With the development of the solid theory and experimental technology,the properties of the surface polaron in a crystal have been of considerable interest.Many investigators studied the properties of the surface polaron in many aspects by a variety of theoretical and experimental methods.Sak and Evans et al.studied theoretically the surface polaron in polar crystals for the first time.Gu et al.discussed ideal surface polaron and the weak,the intermediate and the strong coupling polaron in semi-infinite polar crystal.The properties of the surface polaron in polar crystal and the effective mass of a slow-moving surface polaron in a semi-infinite crystal are investigated using perturbation and linear combination operator methods by the present authors and co-workers,respectively.However,the research of these methods only was restricted to the case of crystals having only one mode of the longitudinal optical(LO) phonon.A large number of polar crystals,with several atoms per unit cell,have more than one LO phonon branch.For example,in cuprite such as CuO_2 there are two LO phonon modes and for SiO_2,GaAs_(1-x) P_x and a large number materials with perovskites structure(SrTiO_3,LiNbO_3,BaTiO_3…) there are more than two modes.The polaron problem with many LO phonon branches has been studied by Matsura and Lepine.The properties of the polaron and the magnetopolaron in a polyatomic polar crystals are investigated by the present authors.However,so far,research of the properties of surface polaron in polyatomic crystals considering both the electron-bulk-longitudinal-optical(LO)-phonon and electron-surface-optical(SO)-phonon interaction,has been very scarce.The properties of the excited state of polaron in polyatomic semi-infinite crystal,which are the strong-coupling with bulk longitudinal optical phonon and surface optical phonon,are studied by using a linear combination operator and unitary transformation.Results show that when the election is infinitely close to the surface of the crystal,we can neglect the contribution of the LO phonons,otherwise,the distance between the election and the surface of the crystals is far more than the semi-diameter of the polaron;we must take into account the SO phonons effect,the LO phonons can be omitted.More commonly,when the distance between the election and surface is at the same magnitude grade of polaron's radii LO and so phonon's contribution must be studied at the same time.
By using variational method of Peakar type,studied the polar slab qubit and its optical phonon effect in finite well,This system in a polar slab can be employed as a system-qubit.When the electron is in the superposition state of the ground state and the first excited state,we obtained the time evolution of the electron density.It is shown that the period of oscillation decreases with the strength of coupling increasing,but increases with the slab thickness.
In recent years,the problem of a magnetopolaron has been of considerable interest.Larsen proposed a fourth-order perturbation method to calculate the ground state energy of two-dimensional polaron in a magnetic field.Employing Haga's perturbation method,Ze et al.derived an effective Hamiltonian for the interface magnetopolaron in polar crystals at zero temperature,in which the interactions of both bulk LO phonons and interface phonons have been taken into account.Using the Green's function method,Wei et al,studied the cyclotron resonance mass of an electron interacting with bulk longitudinal optical(BO)phonons as well as surface optical(SO)phonons in a polar crystals slab at finite temperature and found that the temperature dependence of magnetopolaron depends strongly on the strength of the magnetic field.Wang et al,investigated the magnetic field and temperature dependence of the properties of a magnetopolaron at the interface of polar-polar crystals in an external magnetic field by using the generalized Haga perturbation method.By using variational method of Pekar type,Zhou and co-workers studied the energy levels of strong coupling magnetopolaron in disk-shape quantum dot(QD)and quantum well(QW).Madkour et al. studied the effect of magnetic field on surface polaron states in a polar crystal interface and emphasized the result that the presence of magnetic field leads to a local potential for charge carriers at the interface.Based on Wigner-Brillouin theory,D.E.N.Brancus and G.Stan investigated the state energy of an anisotropic three-dimensional polaron in a magnetica field.One of our authors have done a lot of works on the proterties of the surface magnetopolaron.The properties of surface polaron in a magnetic field have been further discussed by the present authors and co-workers.Tokuda studied the property of the mean number of the optical and the piezoelectric polarons and the mean number of the acoustic and optical polarons via deformation potential by using improved variational method.However,the mean number of optical phonon of surface magnetopolarons at finite temperature has not been studied so far.In this paper,the properties of surface magnetopolaron which is a strong,weak-coupling of optical phonon was discussed by using Tokuda's improved linear combination operator,the unitry transformation and the Lagrange multiplier methods.The mean number of optical phonons of the strong,weak-coupling magnetopolaron are calculated.Numerical calculations for KCl crystals,as an example,are performed.The relation of the vibration frequency and the mean number of optical phonons to magnetic field B,temperature T and Lagrange multiplier u are discussed.The result illustrates that the vibration frequency λ of surface magnetopolaron will increase with increasing magnetic field B,temperature T and Lagrange multiplier u;the mean number of optical phonons will increase with increasing B,T and u.
In this paper,the properties of the bound optical polaron in Coulomb potential is studied,which is valid for the whole range of the electron-phonon coupling.The energy of the ground state and of the first excited state of the bound optical polaron is calculated for different values of the electro-phonon coupling using linear combination operator and unitary transformation methods.
The influences of the magnetic field,the transverse and longitudinal effective confinement length of quantum dot and the electron-phonon coupling strength on the vibrational frequency and the interaction energy of weak coupling magnetopolaron in an asymmetric quantum dot are studied by using an improved linear combination operator and the unitary transformation method.The relation of the vibrational frequency and the interaction energy of weak coupling magnetopolaron in an asymmetric quantum dot with the transverse and longitudinal effective confinement length of quantum dot,the electron-phonon coupling strength and the cyclotron resonance frequency of the magnetic field are derived.Numerical calculations are performed and the results show that the vibrational frequency and the interaction energy of weak coupling magnetopolaron in an asymmetric quantum dot will increase rapidly with decreasing the transverse and longitudinal effective confinement length of quantum dot,and will increase with increasing the cyclotron resonance frequency of magnetic field.The interaction energy of magnetopolaron is a kind of linear relationship,and it increases with the decrease of electron-phonon coupling strength.
The influence of interaction between phonons on properties of weak-couping polaron in quantum wires are studied by using linear-combination operator and perturbation methods.The ground state energy of weak-coupling magnetopolaron in quantum wires is obtained considering the interaction between electron and LO-phonon.The influence of the confinement strength,the electron-LO phonon coupling strength and the interaction between phonons of different wave vectors in the recoil process on the ground state energy of weak- coupling magnetopolaron in quantum wires are discussed. Numerical calculation illustrated that the ground state energy of weak-coupling magnetopolaron will increase rapidly with increasing the confinement strength.At the same value of the confinement strength, ground state energy of magnetopolaron will decrease with increasing the electron-LO phonon coupling strength and will increase with increasing the cyclotron frequency of the magnetic field.For weak magnetic field,the influence of the interaction between phonons on the ground state energy of the magnetopolaron can not be ignored.
Based on a coordinate transformation,the boundary potential of a quantum rods was changed from the ellipsoidal form into an spherical one.The properties of the vibrational frequency,first internal excited state energy,excitation energy and frequency of transition spectral line between first internal excited state and ground state of weak-coupling polaron in a quantum rod in a parabolic potential are studied by using linear combination operator and unitary transformation methods.Relations of the vibrational frequency,first internal excited state energy,excitation energy and frequency of transition spectral line of polaron with transverse and longitudinal effective confinement length,aspect ratio of the ellipsoid and electron-phonon coupling strength were derived.Numerical calculation results show that the vibrational frequency,the first internal excited state energy,excitation energy and frequency of transition spectral line increase rapidly with decreasing transverse and longitudinal effective confinement length.The vibrational frequency and first internal excited state energy are decreasing functions of the aspect ratio of ellipsoid and electron-phonon coupling strength,respectively.The excitation energy and frequency of transition spectral line are increasing functions of the aspect ratio when e'1,whereas it is decreasing function of one when e'1.When e' = 1,the excitation energy and frequency of transition spectral line have minimum values.
The properties of internal excited state of optical polaron are studied by using the linear combination operator and the unitary transformations methods.The numerical evaluations show that the first internal excited state may occur when α is from 3.5 to 12.5,and higher internal excited states don't exist.
With the further development of the epitaxial technique and the the manufacture of the semiconductor materials,considerable interest has been shown in the investigation of the quantum well and semiconductor superlattice because of their wide application as techniques.consequently,understanding the role of impurities in a polar slab is of particular importance.We studied the effective mass of the system when there is a bounding potential and strong coupling with electron-surface optical phonons and weak coupling with electron-bulk longitudinal optical phonons in a slab of polar crystal by using the Huybrecht,s improved linear combination operator and the Lagrange multiplier method.We deduced the variation frequent contacts λ,the effective mass with the slab thickness.The numerical calculations for KCl crystal show that the variation frequent contacts λ and the effective mass are all reduce with the increase of the slab thickness.And the contributions of the interactions between the electron and the different branchs of phonons to the effective mass are greatly difference. We also find that the effective mass and λ all increased when there is a bounding potential.
The properties of the exciton in the surface layer of crystals influence the properties of crystals very remarkably. In recent years,a lot of authors studied the surface polaron and the surface exciton. The properties of the exciton have been studied by many theoretical method by many investigators.Sumi et al. studied self-trapping of excitons (or electrons)interacting with phonons via short-range potential and found that the self-trapping depends strongly on the degree of lattice freedom.Chen et al. calculated the ground state energy of the strongly bound exciton-phonon system by using a concise variational approach.The influence of the interaction between phonons of different wave vectors in the recoil process on the effective potential between electron and hole, the self-trapping energy, and the self-trapping condition of the exciton in polar crystals has been discussed by using a perturbation method by present authors.Using the nearest-neighbor tight-binding approximation Luban et al. calculated the lowest bound-state energy of the effective 1D electron Hamiltonian and the exciton binding energy is obtained.The results for the exciton binding energy are in very good agreement both with experiment and the results of other theoretical calculations.Kasapoglu et al. calculated the binding energy of the exciton in the symmetric and asymmetric quantum wells by using a variational approach.The third-order nonlinear optical absorptions in hyperbolic quantum wires are studied by Guo et al., with most emphasis devoted to the influence of excitons on the third-order nonlinear optical absorptions. The analytic form for the third-order nonlinear optical absorption coefficient of this system is derived by means of density matrix treatment.A variational calculation of the ground-state energy of neutral excitons and of positively and negatively charged excitons (trions) confined in a single-quantum well is presented by Riva et al. They studied the dependence of the correlation energy and of the binding energy on the well width and on the hole mass.By using the method of few-body physics, the binding energy spectra of the second bound state of a negatively charged exciton X - in a GaAs quantum dot with a parabolic confinement have been calculated as a function of the electron-hole mass ratio and of the dot radius by Xie. The properties of the exciton have been investigated by many methods. Many of these mainly concentrated attention on the weak-and intermediate-coupling cases and on the ground state energy. However, the exciton in strong-coupling polar crystals and the excited state energy of the exciton has not been studied so far. Recently we study the internal excited state of the weak-coupling surface magnetopolaron by means of Huybrechts's linear combination operator method. In this paper,the properties of internal excited state of the strong-coupling surface exciton in polar crystals are investigated by using the linear combination operator and the unitary transformation method and the excited state energy, the excitation energy and the mean number of phonon of the strong-coupling surface exciton are calculated. The results show that the self-energy of ground state and excited state, the excitation energy and the mean number of phonon of the strong-coupling surface exciton could be written as a series in α -1 s,the first term being proportion to,the coupling constant α s for Wannier surface exciton.
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