VARIATIONAL CALCULATION ON GROUND-STATE ENERGY OF BOUND POLARONS IN PARABOLIC QUANTUM WIRES

Within the framework of Feynman path-integral variational theory, we calculate the ground-state energy of a polaron in parabolic quantum wires in the presence of a Coulomb potential. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron－phonon coupling constant than the Coulomb binding parameter, and it increases monotonically with decreasing effective wire radius. Moreover, compared to the results obtained by Feynman Haken variational path-integral theory, we obtain better results within the Feynman path-integral variational approach (FV approach). Applying our calculation to several polar semiconductor quantum wires, we find that the polaronic correction can be considerably large.     

AN EFFECTIVE APPROACH FOR TWO-DIMENSIONAL POLARONS IN AN ASYMMETRIC QUANTUM DOT

Within the framework of Feynman-Haken path integral theory, we calculate the ground-state energy of two-dimensional polarons in asymmetric quantum dots for arbitrary electron-phonon coupling constants. From a general three-dimensional Hamiltonian, some interesting problems, such as polarons in quasi-one-dimensional quantum wires and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limit in the whole coupling regime. After the numerical calculation, we find that the relative polaronic correction increases monotonically with the decrease of effective dot size, and it becomes more pronounced with increasing dimension and asymmetry. Moreover, despite the insensitivity of relative polaronic enhancement to the variation of coupling constant at weak coupling, the correction is related to the coupling constant as the latter becomes larger.     

Electron–phonon effect on the ground-state binding energy of hydrogenic impurity in quantum-well wire in presence of an electric field

The hydrogenic impurity binding energy in rectangular quantum well wire including both barriers of finite height and an applied electric field are studied. The polaron effects on the ground-state binding energy in electric field are investigated by means of Landau-Pekar variation technique. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied electric field and the position of the impurity. Our calculations are compared with previous results in quantum wires of comparable dimensions.     

Rayleigh-Schrödinger perturbation theory for electron-phonon interaction in two dimensional quantum dots with asymmetric parabolic potential

Within the framework of the second-order Rayleigh-Schr?dinger perturbation theory, we investigate the effects of the interaction of the electron and longitudinal-optical phonons in two-dimensional semiconductive quantum dots with respect to a general potential. We propose a simple expression for the ground state energy, and compare it with those obtained by Landau-Pekar strong coupling theory. It is shown both analytically and numerically that the results obtained from the second-order Rayleigh-Schr?dinger perturbation theory could be better than those from Landau-Pekar strong coupling theory when the coupling constant is sufficiently small. Moreover, some interesting problems, such as polarons in quasi-one-dimensional quantum wires, and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limits. After the numerical calculations, we find that there exists a simple dimensional scaling and symmetry relation for the ground state polaron energy. Furthermore, we apply our results to some weak-coupling polar semiconductors such as GaAs, CdS. It is shown that the polaronic effects are found to be quiet appreciable if the confinement lengths and smaller than a few nanometers. Received: 3 December 1997 / Revised: 6 July 1998 / Accepted: 17 September 1998     

Influence of Electric and Magnetic Fields on the Polaron in a Quantum Well

A combinative method of variational wavefunction and harmonic oscillator operator algebra, the ground-state energy correction to an electron confined in the quantum well of GaAs/Ga_1-xAl_x, As in the electric and magnetic fields along the growth axis has been studied by taking into account the interaction of different optical phonon modes with the electron. The ground-state energy is obtained as a function of the well width and the strength of electric and magnetic fields. The results show that the magnetic field greatly enhances the in terface-phonon part of the polaronic correction to electron ground-state energy in the well width d ≤ 300 Å. The electric field also enhances the polaron effect of interface mode, but decreases the part of bulk longitudinal mode.     

Polaron effects on the binding energy of a hydrogenic impurity in parabolic quantum wires in perpendicular electric and magnetic fields

Using a variational approach, the binding energy of shallow hydrogenic impurities in a parabolic quantum wire is calculated within the effective mass approximation. The polaron effects on the ground-state binding energy in electric and magnetic fields are investigated by means of the Pekar–Landau variation technique. The results for the binding energy as well as a polaronic correction are obtained as a function of the applied fields and the impurity positions.     

Bound polaron in a two- and three-dimensional quantum dot for arbitrary electron–phonon coupling strength

A variational approach is presented for calculating the ground-state (GS) binding energies of an electron bound to a Coulomb impurity in a polar semiconductor quantum dot (QD) with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron-phonon coupling constant and the Coulomb binding parameter and for arbitrary confinement length. It is found that the polaronic effect is stronger in a two dimensions (2D) dot than in a three dimensions (3D) dot and this trend is more pronounced with the increase of the coupling constant. Furthermore, the GS binding energy increases with increasing the Coulomb binding parameter in both 2D and 3D QDs for the same electron–phonon coupling constant. The results also indicate that this effect becomes much more pronounced with decreasing dimensionality.     

Polaronic correction to the first excited electronic energy level in an anisotropic semiconductor quantum dot

Within the framework of second-order Rayleigh-Schrödinger perturbation theory, the polaronic correction to the first excited state energy of an electron in an quantum dot with anisotropic parabolic confinements is presented. Compared with isotropic confinements, anisotropic confinements will make the degeneracy of the excited states to be totally or partly lifted. On the basis of a three-dimensional Fröhlichs Hamiltonian with anisotropic confinements, the first excited state properties in two-dimensional quantum dots as well as quantum wells and wires can also be easily obtained by taking special limits. Calculations show that the first excited polaronic effect can be considerable in small quantum dots.     

Density-functional theory of inhomogeneous electron systems in thin quantum wires

Motivated by current interest in strongly correlated quasi-one-dimensional (1D) Luttinger liquids subject to axial confinement, we present a novel density-functional study of few-electron systems confined by power-low external potentials inside a short portion of a thin quantum wire. The theory employs the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham treatment and transfers the Luttinger ground-state correlations to the inhomogeneous electron system by means of a suitable local-density approximation (LDA) to the exchange-correlation energy functional. We show that such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but fails to account for the transition to a “Wigner molecules” regime of electron localization as observed in thin quantum wires at very strong coupling. A detailed analyzes is given for the two-electron problem under axial harmonic confinement.     

Polaronic effect on the binding energy of an impurity with varying position in parabolic quantum dots

The Feynman-Haken variational path integral theory is generalized to calculate the binding energy E_b of an electron coupled simultaneously to an impurity with varing position and to a longitudinal-optical (LO) phonon field in parabolic quantum dots. Our calculations are applied to some semiconductor materials and the results for the binding energy are obtained for different confinement length R of the dot and arbitrary position of the impurity. It is shown that the polaronic correction to E_b decreases with the displacement of the impurity and increases with the confinement length of the dot. More interestingly, it is not so strong as the polaronic correction to the ground-state energy of the system, and the behaviours of their variation with R are totally different.     

Polaronic effects on the energy levels of a double donor impurity in quantum wells in the presence of a magnetic field

In the presence of a magnetic field the Hamiltonian of the single or double polaron bound to a helium-type donor impurity in semiconductor quantum wells (QWs) are given in the case of positively charged donor center and neutral donor center. The couplings of an electron and the impurity with various phonon modes are considered. The binding energy of the single and double bound polaron in Al_xlGa _1-xlAs/GaAs/Al_xrGa _1-xrAs QWs are calculated. The results show that for a thin well the cumulative effects of the electron-phonon coupling and the impurity-phonon coupling can contribute appreciably to the binding energy in the case of ionized donor. In the case of neutral donor the contribution of polaronic effects are not very important, however the magnetic field significantly modifies the binding energy of the double donor. The comparison between the binding energies in the case of the impurity placed at the quantum well center and at the quantum well edge is also given. Received 16 February 1999     

Pair Tunneling through Single Molecules

By a polaronic energy shift, the effective charging energy of molecules can become negative, favoring ground states with even numbers of electrons. Here we show that charge transport through such molecules near ground-state degeneracies is dominated by tunneling of electron pairs which coexists with (featureless) single-electron cotunneling. Because of the restricted phase space for pair tunneling, the current-voltage characteristics exhibit striking differences from the conventional Coulomb blockade. In asymmetric junctions, pair tunneling can be used for gate-controlled current rectification and switching.     

The ground state description of the Fröhlich polaron in a symmetric quantum dot within the framework of LLP-H approach

Within the framework of LLP-H method we have derived an analytical expression for the polaronic correction to the ground state energy and the effective mass of an electron confined in a symmetric quantum dot potential in polar semiconductor in both two and three dimensions. We have also calculated the number of phonons in the cloud of this bound polaron. We observe that polaronic correction is more pronounced in two dimension than that in three dimensional one and increases with the decrease in size of the quantum dot.     

Excitonic polarons in quasi-two-dimensional structures

A theory of excitonic polarons in semiconductor quantum wells is presented. Using a unitary transformation, we have diagonalized the exciton-phonon interaction operator in a quasi-two-dimensional system partially and then calculated the ground-state energy of an excitonic polaron. We have numerically evaluated the energy gap shift and effective mass of an excitonic polaron. We have numerically evaluated the energy gap shift and effective mass of an excitonic polaron in GaAs-Al _x Ga_1–x As systems. The results obtained here indicate that the polaronic effect is significant in the case of the light hole excitons in quantum wells of small well widths.     

磁场对量子阱中弱耦合束缚极化子性质的影响

采用线性组合算符及幺正变换方法研究了磁场对量子阱中弱耦合束缚极化子的性质的影响。导出了量子阱中束缚极化子的基态能量与振动频率、库仑束缚势、磁场和阱宽之间的变化关系。同时也讨论了振动频率与库仑束缚势、磁场之间的变化关系。通过数值计算结果表明:量子阱中束缚极化子的基态能量因振动频率、库仑束缚势、磁场和阱宽的不同而不同,它随振动频率和磁场的增加而增大,随库仑束缚势和阱宽的增大而减小。量子阱中束缚磁极化子的基态能量与振动频率无关,随库仑束缚势和阱宽的增大而减小,随磁场的增大而增大。     

Polaronic shift of the Wannier-Mott exciton binding energy in a quantum wire with allowance for the phonon confinement effect

Within the framework of the Li-Low-Pines model the interaction of a Wannier-Mott exciton with polar optical phonons in a cylindrical semiconductor wire is studied, taking into account the phonon confinement effect. An analytical expression for the exciton binding energy with allowance for the polaronic effect is obtained. Numerical calculations of the binding energy are carried out for AlAs/GaAs/AlAs and ZnSe/CdSe/ZnSe wires with a various degree of polarity of quantum wire materials. The polaronic shift of the binding energy of light and heavy hole excitons is calculated.     

Two-site two-electron generalized Hubbard-Holstein model: a perturbation study

The two-site two-electron generalized Hubbard-Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found including up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections to the ground state energy, as well as to the correlation functions, are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon(e-ph) coupling and electron-electron interactions for different values of the adiabaticity parameter. The simultaneous effect of the e-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.     

The isotropic-to-nematic transition in a two-dimensional fluid of hard needles: a finite-size scaling study

Laser dependence of binding energy on exciton in a GaAs quantum well wire embedded on an AlGaAs wire within the single band effective mass approximation is investigated. Laser dressed donor binding energy is calculated as a function of wire radius with the renormalization of the semiconductor gap and conduction valence effective masses. We take into account the laser dressing effects on both the impurity Coulomb potential and the confinement potential. The valence-band anisotropy is included in our theoretical model by using different hole masses in different spatial directions. The spatial dielectric function and the polaronic effects have been employed in a GaAs/AlGaAs quantum wire. The numerical calculations reveal that the binding energy is found to increase with decrease with the wire radius, and decrease with increase with the value of laser field amplitude, the polaronic effect enhances the binding energy considerably and the binding energy of the impurity for the narrow well wire is more sensitive to the laser field amplitude.     

Polaronic effects due to surface optical vibration modes in a freestanding cylindrical wurtzite nanowire

The ground-state polaron self-trapped energy and effective mass due to the surface optical (SO) phonon modes in a freestanding wurtzite GaN nanowire (NW) were studied by means of the Lee–Low–Pines variational approach. Based on the dielectric continuum and Loudon’s uniaxial crystal models, the polar optical phonon modes in the one-dimensional (1D) systems are analyzed, and the vibrating spectra of SO modes and electron–SO phonon coupling functions are discussed and analyzed. The calculations on the ground-state polaron self-trapped energy and correction of effective mass due to the SO phonon modes in the 1D GaN NWs reveal that the polaron self-trapped energy and correction of effective mass are far larger than those in 1D GaAs NW systems. The reasons resulting in this obvious difference in the two 1D structures are mainly due to the different electron–phonon coupling constants and electron effective masses of bulk materials constituting the two types of 1D confined system. Finally, the polaronic properties of the wurtzite 1D GaN NWs have been compared with those of the wurtzite GaN-based two-dimensional quantum wells. The physical origination of these characteristics and their distinction in the different-dimensionality systems has been analyzed in depth.     

抛物量子点中弱耦合束缚极化子的相互作用能

研究了抛物量子点中弱耦合束缚极化子的性质,采用改进的线性组合算符和幺正变换方法导出了束缚极化子的振动频率、有效质量和相互作用能。讨论了量子点的有效受限长度、电子LO声子耦合强度和库仑场对抛物量子点中弱耦合极化子的振动频率、有效质量和相互作用能的影响。数值计算结果表明:弱耦合束缚极化子的振动频率和相互作用能随有效受限长度的减少而急剧增大,振动频率随库仑势以及电子LO声子耦合强度的增加而增加,而相互作用能随库仑势以及电子LO声子耦合强度的增加而减小。有效质量仅与电子LO声子耦合强度有关。