2010/02/09 by D. K. Sunko, Sunko, D. K.
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Quantum Dots Synthesis And Properties #Semiconductor Quantum Structures and Devices #cond-mat.mes-hall #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.1002.1901
arxiv created 2010/02/09 · arxiv updated 2010/02/26
Deviations from the uniform oscillator spacing, related to the shape of the confining potential, have a strong influence on few-electron states in quantum dots when Coulomb effects are included. Distinct signatures are found for level spacings increasing (pot shape) and decreasing (cone shape) with energy. Cone deformations affect the levels near the ground state, such that observable effects are predicted. Pot deformations partially negate the effect of the Coulomb force, thus their spectra are similar to those of a perfect oscillator with a smaller Coulomb repulsion. The Coulomb force is treated by exact diagonalization, for which purpose efficient closed-form expressions for the matrix elements are derived. The Coulomb matrix element in relative coordinates is reduced to a single sum over four binomial coefficients, for which simple analytic approximations are found.