Equivalence of Two Definitions of the Effective Mass of a Polaron

Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈E(0)+P ²/2M of the translation invariant system constrained to have momentum P and 2. the mass M of a simple particle in an arbitrary slowly varying external potential, V, described by the nonrelativistic Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.     

柱形量子线中体纵光学声子平均数

考虑电子与体纵光学声子相互作用时,采用LLP变分方法,研究柱形量子线中极化子性质,导出了柱形量子线中极化子光学声子平均数随量子线截面半径和电子-LO声子耦合强度的变化关系.结果表明柱形量子线中极化子的光学声子平均数随量子线截面半径减小而减小,随电子-LO声子耦合强度增强而增加.     

无限深量子阱中强耦合极化子的基态结合能

研究了无限深量子阱中极化子的基态性质,采用线性组合算符和变分相结合的方法导出了强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b,讨论了阱宽L和电子-LO声子耦合强度α对强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b的影响。通过数值计算,结果表明:强耦合极化子的振动频率和基态结合能随阱宽L的增大而减小,随电子-LO声子耦合强度α的增强而增大;基态能量随阱宽L的增大而减小,其绝对值随电子-LO声子耦合强度α的增强而增大;当量子阱阱宽L趋近于无限大和无限小两种极限情况下,分别与三维和二维极化子的结果相一致。     

Polaron in a superlattice with δ-like potentials

The problem of the polaron spectrum is studied in a superlattice having narrow quantum wells and relatively wide potential barriers. A δ-like superlattice potential is chosen to solve the problem. This model is adequate, if the penetration depth of the electron wave function into the barrier region is much greater than the width of the quantum well. A weak-coupling polaron at low temperature is studied. Only volume phonons are considered. Expressions are obtained for the polaron mass and the shift of the polaron energy under these assumptions. To test the model, numerical calculations were performed for an InAs-GaSb superlattice, whose quantum wells are quite deep (the energy offset of the conduction bands in InAs and GaSb equals 830 meV), narrow (the width of a quantum well corresponds to the width of an InAs monolayer 6 Å), and the barrier width corresponding to the thickness of the GaSb layers equals 150 Å. The assumption that the penetration depth of the wave function is much greater than the barrier width holds well.     

耦合强度和磁场对极化子基态的影响

利用线性组合算符和幺正变换相结合的方法,推导出极化子基态与耦合强度和磁场强度的关系。数值计算表明:当磁场强度给定时,随着耦合常数α的增加,振动频率λ先减小后增大;基态能量E₀单调下降;自陷能E_0tr单调增大;Landau能E_0L先增大,达到最大值后又下降。当耦合强度给定时,随着磁场强度的增大,λ单调增大,且α愈小,λ增加愈快;基态能量E₀随磁场强度的增大而增大;自陷能E_0tr随着磁场强度的增大而略有增加;Landau能E_0L随着磁场强度的增大先增大,达到最大值后,又开始下降。     

STRONG-COUPLING SURFACE OPTICAL POLARON IN A MAGNETIC FIELD

A variational scheme of the Pekar type is employed to study the strong-coupling optical polaron on the outer surface of the polar crystal under the influence of a magnetic field. The ground state energy and the effective mass of the polaron are obtained as functions of the magnetic field strength and the electron-surface optical phonon coupling constant. It is shown that the effective mass of the surface polaron appears in nonisotropic nature due to the coupling between the electron and the surface optical phonon.     

The inertial mass tensor of a polaron in an isotropic medium

Owing to a funadmentally erroneous approach to calculations of the effective polaron mass (calculations that use a model without spatial dispersion of the lattice polarizability), the polaron inertial mass has never before been distinguished from the mass as a measure of kinetic energy. In this paper we derive an expression for the tensor of the inertial mass of a large polaron. The tensor is found to be fully determined by two components: the longitudinal component, corresponding to the case where the force acting on the polaron is parallel to the polaron velocity, and the transverse component, corresponding to the case where the acceleration is perpendicular to the polaron velocity. The components of the polaron inertial mass tensor depend quasirelativistically on the polaron velocity due to the quasirelativistic compression of the polarization field in the direction of motion, which constitutes the effect of spatial dispersion of the lattice polarizability. We derive a formula that approximates the dependence of the components of the polaron mass tensor on all the parameters: the frequency and dispersion of the phonons, the polaron velocity, and the effective dielectric constant. Zh. éksp. Teor. Fiz. 115, 180–186 (January 1999)     

抛物量子线中强耦合极化子的有效质量

采用改进的线性组合算符法、Lagrange乘子和变分法,在考虑电子与LO声子相互作用情况下,研究了抛物量子线中强耦合极化子的有效质量和光学声子平均数。通过数值计算,讨论了约束强度ω₀和拉格朗日乘子u对极化子的有效质量m^*和光学声子平均数N及极化子振动频率λ的影响。计算结果表明:有效质量m^*和光学声子平均数N及极化子振动频率λ都随着约束强度ω₀和拉格朗日乘子u的增加而增大。     

Properties of a Bound Polaron under a Perpendicular Magnetic Field

We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit （SO） interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.     

Unitary transformation treatment of a single hole in an Ising antiferromagnet

The behavior of a single hole in a two-dimensional Ising antiferromagnet (t-J ^z model), is studied in the generalized Dyson-Maleev representation, where the spins are mapped on boson operators and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that thet-J ^z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. Our approach yields an upper bound to the exact ground state energy, as well as the corresponding ground state eigenvector. Fork=0 our energy bound is remarkably close to the result of the self-consistent Born approximation over a wide range of the coupling parameter, which includes the range typically assumed for the high-T _c materials. The ground state eigenvector is used to calculate the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obtained in previous work, showing that our ground state eigenvector accounts quite well for the small size of the “spin polaron” in thet-J ^z model.     

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn_1-xCd_xSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models. Received 17 September 1998     

On the vacancy in a metal

The self-consistent calculations of spatial distributions of electrons and potentials in an isolated spherical cavity (with atomic radius R _WS) of the Wigner-Seitz cell, the energy of the vacancy formation, and the vacancy contribution to the electrical resistance have been performed in terms of the modified Kohn-Sham method and the stabilized jellium model. The energy shift of the ground state of electrons in the Wigner-Seitz cell with radius R _v ? R _WS (where R _v is the average distance between vacancies), the contribution of vacancies to the electron work function, and the effective mass of electrons have been found using the calculated phase shifts of the scattering wave functions and the representation of a system of vacancies as a “superlattice” in a metal.     

Polarons in thet-J model

A convenient form of the Peierls-Hubbard Hamiltonian is obtained for the case when the Hubbard repulsion is the largest energy parameter. It allows to consider in the spin-wave approximation the properties of the one-hole low-lying excitations of a 2d lattice. For the parameters approximately corresponding to La₂CuO₄ it is shown that the hole polarons in the CuO₂ planes of lightly doped samples are of large size with a solitonlike-shaped highly asymmetric wave function oriented along the diagonals of the planes or of small size depending on the value of the electron-phonon coupling. In both cases the cooperative effect of the electron-phonon and electron-magnon interactions leads to a large effective mass and to hopping transport of the excitations, with preferential jumps along the diagonals in the former case and rotationally symmetric in the latter. For hoping matrix elements which are small in comparison with a phonon quantum the competition between the interactions leads to the decrease of the total spin in the ground state with increasing electron-phonon coupling.     

Exact results of an alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies are solved exactly by means of a mapping of the spin-1/2 transverse Ising chain and the Jordan-Wigner transformation. The ground state quantities are strongly dependent on the model Hamiltonian parameters J₁, J₂, D_x and D_z. We obtain the quasi-particles' spectra Λ_k, the dimerization gap Δ_d, the minimal energy Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole and the ground state energy E_g. The phase diagram of the ground state is also given. The results show that the alternating bond just quantitatively changes the ground state properties; no matter the nearest-neighbor exchange interactions J₁ and J₂ are equal or not, when D_z≥0 for any finite value of D_x, there is no quantum critical point and the ground state is always in a spin ordered phase.     

Cyclotron resonance of polarons in AgBr at high microwave fields

A cyclotron resonance experiment on polarons in pure AgBr has been extended to the microwave field of 3 kV cm^?1 by using a pulsed magnetron at 35 GHz at lattice temperatures of 4.2 and 17 K in magnetic fields up to 58 kOe. It was established that the ground state polaron mass is m¹_p(0)=(0.287±0.003)m_e. From microwave field dependences of the peak position and the width of resonance lines, it was established that the electron polaron follows the streaming motion repetitively emitting LO-phonons in the microwave field region above 80 V cm^?1. Further, it was also suggested that, when streaming, the polaron has an enhanced effective mass of (0.353±0.006)m_e rather than the ground state mass m¹_p(0).     

有限深势阱里量子盘中极化子的基态性质

采用平面波展开、幺正变换和变分相结合的方法推导出有限深势阱里量子盘中极化子的基态能量公式.采用极化子单位进行数值计算,结果表明极化子的基态能量随势垒高度和势垒宽度的增大而增大,原因是势垒愈高、愈宽,电子穿透势垒的可能性愈小,导致电子能量增大,进而导致极化子基态能量增大.数值计算结果还表明极化子的基态能量随量子盘有效受限长度和量子盘半径的增大而减小;声子效应导致极化子能量较电子能量低.     

Spin interactions in a quantum ring containing a magnetic impurity

The exciton states in a CdTe semiconductor quantum ring containing a single magnetic impurity are considered in an external magnetic field. The electron-hole spin interaction and s,p-d interactions between electron, hole and magnetic impurity are also taken into account in the calculations. It is shown that due to the s,p-d spin interactions the ground state exciton energy splits into 12 doubly degenerated energy levels. The external magnetic field removes this degeneracy. A novel method is proposed here to determine the values of the strengths of s,p-d interactions. The optical spectrum of the system for different polarizations of the incident light and for different initial states of the magnetic impurity spin projection is also studied.     

强耦合表面极化子的激发能量

采用线性组合算符方法及幺正变换方法研究了电子与表面光学(SO)声子和体纵光学(LO)声子均为强耦合的表面极化子的激发态性质.计算了体系的有效哈密顿量、振动频率和体系由基态向第一激发态跃迁所需的激发能量.     

声子和磁场对量子环中极化子性质的影响

采用求解能量本征方程、幺正变换和变分相结合的方法,研究声子和磁场对量子环中极化子性质的影响. 对KBr量子环的数值计算表明,电子或极化子的基态能量随量子环频率(或平均半径)的增大而增大,极化子基态能移随量子环频率的增大(或平均半径的减小)而减小,极化子中的平均声子数随量子环频率的增大(或平均半径的减小)而增大. 当有垂直磁场时,极化子基态能量和基态能移与外磁场及电子转动状态有关. 随着磁场强度的增大,基态能量出现简并且呈现非周期性振荡;能移随磁场强度的增大(或转动量子数绝对值的减小)而减小.     

一维分子晶体系统的极化子-孤子压缩态、系统基态性质和量子涨落

基于一维分子晶体系统的 Holstein 模型,采用压缩-相干态展开方法,计及电子-声子间量子关联和重整化平移修正,分析和研究电子-双声子相互作用对极化子-孤子系统基态性质和量子涨落的影响.推导了一维极化子-孤子系统的封闭形式非线性方程.应用非线性项展开方法,给出非线性方程的解析解和相关基态特性结果.研究表明,仅当电子-双声子耦合强度 g₁<0时非线性方程才有孤波解,此时声子量子涨落效应随着压缩的增加,极化子-孤子系统基态能量变得更负,孤子局域减少,孤子态更加稳定;另一方面,电子密度涨落〈Δ²n〉和声子坐标-动量的不确定量〈Δ²p〉〈Δ²q〉比无声子压缩效应的大,极化子结合能变得更负.特别是,当g₁<0时,双声子效应的量子涨落〈Δ²n〉与〈Δ²p〉〈Δ²q〉的值比单声子情况有明显增加. 关键词： 压缩-相干态展开 极化子-孤子态与量子涨落 电子-双声子相互作用 非线性薛定谔方程