Effect of Parabolic Potential on Bipolaron

We apply a Feynman path-integral variational approach combining with the average for the relative motion to study the stability of bipolaron in a quantum dot. The binding energy is calculated in different parameters. We find that an optimum quantum potential favors the formation of bipolaron. Compared with other methods in literature, the present approach is better than Laudau Pekar one in all coupling regime and full path-integral one in the strong coupling regime.     

过苯胺黑聚合物的双极化子态

利用改进的Ginder-Epstein模型研究聚苯胺黑的双极化子态, 给出其键序波幅、芳环扭角、电子能级、理论吸收谱和电荷分布,并与极化子进行对比。结果发现双极化子激发能为3.08eV, 晶格驰豫宽度涉及12格点与极化子相当;键交错驰豫深度大约为极化子的2倍,畸变中心芳环扭角高达68.35°大于极化子中心扭角的2倍。两个能隙态几乎简并,吸收谱低能峰为1.6eV。     

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.     

Isotropic Bipolaron–Fermion Exchange Theory and Unconventional Pairing in Cuprate Superconductors

The appearance of unconventional pairing in superconducting cuprates is examined from a microscopic model, taking into account important properties of hole‐doped copper oxides. An exchange interaction between fermions and dominantly inter‐site bipolarons is considered to be the mechanism which leads to the pairing. Its momentum dependency is connected to the well‐established fermion–phonon anomalies in cuprate superconductors. Since charge carriers in these materials are strongly correlated, a screened Coulomb repulsion is added to this exchange term. Any ad hoc assumptions like anisotropy are avoided, but a microscopic explanation of unconventional pairing for coupling strengths that are in accordance with experimental facts is provided. One important outcome is a mathematically rigorous elucidation of the role of Coulomb repulsion in unconventional pairing, which is shown to be concomitant with a strong depletion of superconducting pairs. The theory, applied to the special case of LaSr 214, predicts at optimal doping i) a coherence length of $21\AA$, which is the same as that obtained from the Ginzburg–Landau critical magnetic field measured for this material, and ii) d‐wave pair formation in the pseudogap regime, that is, at temperatures much higher than the superconducting transition temperature.     

过苯胺黑聚合物的双极化子态

利用改进的Ginder-Epstein模型研究聚苯胺黑的双极化子态,给出其键序波幅、芳环扭角、电子能级、理论吸收谱和电荷分布,并与极化子进行对比.结果发现双极化子激发能为3.08 eV,晶格驰豫宽度涉及12格点与极化子相当;键交错驰豫深度大约为极化子的2倍,畸变中心芳环扭角高达68.35°大于极化子中心扭角的2倍.两个能隙态几乎简并,吸收谱低能峰为1.6 eV.     

共轭高分子链中极化子间相互作用对电荷迁移率的影响

基于综合考虑了电子与声子以及电子与电子相互作用的理论模型,采用数值方法计算了在外电场作用下共轭高聚物分子中电荷的迁移率,讨论了大小极化子共存并相互作用对分子链内电荷迁移率的影响。研究发现,电荷迁移率明显受大小极化子的载荷性质的影响,当大小极化子具有相同电性时,在低电场范围内,分子内电荷迁移率由大极化子运动性质主导,而在高电场范围内,分子内电荷迁移率由小极化子主导;另一方面,当大小极化子具有相反电性时,电荷迁移率只由大极化子运动性质主导,与电场强度无关。此外,还讨论了电子与电子相互作用对电荷迁移率"的影响。     

共轭高分子链中大极化子与小极化子的弹性碰撞

基于Su-Schrieffer-Heeger(SSH)模型,考虑电子-电子相互作用,以及在哈密顿量中引入Brazovskii-Kivova对称破缺项,采用动力学演化的方法研究了在外电场作用下共轭高聚物分子链中大极化子与小极化子之间的弹性散射过程.研究发现,载流子的载荷性质不但决定大小极化子之间的相互作用性质,也深刻地影响了其发生散射后的载流子输运性质.在较低电场的作用下,当两载流子电性相同时,发生碰撞后,小极化子将推动着大极化子一起运动;而当两者电性相反时,碰撞后,大极化子将拖曳着小极化子一起运动.当电场强度超过临界值时,将产生量子隧穿效应,即,大小极化子相互迅速穿透,且不受载流子的载荷影响.     

Effect of Parabolic Potential on Bipolaron

We apply a Feynman path-integral variational approach combining with the average for the relative motion to study the stability of bipolaron in a quantum dot. The binding energy is calculated in different parameters. We find that an optimum quantum potential favors the formation of bipolaron. Compared with other methods in literature, the present pproach is better than Laudau-Pekar one in all coupling regime and full path-integral one in the strong coupling regime.     

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.     

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.