Distribution of oscillator strength in Gaussian quantum dots: An energy flow from center-of-mass mode to internal modes

Abstract

The energy spectra and oscillator strengths of two, three and four electrons confined by a quasitwo-dimensional attractive Gaussian-type potential have been calculated for different strength of confinement ω and potential depth D by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set. A substantial red shift has been observed for the transitions corresponding to the excitation into the center-of-mass mode (CM). The oscillator strengths, concentrated exclusively in the center-of-mass excitation in the harmonic limit, are distributed among the near-lying transitions as a result of the breakdown of the generalized Kohn theorem. The distribution of the oscillator strengths is limited to the transitions located in the lower-energy region when ω is large but it extends towards the higher-energy region when ω becomes small. The analysis of the CI wavefunctions shows that all states in the energy range covered by the present study can be classified according the polyad quantum number vp. It is shown that the distribution of the oscillator strengths for large ω occurs among transitions involving excited states with the same value of vp as the center-of-mass excited state, vp,cm, while it occurs among transitions involving the excited states with vp = vp,cm and vp = vp,cm + 2 for small ω.

Spectra and correlated wave functions of two electrons confined in a quasi-one-dimensional nanostructure

“…The anharmonicity of the Gaussian potential in Eq. (2) can be characterized as defined in a previous study [32] by the ratio of the confinement strength ω z over the depth of the Gaussian potential D as…”

“…In previous studies of this series [18,19,32,37] it has been demonstrated that a set of properly chosen Cartesian anisotropic Gaussian-type orbitals (c-aniGTOs) is the most convenient choice to correctly approximate the wavefunction of electrons confined in anisotropic potentials. A c-aniGTO basis set can be transformed into a set of eigenfunctions of the corresponding three-dimensional anisotropic harmonic oscillator [19].…”

“…The orbital exponents for the x and y directions have been chosen as ω xy /2 while that for the z direction accounting for the Gaussian potential in Eq. (2) has been determined in the same way as described in a previous study [32]. Since ω xy is much larger than ω z those functions that have nodal lines only along the z direction without nodal lines along the x and y directions have been selected and used in the basis sets [20,32].…”

“…(2) have been calculated as the eigenvalues and eigenvectors of the full CI matrix. All calculations have been performed by using OpenMol [34] that has been extended to account for Gaussian and power-series potentials and anisotropic Gaussian basis functions [32]. The results are presented in atomic units and can be scaled by the effective Bohr radius of 9.79 nm and the effective Hartree energy of 11.9 meV for GaAs semiconductor quantum dots [35,36].…”

“…Introducing anharmonicity into the confining potential is important for simulating realistic confining potentials [25] as well as for studying the breakdown of the generalized Kohn theorem [24,[26][27][28][29][30][31]. The eigenvalues and wave functions of the two electrons confined in the quasi-one-dimensional Gaussian potential have been calculated by using the quantum chemical full configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set with large angular mo-mentum functions [32]. The computed energy spectra and wave functions have been examined by focusing on the nodal pattern in the CI wavefunctions.…”