Resonant states of N-electron quantum dots in eletric and magnetic fields

In this work, we calculated the resonant energies and level widths of interacting electrons in a quantum dot subjected to electric and magnetic fields using the complex coordinate rotation method. The quantum dot model we consider is disk-like. There are two barriers along the growth direction (z), sandwiching a potential well at z=0, the in-plane(x-y) confinement is represented by a parabolic potential 1/2mω_0^2(x^2+y^2). The external electric and magnetic fields are both applied along the z direction. By a complex rotation of the electron position vectors r_iarrow e^iθr_i, we rotate the N-electron Hamiltonian hatH(r_1,r_2,...,r_N) into a complex non-Hermitian operator hatH'(e^iθr_1,e^iθr_2,...,e^iθr_N). hatH' is then diagonalized to obtain its eigen-values E_j and eigen-functions Ψ_j, as usual. The eigen-values are complex in general and can be written as E_j=(ɛ_j,Γ_j/2), where ɛ_j defines the resonant energy and Γ_j the resonant width. The bound and the reosonant states are determined by the stability condition partial E_j/partialθ=0. We focus on the effect of electron-electron interaction and the effect of external fields.