the first bound state of the optical polaron appears only provided that the dimensionless coupling constant obeys the inequality α_c≥2.8.     

Electron correlations and instability of a two-center bipolaron

The energy of a large bipolaron is calculated for various spacings between the centers of the polarization potential wells of the two polarons with allowance made for electron correlations (i.e., the explicit dependence of the wave function of the system on the distance between the electrons) and for permutation symmetry of the two-electron wave function. The lowest singlet and triplet 2³S states of the bipolaron are considered. The singlet polaron is shown to be stable over the range of ionic-bond parameter values η≤η_m≈0.143 (η=?_∞/?₀, where ?_∞ and ?₀ are the high-frequency and static dielectric constants, respectively). There is a single energy minimum, corresponding to the single-center bipolaron configuration (similar to a helium atom). The binding energy of the bipolaron for η → 0 is J_bp=?0.136512e⁴m^*/?²? _∞ ² (e and m* are the charge and effective mass of a band electron), or 25.8% of the double polaron energy. The triplet bipolaron state (similar to an orthohelium atom) is energetically unfavorable in the system at hand. The single-center configuration of the triplet bipolaron corresponds to a sharp maximum in the distance dependence of the total energy J_bp(R); therefore, a transition of the bipolaron to the orthostate (e.g., due to exchange scattering) will lead to decay of the bound two-particle state. The exchange interaction between polarons is antiferromagnetic (AFM) in character. If the conditions for the Wigner crystallization of a polaron gas are met, the AFM exchange interaction between polarons can lead to AFM ordering in the system of polarons.     

Al_xGa_(1-x)As:Si中DX中心的双极化子机制及统计分析

基于极化子和双极化子的物理图像,采用无拟合参数的巨正则统计方法计算了Si掺杂的AlxGa1-xAs的导带载流子浓度,计算得到的理论结果从高温到低温都与实验结果定量一致.计算证实了AlxGa1-xAs:Si中的DX中心的基态DX-是电子-晶格相互作用产生的负电双极化子.处于热平衡状态时,施主Si在AlxGa1-xAs中除了电离状态,处于不同晶格构型的单、双极化子态共存,低温时双极化子态被冻结;光照下发生持续光电导时,双极化子态变成单极化子态同时向导带释放一个电子,此过程伴随着进一步的晶格弛豫.理论与实验的对照说明单电子局域的DX0态在热平衡时并不能稳定存在,这和提出的双极化子机制是完全一致的.     

Chaotic polaronic and bipolaronic states in the adiabatic Holstein model

A rigorous proof for the existence of bipolaronic states is given for the adiabatic Holstein model for any lattice at any dimension, periodic or not, and for an arbitrary band filling, provided that the electron-phonon coupling (in dimensionless units) is large enough. The existence of mixed polaronic-bipolaronic states is also proven, but for larger electron-phonon coupling. These states consist of arbitrary distributions of bipolarons (or of bipolarons and polarons) localized in real space which can be simply labeled by pseudospin configurations as for a lattice gas model. The theory not only applies to periodic crystals, but also to quasicrystals, amorphous structures, polymer network, etc.When these bipolaronic and mixed polaronic-bipolaronic states exist, it is proven that: (1) These bipolaronic (and mixed polaronic-bipolaronic) states exhibit a nonzero phonon gap with a nonvanishing lower bound and an electronic gap at the Fermi energy. (2) These structures are insulating. The perturbation generated by any local change in the bipolaronic or polaronic distribution or by any charged impurity or defect decays exponentially at long distance. (3) These bipolaronic (and mixed polaronic-bipolaronic) states persist for any uniform magnetic field. (4) For large enough electron-phonon coupling, the ground state of the extended adiabatic Holstein model is a bipolaronic state when there is no uniform magnetic field or when it is small enough. It becomes a mixed polaronic-bipolaronic state for large enough magnetic field (note that the mixed polaronic-bipolaronic states are magnetic).In one-dimensional models, the ground state is an incommensurate (or commensurate) charge density wave (CDW) as predicted by Peierls (this result is not rigorous, but has been confirmed numerically). It is proven that the ground state becomes a bipolaronic charge density wave (BCDW) at large enough electron-phonon coupling. The existence of a transition by breaking of analyticity (TBA), which was numerically observed as a function of the electron-phonon coupling, is then confirmed. In that case, the shape of the effective bipolaron can be numerically calculated. It is observed that its size diverges at the TBA. The physical properties of BCDWs are rather different from those predicted by standard charge density wave theory. Bipolaronic charge density waves can also exist in models which are not only low-dimensional, but purely two- or three-dimensional.The technique for proving these theorems is an application of the concept of anti-integrability initially developed for Hamiltonian dynamical systems. It consists in proving that the eigenstates of the (trivial) Hamiltonian (called antiintegrable) obtained by canceling all electronic and lattice kinetic terms survive as a uniformly continuous function of the electronic kinetic energy terms in the Hamiltonian up to a certain threshold.     

Optical properties of BiTeI semiconductor with a strong Rashba spin-orbit interaction

We have modeled the 4f ¹-5d ¹ absorption spectrum of a LiYF₄:Ce³⁺ crystal at zero temperature using a microscopic model of the electron-phonon interaction and the real spectrum of LiYF₄ lattice vibrations. Effects caused by mixing of the wave functions of different states of the 5d ¹ excited configuration of the Ce³⁺ ion, which is induced by the electron-phonon interaction, are considered based on the calculations of the second-, third-, and fourth-order exact moments of curvature of the spectrum envelope. We have shown that the large value of the splitting between the maxima of the bands in the absorption spectrum that correspond to transitions to the third and fourth 5d ¹ levels is a result of the nonadiabatic interaction of 5d electrons with lattice vibrations.     

Local and pseudolocal Jahn-Teller states of a crystal with impurity Γ8 term

The multimode Jahn-Teller effect for an impurity in the Γ₈ ground state of a double point group is considered. The vibronic coupling with the trigonal (t₂) crystal vibrations is taken into account. It is shown that the vibronic coupling leads to the appearance of local and pseudolocal electron-phonon states. The spectral and symmetry characteristics of these states are obtained.     

The bound state of two-electrons in crystals

The bound state of two-electrons and the existence of a bipolaron are studied using the expression of the effective potential of interactions in crystals by considering in addition to the electron-lattice, i.e. electron-phonon interaction, also the electron-electron, i.e. electron-plasma interaction. It is shown that the electron-electron interaction strengthens the bound state, making the potential gap deeper and wider, and leads to the appearance of a supplementary narrow gap, the so-called plasma gap. The conditions for the existence of the bound state of two electrons, i.e. a bipolaron, are established and the case of germanium is analyzed in detail. The result of calculating the energy minimum value and the effective potential contains — as limit cases in the single-electron approximation — the well-known results given in literature.     

Critical value computation for H∞-Riccati difference equations

In designing finite horizon discrete time H_∞ controllers, the associated H_∞-Riccati difference equations must be solved. But the Riccati equation has a non-negative solution only when γ⁻² is small enough. So it is important to get the upper bound of the parameter, i.e., the critical value that ensures the existence of the solution to the Riccati equation. The solution sequence of the Riccati difference equation can be constructed by the conjoined basis of an associated linear Hamiltonian difference system. Based on this expression and the Hamiltonian difference system eigenvalue theorems, the equivalence between the critical value and the first order eigenvalue of the linear Hamiltonian difference system is presented. Since the critical value is also shown to be the fundamental eigenvalue of a generalized Rayleigh quotient, an extended form of Wittrick-Williams algorithm is presented to search this value.     

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The ground-state (GS) and excited-state energies of the Fröhlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.     

The internal coordinate path Hamiltonian; application to methanol and malonaldehyde

The internal coordinate path Hamiltonian is introduced for the study of the vibrations of molecules which have one large amplitude motion. The Hamiltonian is represented in terms of a one path coordinate and 3N—7 normal coordinates. The variational method is used to solve the Schrödinger equation. The molecules studied are methanol and malonaldehyde. For methanol the internal coordinate is a dihedral angle, for malonaldehyde it is the difference in the distances between the migrating hydrogen and the neighbouring oxygen atoms. For methanol there is little coupling between the path and the normal coordinates and so no complications were encountered in the calculations which used harmonic surfaces generated by density functional and M?ller—Plesset theory. Fundamental frequencies were predicted. Malonaldehyde is a different story. There is substantial coupling between the path coordinate and several of the normal coordinates. This introduces many complications: an anharmonic surface is essential and large variational configuration interaction calculations are essential for convergence. Furthermore, because the Coriolis terms require the evaluation of derivatives of both the nuclear coordinates and the normal coordinate eigenvectors along the path, great care must be taken with these numerical procedures. B3LYP predicts too low a transition state which overemphasizes the large Coriolis terms near the transition state. This may be one of the reasons why our fundamental vibrations are in poor agreement with observation. It is most encouraging that the tunnelling splitting is 58 cm^?1 (obs. 21.56 cm^?1), obtained with our quartic density functional surface.     

Microwave spectrum of torsionally excited acetic acid

The microwave spectrum corresponding to the first excited state of the methyl torsion in acetic acid has been identified by means of microwave-microwave double resonance. Although the A-E splittings are extremely large, a reasonable fit has been obtained for the v = 0 and v = 1 states simultaneously by using a Hamiltonian which allows for geometry relaxation upon internal rotation. Barrier parameters are V₃ = 169.90 ± 0.06 cm^?1 and V₆ = ?6.74 ± 0.02 cm^?1. An interpretation of the parameters describing nonrigidity is given in terms of a model with two relaxing bond angles, which is qualitatively supported by ab initio calculations.     

The vibration-rotation problem in triatomic molecules allowing for two large-amplitude stretching vibrations

An expression for the Hamiltonian of a vibration-rotating triatomic molecule is derived, using two curvilinear stretching coordinates ?₁ and ?₃ and one rectilinear bending coordinate S₂, in such a way that the Hamiltonian obtained is applicable to any bent triatomic molecule and allows for large displacements along the stretching coordinates. From this, a zeroth-order Hamiltonian H_s⁰ (?₁, ?₃) is obtained, describing the energy levels associated with the two stretching vibrations ν₁ and ν₃. The vibrational energy levels (v₁, v₃^even) of an XY₂ molecule having unequal bond lengths at equilibrium are then calculated. The kinetic energy T₀ (?₁, ?₃) of the Hamiltonian effectively takes into account the two large-amplitude motions in ν₁ and ν₃ together with their interaction. A model calculation is described for a bent XY₂ molecule (SO₂ in its ¹A′ (¹B₂) excited state) in which the ν₃ oscillation occurs in a double-minimum potential. Coupling by kinetic energy terms in the Hamiltonian turns out to be very small in this example.     

Fluorescence from the 2B1 state of NO2 excited at 4545 Å

The 4545 Å line of the Ar⁺ laser has been used to excite a ^pR₁ line of a vibrational band of the ²B₁-²A₁ system of nitrogen dioxide. Fluorescence from the upper level to the ground electronic state forms a long progression in the bending vibration. This progression can be followed from v″₂ = 0 up to v″₂ = 12, and the fluorescence intensity passes through several local minima as a function of v″₂. The main features of the intensity distribution can be reproduced using a model Hamiltonian which separates the bending and rotation from the stretching vibrations. This Hamiltonian can also be used to reproduce the fluorescence frequencies by adjusting the potential function of the lower state.     

Fourier Transform Infrared Spectroscopic Investigation of the Binary and Ternary Cyanide Adducts of the Oxidized Horseradish Peroxidase: Identification of a Second Stretching Mode for the Carbon-Nitrogen Bond of the Bound Cyanide Ion

The binary and ternary cyanide adducts of the ferric horseradish peroxidase were investigated by Fourier transform infrared spectroscopy. The carbon-nitrogen bond of the bound cyanide ion in the binary ferric cyanohorseradish peroxidase exhibits two stretching vibrations at 2130 cm^?1 and 2127 cm^?1 with the latter mode being observed in this work for the first time. This finding supports the results of the resonance Raman study of cyanohorseradish peroxidase, which identified two iron-carbon-nitrogen bending vibrations and two iron-carbon stretching vibrations, proving the existence of two conformational states. The identification of the latter carbon-nitrogen stretching frequency allowed the assignment of all of the vibrational modes of the iron-carbon-nitrogen groups of the two conformational states of the ferric cyanohorseradish peroxidase. The first conformer is characterized by a carbon-nitrogen stretch at 2130 cm^?1, an iron-carbon stretch at 453 cm^?1, and an iron-carbon-nitrogen bending mode at 405 cm^?1. The second state has a carbon-nitrogen stretch at 2127 cm^?1, an iron-carbon stretch at 360 cm^?1, and an iron-carbon-nitrogen bending mode at 422 cm^?1. The iron-carbon stretching band is weakly sensitive to pH changes, but it is sensitive to H₂O/D₂O substitution, indicating that the bound cyanide ion in cyanohorseradish peroxidase is hydrogen bonded to the surrounding protein. The two states were attributed to variation in the extent of hydrogen bonding of the iron-carbon-nitrogen groups in the two states. The carbon-nitrogen stretching vibrations of the ternary complexes of cyanohorseradish peroxidase with ferulic acid, benzamide, and benzhydroxamic acid have been investigated for the first time. The binding of the substrate to cyanohorseradish peroxidase does not always lead to the vanishing of one of the conformational states as in the carbon monoxide adducts of the ferrous horseradish peroxidase, but can cause shifts in the νC-N frequency and in the relative population of both conformational states.     

Fluorescence and fluorescence excitation spectra of jet-cooled carbazole

The fluorescence excitation spectra of jet-cooled carbazole molecules at vibrational temperatures of 55 and 80 K and the fluorescence spectrum of these molecules excited by radiation at the frequency of a pure electronic transition are measured. As the vibrational temperature increases, the excitation spectra exhibit a series of lines of the same symmetry, which are caused by the interaction of the active vibration with a subensemble of optically inactive vibrations. The final symmetry of the totally and nontotally symmetric vibrations is determined from the shape of the rotational contours of the lines of vibronic transitions. The values of a decrease in the frequency of the nontotally symmetric vibrations in the first excited electronic state S ₁ due to their interaction with the electronic state S ₂ are calculated to be up to 100 cm^?1. The frequencies of the pure electronic transitions in the absorption and fluorescence spectra coincide with each other and are equal to 30809 cm^?1, the frequencies of vibrations in the ground state S ₀ exceeding the frequencies of the corresponding vibrations in the excited state S ₁. The degree of polarization of the integral fluorescence is determined for a series of vibronic transitions of the a ₁ and b ₂ final symmetry that are observed in the fluorescence excitation spectra, and the contribution of the intensity with the borrowed polarization θ_⊥ to the integral fluorescence is calculated. It is found that the intensity θ_⊥ is higher for the transitions of the b ₂ symmetry and can reach ≈50%.     

Ionization of Atoms in a Thermal Field

We study the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature. The stationary states of the non-interacting system are given by product states, where the particle is in a bound state corresponding to an eigenvalue of the particle Hamiltonian, and the field is in its equilibrium state. We show that if Fermi's Golden Rule predicts that a stationary state disintegrates after coupling to the radiation field then it is unstable, provided the coupling constant is sufficiently small (depending on the temperature). The result is proven by analyzing the spectrum of the thermal Hamiltonian (Liouvillian) of the system within the framework of W ^*-dynamical systems. A key element of our spectral analysis is the positive commutator method.