A Fractional-Dimension Variational Approach for the Bound Polaron in Parabolic Quantum Wells

The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.

Plasmons in a free-standing nanorod with a two-dimensional parabolic quantum well caused by surface states

The collective charge density excitations in a free-standing nanorod with a two-dimensional parabolic quantum well are investigated within the framework of Bohm-Pine＇s random-phase approximation in the two-subband model.The new simplified analytical expressions of the Coulomb interaction matrix elements and dielectric functions are derived and numerically discussed.In addition,the electron density and temperature dependences of dispersion features are also investigated.We find that in the two-dimensional parabolic quantum well,the intrasubband upper branch is coupled with the intersubband mode,which is quite different from other quasi-one-dimensional systems like a cylindrical quantum wire with an infinite rectangular potential.In addition,we also find that higher temperature results in the intersubband mode（with an energy of 12 meV（～ 3 THz）） becoming totally damped,which agrees well with the experimental results of Raman scattering in the literature.These interesting properties may provide useful references to the design of free-standing nanorod based devices.

Optical Conductivity of Impurity-Doped Parabolic Quantum Wells in an Applied Electric Field

The optical conductivity of impurity-doped parabolic quantum wells in anapplied electric field is investigated with the memory-function approach, and the analyticexpression for the optical conductivity is derived. With characteristic parameters pertaining toGaAs/Ga_(1-x)Al_xAs parabolic quantum wells, the numerical results are presented. It is shown that,the smaller the well width, the larger the peak intensity of the optical conductivity, and the moreasymmetric the shape of the optical conductivity; the optical conductivity is more sensitive to theelectric field, the electric Geld enhances the optical conductivity; when the dimension of thequantum well increases, the optical conductivity increases until it reaches a maximum value, andthen decreases.

Studies on the Second-Order Nonlinear Optical Properties of Parabolic andSemi-parabolic Quantum Wells with Applied Electric Fields

Within the framework of compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG)susceptibility tensor is given in the electric-field-biased parabolic and semi-parabolic quantum wells (QWs). The simple analytical formula for the SHG susceptibility in the systems is also deduced. Numerical results on typical AlGaAs/GaAs materials show that, for the same effective width,the SHG susceptibility in semi-parabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semiparabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably.Moreover, the SHG susceptibility is also related to the parabolic confinement frequency and the relaxation rate of the systems.

Intersubband optical absorption of electrons in double parabolic quantum wells of Al_xGa_(1-x)As/Al_yGa_(1-y)As

Some realizable structures of double parabolic quantum wells（DPQWs） consisting of Al_xGa_（1-x）As/Al_yGa_（1-y）As are constructed to discuss theoretically the optical absorption due to the intersubband transition of electrons for both symmetric and asymmetric cases with three energy levels of conduction bands. The electronic states in these structures are obtained using a finite element difference method. Based on a compact density matrix approach, the optical absorption induced by intersubband transition of electrons at room temperature is discussed. The results reveal that the peak positions and heights of intersubband optical absorption coefficients（IOACs） of DPQWs are sensitive to the barrier thickness, depending on Al component. Furthermore, external electric fields result in the decrease of peak, and play an important role in the blue shifts of absorption spectra due to electrons excited from ground state to the first and second excited states. It is found that the peaks of IOACs are smaller in asymmetric DPQWs than in symmetric ones. The results also indicate that the adjustable extent of incident photon energy for DPQW is larger than for a square one of a similar size. Our results are helpful in experiments and device fabrication.

Effect of a magnetic field on the energy levels of donor impurities in the ZnO parabolic quantum well

Energy levels of a donor impurity in the ZnO parabolic quantum well under the magnetic field are investigated using the variational method.The binding energy of the ground state,the energies of 2p±state and 1 s→2p±transition energies of a hydrogenic donor in the ZnO parabolic quantum well are numerically calculated as a function of the strength of magnetic field for different parabolic potential fields.The results show that the external magnetic field has an obvious influence on the binding energies and the 1 s→2p±transition energies of a hydrogenic donor.The Is to 2p±transition energy increases linearly with the strength of magnetic field,but the Is to 2p;transition energy decreases when the strength of magnetic field increases for the small field strength. Compared to the GaAs parabolic well,the donors are more tightly bound to the ZnO parabolic well and the influence of external magnetic field on the binding energy of a donor is much stronger in the ZnO parabolic well.

Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field

We study the multisubband electron mobility in a barrier delta doped AlχGal-χAs parabolic quantum well structure under the influence of an applied electric field perpendicular to the interface plane. We consider the alloy fraction χ = 0.3 for barriers and vary x from 0.0 to 0.1 for the parabolic well. Electrons diffuse into the well and confine within the triangular like potentials near the interfaces due to Coulomb interaction with ionized donors. The parabolic structure potential, being opposite in nature, partly compensates the Coulomb potential. The external electric field further amends the potential structure leading to an asymmetric potential profile. Accordingly the energy levels, wave functions and occupation of subbands change. We calculate low temperature electron mobility as a function of the electric field and show that when two subbands are occupied, the mobility is mostly dominated by ionised impurity scattering mediated by intersubband effects. As the field increases transition from double subband to single subband occupancy occurs. A sudden enhancement in mobility is obtained due to curtailment of intersubband effects. Thereafter the mobility is governed by both impurity and alloy disorder scatterings. Our analysis of mobility as a function of the electric field for different structural parameters shows interesting results.

Temperature Effects on the Self-trapping Energy of a Polaron in a GaAs Parabolic Quantum Dot

The temperature and the size dependences of the self-trapping energy of a polaron in a GaAs parabolic quantum dot are investigated by the second order Rayleigh-Schrodinger perturbation method using the framework of the effective mass approximation. The numerical results show that the self-trapping energies of polaron in GaAs parabolic quantum dots shrink with the enhancement of temperature and the size of the quantum dot. The results also indicate that the temperature effect becomes obvious in small quantum dots

Parameter-Dependent Third-Order Susceptibility of In_xGa_(1-x)N/GaN Parabolic Quantum Dots

The electron states confined in wurtzite InxGa1-xN/GaN strained quantum dots （QDs） have been investigated in the effective -mass approximation by solving the Schrtdinger equation, in which parabolic confined potential and strong built-in electric field effect （due to the piezoelectricity and spontaneous polarization） have been taken into account. The real part Rex^（3）（0,0,ω） and the imaginary part Imx^（3）（0,0,ω） of the third-order susceptibil- ity describe quadratic electro-optic effects and electro-absorption process of the QDs respectively. And both of them have been calculated in directions parallel and vertical to z axis. Furthermore, the study shows Rex^（3）（0,0,ω） and Imx^（3）（0,0,ω） increase under resonant conditions with the QDs＇ radius and height increase, and the same results occur when the content increase. In addition, the resonant position shift to the lower energy region when the parabolic frequencies increase.

Influence of the Interaction Between Phonons and Coulomb Potential on the Properties of a Bound Polaron in a Quantum Dot

The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method. The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed. Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons. When l0〉1.0, the influence of the interaction between phonons on the ground state energy cannot be ignored.

Polaron Effect of a Two Electron Parabolic Quantum Dot

Polaron induced double electron in a quantum dot is investigated using the exact diagonalization techniques and the compact density-matrix approach. The dependence of nonlinear optical processes on the incident photon energies and the polaronic effect are brought out. The linear, third order non-linear optical absorption coefficients and the refractive index changes of singlet and triplet states as a function of photon energy are obtained with and without the inclusion of polaronic effect. It is found that the geometrical confinement and the effect of polaron have great influence on the optical properties of dots.