Soma Mukhopadhyay

Formation and stability of a singlet optical bipolaron in a parabolic quantum dot

The stability of a strong-coupling singlet optical bipolaron is studied for the first time in two- and three-dimensional parabolic quantum dots using the Landau - Pekar variational method. It is shown that the confining potential of the quantum dot reduces the stability of the bipolaron.

The ground and the first excited states of an electron in a multidimensional polar semiconductor quantum dot: an all-coupling variational approach

A variational calculation is performed to obtain the polaronic corrections to the ground and the first-excited-state energies of an electron in a parabolic quantum dot of a polar semiconductor for the entire range of the electron-phonon coupling constant and the confinement length. The number of virtual phonons, the size of the polaron and the polarization potential in the polaron ground state are also calculated. The theory is applied to both two- and three-dimensional GaAs quantum dots and it is shown that both the ground and the first-excited-state polaronic corrections in these dots can be considerably large if the dot sizes are of the order a few nanometres.

Rayleigh-Schrödinger perturbation theory for electron-phonon interaction effects in polar semiconductor quantum dots with parabolic confinement

Abstract We use the Rayleigh-Schrodinger perturbation theory to obtain a simple closed-form analytical expression for the polaronic correction to the ground state energy of an electron in a polar semiconductor quantum dot in both two and three dimensions. We find that there exists a simple dimensional scaling relation for the ground state polaron energy. We apply our results to GaAs, InSb, CdTe, CdS and CdSe dots and show that the polaronic effects can be quite appreciable if the confinement lengths are smaller than a few nanometers. Furthermore, the polaronic effects are found to be more pronounced in two-dimensional dots than in three-dimensional ones. However, the relative polaronic enhancement in a quantum dot with respect to the corresponding bulk value is independent of both the dimensionality and the electron-phonon coupling constant, but depends on the phonon frequency.

PATH-INTEGRAL APPROACH FOR ELECTRON–PHONON INTERACTION EFFECTS IN HARMONIC QUANTUM DOTS

We use the Feynman–Haken path-integral formalism to obtain the polaronic correction to the ground state energy of an electron in a polar semiconductor quantum dot with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron–phonon coupling parameter and for arbitrary confinement length. We apply our results to several semiconductor quantum dots and show that the polaronic effect in some of these dots can be considerably large if the dot sizes are made smaller than a few nanometers.

PHONON INDUCED SUPPRESSION OF THE ZEEMAN SPLITTING IN POLAR SEMICONDUCTOR QUANTUM DOTS: A QUANTUM SIZE EFFECT

The effect of the electron–phonon interaction on the Zeeman splitting of the first excited level of a two-dimensional parabolic quantum dot is studied using the nondiagonal Hartree–Fock variational approximation within the framework of Greens function formalism for the entire range of the electron–phonon interaction strength and arbitrary confinement length. The results are applied to GaAs and CdS quantum dots and it is shown that polaronic interaction can cause a strong size-dependent suppression of the Zeeman splitting in these dots if their sizes are made sufficiently small.

OPTICAL ABSORPTION IN QUANTUM DOTS

The optical absorption behaviour of polar semiconductor quantum dots has been investigated in the strong confinement regime using the adiabatic approximation of Landau and Pekar. It has been shown that optical absorption coefficient becomes strongly size dependent below a certain value of the confinement length and also exhibits interesting crossing behaviour when studied as a function of the electron–phonon coupling constant for different values of the confinement length. It has furthermore been shown that the ratio of the one-phonon part of the oscillator strength to the zero-phonon contribution can be significantly large in a small quantum dot and can also exhibit an interesting minimum structure at certain value of the confinement length for intermediate electron–phonon coupling.

Specific heat of parabolic quantum dot with Dresselhaus spin-orbit interaction

The heat capacity of a two electron quantum dot with parabolic confinement in magnetic field in the presence of electron-electron interaction, Dresselhaus spin-orbit interaction (DSOI) has been studied. The electron-electron interaction has been treated by a model potential which makes the Hamiltonian to be soluble exactly. The RSOI has been treated by a unitary transformation and the terms up to second order in DSOI constants have been considered. The heat capacity is obtained by canonical averaging. So far no study has been reported in literature on the effect of DSOI on the heat capacity of quantum dot.

Effect of Rasbha spin-orbit interaction on the ground state energy of a hydrogenic D0 complex in a Gaussian quantum dot

The ground state energy of a hydrogenic D0 complex trapped in a three-dimensional GaAs quantum dot with Gaussian confinement is calculated variationally incorporating the effect of Rashba spin-orbit interaction. The results are obtained as a function of the quantum dot size and the Rashba spin-orbit interaction. The results show that the Rashba interaction reduces the ground state energy of the system.

Magnetization of a parabolic quantum dot in the presence of Rashba and Dresselhaus spin-orbit interactions

The magnetization of a parabolic quantum dot has been studied as a function of temperature and external magnetic field in the presence of Rashba, Dresselhaus Spin Orbit Interactions (SOI) and the electron-electron interactions. By the introduction of a simple and physically reasonable model potential, the problem has been solved exactly up to second order in both the SOI terms. Both the SOI found to be showing considerable effects on the magnetization of the quantum dot. The effect of electron-electron interaction on the magnetization also has been studied.

The momentum distribution function of a Luttinger liquid

The momentum distribution function of a one-dimensional interacting many electron-phonon system is calculated analytically within the framework of the Luttinger model. We have shown that, even a small electron-electron interaction destroys the fermi surface and in the presence of the electron-phonon interaction the residual fermi surface vanishes completely and the function becomes a continuous function of the wave vector as we increase the coupling strength. It shows that in one dimension, the Fermi liquid theory breaks down completely, if we include the electron-phonon interactions along with the electron-electron interaction.