Analysis and Efficient Solution of Stationary Schrodinger Equation Governing Electronic States of Quantum Dots and Rings in Magnetic Field

作者：Betcke Marta M^*; Voss Heinrich

来源：Communications in Computational Physics, 2012, 11(5): 1591-1617.

DOI：10.4208/cicp.110910.250511a

• Quantum dot
• quantum ring
• nonlinear eigenvalue problem
• minmax characterization
• iterative projection method
• electronic state
• spin orbit interaction
• magnetic field

In this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number +/- l. We show, that each of those pair/quadruple of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions, which are satisfied for our examples and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40% of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately.

• 出版日期2012-5