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

Abstract

The energy spectra and wave functions of two electrons confined by a quasi-one-dimensional Gaussian potential have been calculated for different strength of confinement ω z and anharmonicity by using the quantum chemical full configuration interaction method employing a Cartesian anisotropic Gaussian basis set. The energy spectra for a nearly harmonic Gaussian potential have been studied and analyzed in three regimes of ωz, namely, large (ωz = 5.0) medium (ωz = 1.0), and small (ωz = 0.1). For large and medium ω z the energy spectrum shows a band structure which is characterized by the polyad quantum number v p while for small ω z it is characterized by the extended polyad quantum number v * p . The energy levels for small ω z form doublet pairs each of which consists of a pair of singlet and triplet states. The nodal pattern of their wave functions are almost identical to each other except for their phases. The energy spectra for the strongly anharmonic Gaussian potential look quite similar to those of the nearly harmonic case except that an irregular level structure appears in the high energy region for ω z = 0.1. The wave functions of the states in this high energy region have curved nodal lines which align along a pair of bent nodal coordinates. Two types of pairs of bent nodal coordinates have been identified, namely, those passing through the valley of the confining potential and the others passing on the hillside. It is shown that the wave functions with these nodal coordinates correspond to new types of classical local -mode motions of electrons.

The Energy Level Structure of Low-dimensional Multi-electron Quantum Dots

“…The convergence characteristic for the case of two electrons was given already in Ref. [20] and for the case of three electrons in Ref. [21].…”

“…This indicates that the anharmonicity is large. The extent of anharmonicity may be specified by the parameter α [20] which is defined for the quasione-dimensional quantum dots by…”

“…(2) and (3) have been chosen as one half of the strength of the confinement, ω xy and ω z , respectively, while the exponents for the Gaussian potentials have been determined in the same way as described in a previous study [19]. Since the strength of the confinement for the harmonic-oscillator potential is much larger than that for the Gaussian potential, only functions without nodes along the direction of the harmonic-oscillator potential have been selected and used in the basis sets [18][19][20]. The size of the basis set required for calculating a reliable energy spectrum has been determined by following the convergence of the energies while stepwise increasing its size.…”

“…Energy levels belonging to different polyad quantum numbers and having different spin multiplicities are converging to nearly degenerate levels as the strength of confinement becomes smaller. This convergence is caused by increasingly stronger potential walls of the electron-electron interaction potentials that modify significantly the nodal pattern of the wave function of lower spin states while affecting little the wave function of the highest spin states [20,21].…”

“…The polyad quantum number and its extension can be used to characterize the energy spectra of quasi-one-dimensional quantum dots of two and three electrons for the whole range of the strength of confinement [20,21]. Energy levels belonging to different polyad quantum numbers and having different spin multiplicities are converging to nearly degenerate levels as the strength of confinement becomes smaller.…”