Electronic structure of few-electron concentric double quantum rings

Climente, Juan I.; Planelles, Josep; Barranco, M.; Malet, Francesc; Pí, M.

doi:10.1103/physrevb.73.235327

Cited by 38 publications

(31 citation statements)

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“…It can be seen that electrons are fairly delocalized within the CDQR; for the chosen confining potential, localized configurations would only appear at larger interring distances. 6 It is known that for an N-electron single quantum ring, sp states with small l values become progressively empty as B increases. This can be intuitively understood as follows.…”

Section: Ll Serramentioning

confidence: 99%

“…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][4][5][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. 2 The singular geometry of CDQR has been found to introduce characteristic features in the addition spectrum compared to that of other coupled nanoscopic quantum structures.…”

Section: Ll Serramentioning

confidence: 99%

“…In three dimensions, more realistic confining potentials, better suited to model the experimental devices, 2 have been considered. 6 On the CDQR system it may act a constant magnetic field B in the z direction, to which a cyclotron frequency c = eB / mc is associated. We have taken for the dielectric constant, electron effective mass, and effective gyromagnetic factor, the values appropriate for GaAs, namely, ⑀ = 12.4, m * = 0.067, and g * = −0.44, and have solved the KS equations for up to N = 6 electrons, and for B values up to 4 -5 T, depending on N. In the following, we discuss some illustrative results.…”

Section: Ll Serramentioning

confidence: 99%

“…8 A more realistic description of the CDQR confining potential 6 demands a three-dimensional approach. 11 Work along this line is in progress.…”

Section: Ll Serramentioning

confidence: 99%

“…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.…”

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

et al. 2006

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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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Section: Ll Serramentioning

confidence: 99%

Section: Ll Serramentioning

confidence: 99%

Section: Ll Serramentioning

confidence: 99%

“…8 A more realistic description of the CDQR confining potential 6 demands a three-dimensional approach. 11 Work along this line is in progress.…”

Section: Ll Serramentioning

confidence: 99%

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

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Electron ground state in concentric GaAs‐(Ga,Al)As single and double quantum rings

Culchac

Granada

Porras‐Montenegro

2007

Phys. Status Solidi (c)

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We study the effect of geometric confinement on the electron states in a concentric double quantum ring. We calculate the energy of the electron ground state for both symmetric and asymmetric double quantum rings as a function of the radius of the inner and outer rings, the barrier height and as a function of an applied magnetic field. We found that the probability amplitude for the electron state is approximately the same in the inner and outer wells of the structure when the width of the wells is the same, but there is a noticeable change in the probability amplitude in the well regions when the width of the inner well is slightly different from the outer one (asymmetric rings). As a result the carrier energy changes considerably from one situation to the other. On the other hand the barrier width between the inner and outer ring plays an important role in the definition of the energy of the electron ground state up to the extent that for certain values of the barrier and well widths, the energy of the ground state does not depend any more on the barrier width.1 Introduction Semiconductors quantum rings (QR) are structures in which quantum confinement produces levels of discrete energy, which have been seen in low-temperature photoluminescence studies. The difference between a quantum dot (QD) and a quantum ring is due to the hole in the center of the ring. Semiconductor QR can be fabricated in a variety of sizes and shapes by using different techniques, like Self-assembled growth, Molecular Beam Epitaxy, chemical synthesis, chemical etching and other techniques as it is mentioned by Petroff et al. [1]; however, well-controlled methods for fabricating such structures remain a challenge. Although is not possible to determine the profile form of the radial confinement potential directly from these methods, Petroff et al. [1] showed that for a self-assembled QR the confinement potential profile is parabolic. On the other hand McCarthy [2] proposed that the radial confinement profile for an etched ring is a finite deep square potential well. Song and Ulloa [3], showed the behavior of the magneto-exciton binding energy and magnetic susceptibility as function of the ring width and the magnetic field, for a 2D QR using a parabolic profile as radial confinement potential. Mano et al. [4] demonstrate the self-assembled formation of concentric double quantum rings formation with high uniformity and rotational symmetry using the droplet epitaxy technique. They show that varying the growth process conditions can control the size of each ring. Photoluminescence spectra emitted from an individual quantum ring complex show quantized levels, signature of the carrier orbital state. Making use of a droplet-epitaxial technique Kuroda et al. [5], investigated within the local spin density approximation the state structure of few-electron concentric double quantum ring (DQR). These authors explore the role of the coupling inter ring distances finding that the energy structure of low lying electron states is essentially that of sin...

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Theoretical Modelling of Electronic and Optical Properties of Semiconductor Quantum Rings

Marquardt

2013

Physics of Quantum Rings

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Electronic structure of few-electron concentric double quantum rings

Cited by 38 publications

References 17 publications

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

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

Electron ground state in concentric GaAs‐(Ga,Al)As single and double quantum rings

Theoretical Modelling of Electronic and Optical Properties of Semiconductor Quantum Rings

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