Dynamical screening of the Coulomb interaction for two confined electrons in a magnetic field

Abstract

We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by means of the effective two-dimensional Hamiltonian with a screened Coulomb interaction. Using an adiabatic approximation based on action-angle variables, we present solutions for the effective charge of the Coulomb interaction (screening) for a vertical confinement potential simulated by parabolic, square, and triangular wells. While for the parabolic potential the solution for the effective charge is given in a closed anlytical form, for the other cases similar solutions can be easily calculated numerically.

arXiv comment10 pages, 6 figures

References in corpus (4)

• Cotunneling Spectroscopy in Few-Electron Quantum Dots
• Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality
• Intermediate Low Spin States in a Few-electron Quantum Dot in the $\nu \le 1$ Regime
• Finite-thickness effects in ground-state transitions of two-electron quantum dots

Cited by in corpus (6)

• Effects of symmetry breaking in finite quantum systems
• Magnetic alteration of entanglement in two-electron quantum dots
• Separability and Dynamical Symmetry of Quantum Dots
• Entanglement as an indicator of a geometrical crossover in a two-electron quantum dot in a magnetic field
• A geometrical crossover in excited states of two-electron quantum dots in a magnetic field
• Geometrical crossover in two-body systems in a magnetic field