Spin-singlet–spin-triplet oscillations in quantum dots

Abstract

Two interacting electrons confined to a disk on a semiconductor surface are considered in a perpendicular magnetic field. As it is appropriate for experimental realizations, we use a two-dimensional harmonic-oscillator well to confine the electrons in the plane of the disk. We predict oscillations between spin-singlet and spin-triplet ground states as a function of the magnetic field strength. Phase diagrams describing this peculiar manifestation of the electron-electron interaction in a quantum dot are calculated for GaAs and experiments to verify them are proposed. Nanostructuretechnologies allow the lateral confinement of two-dimensional electron gases in heterojunctions or metal-oxide-semiconductor structures to widths comparable to the effective Bohr radius a* of the host semiconductor. ' In this case we have electron systems with discrete energy spectra that are commonly called zero-dimensional systems or quantum dots. Since their widths in the x-y plane are much larger than their extent in the z direction, which is the growth direction of the underlying semiconductor structure, quantum dots may be regarded as artificial atoms with disklike shapes. Electron numbers as low as one or two per dot have already been realized. ' So far, quantum dots have been investigated experimentally by capacitance-voltage spectroscopy and transport measurements, as well as by far-infrared spectroscopy.Capacitance-voltage and transport measurements are not favorable for the study of isolated dots since they require coupling to external contacts. Particularly for small dots their interpretation is additionally hampered by Coulomb blockade. Despite these difficulties, much information on the single electron ene-rgy spectra could be deduced from transport data. In many cases the value of far-infrared spectroscopy is limited as a consequence of the approximately harmonic shapes of the confining potentials and the associated validity of the generalized Kohn theorem. ' " This theorem states that, for strictly harmonic potentials, dipole radiation can only probe the center-of-mass motion of all electrons but is inadequate to see any effect due to the electron electron interaction.Here, we predict spin oscillations of the ground state of two electrons in a harmonic quantum dot as a function of the magnetic field strength, which are a peculiar consequence of the electron-electron interaction and the Pauli exclusion principle. Hence, they are a direct manifestation of the t~o-electron states in the quantum dot. The oscillations should be accessible to a different type of experiment, namely spin susceptibility ' and magnetization measurements ' that previously have been successfully applied to study electronic properties of two-dimensional electron gases in GaAs/Ga~-, AI"As and related heterostructures.In experimentally realized dots, the motion in the z direction is always frozen out into the lowest electric subband F;-0. Since the corresponding extent of the wave function is much less than the one in the x-y plane, we can treat the do...

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

“…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].…”

Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

“…For general values of this quantity a numerical treatment is required. As mentioned above, the most straightforward one is an integration of the radial equation 7,15 but, nevertheless, other methods such as diagonalization in a basis 16,17 and the Monte Carlo method 18,19 have also been applied. One of us has used the so-called oscillator representation method, perturbatively treating the residual interaction, to derive analytical expressions for the energy levels.…”

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

“…The electron density plots have been generated by using the gOpenMol program [21,22]. The computational results are represented 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 [23,24].…”