Optical response of two-dimensional few-electron concentric double quantum rings: A local-spin-density-functional theory study

Abstract

We have investigated the dipole charge-and spin-density response of few-electron two-dimensional concentric nanorings as a function of the intensity of a perpendicularly applied magnetic field. We show that the dipole response displays signatures associated with the localization of electron states in the inner and outer ring favored by the perpendicularly applied magnetic field. Electron localization produces a more fragmented spectrum due to the appearance of additional edge excitations in the inner and outer ring. DOI: 10.1103/PhysRevB.74.193309 PACS number͑s͒: 73.21.Ϫb, 73.22.Ϫf, 71.15.Mb Progress in nanofabrication technology has allowed one to produce self-assembled, strain-free, nanometer-sized quantum complexes consisting of two concentric, welldefined GaAs/ AlGaAs rings 1,2 whose theoretical study has recently attracted some interest.3-6 Most of these works are concerned with the properties of their ground state, although the optical properties of one-and two-electron concentric double quantum rings ͑CDQR͒ at zero magnetic field have been addressed using a single-band effective-mass envelope model discarding Coulomb correlation effects. 2The singular geometry of CDQR has been found to introduce characteristic features in the addition spectrum compared to that of other coupled nanoscopic quantum structures. As a function of the interring distance, the localization of the electrons in either ring follows from the interplay between confining, Coulomb, and centrifugal energies. Each of them prevail in a different range of interring distances, affecting in a different way the CDQR addition spectrum. 6 It is thus quite natural to investigate whether and how localization effects may show up in the dipole response, using a perpendicularly applied magnetic field instead of the interring distance to control the electron localization in either ring.The aim of this paper is to use local-spin-densityfunctional theory ͑LSDFT͒ as described in detail in Ref. 7, to investigate the dipole longitudinal response of CDQR. The method has been used in the past to address the response of single quantum rings ͑see, e.g., Ref. 8 and references therein͒. We address here the few-electron case, and consider the CDQR's as strictly two-dimensional systems.Within LSDFT, the ground state of the system is obtained by solving the Kohn-Sham ͑KS͒ equations. The problem is simplified by the imposed circular symmetry around the z axis, which allows one to write the single particle ͑sp͒ wave functions as nl ͑r , ͒ = u nl ͑r͒e −ıl , being −l the projection of the sp orbital angular momentum on the z axis. The confining potential has been taken in a form that slightly generalizes that of Ref. 4,with R 1 = 20 nm, R 2 = 40 nm, 1 = 30 meV, and 2 = 40 meV. The radii have been fixed to the experimental values, 2 while the frequencies are rather arbitrary. We have considered large frequencies to mimic the strong confinement felt by the CDQR, and have taken 2 Ͼ 1 to somewhat compensate that, as R 2 Ͼ ϾR 1 , the "surface" of the outer ring might hav...

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“…More complicated geometries, such as double coaxial quantum rings [19], were also studied. The recent advances in this area included the calculation of the absorption coefficients of single electron states for various configurations of the system [20,21,22,23], model [24,25] and first-principle [26] analysis of few-electron states, and investigation of the possibility of photon antibunching [27].…”