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Chakraborty, K.G.

doi:10.1088/0953-8984/4/21/015

Cited by 23 publications

(36 citation statements)

References 24 publications

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“…1 The theoretical interest in these systems arises largely from the fact that they provide a few-electron realization of physical states that, in the macroscopic limit, are responsible for the occurrence of the quantum Hall effect. 2 The simplest example of such a state is the so-called maximum-density droplet ͑MDD͒, which, in the limit of a high magnetic field, can be written as a Slater determinant of lowest Landau level ͑LLL͒ orbitals with angular momenta 0,1, .…”

Section: ͓S0163-1829͑97͒06443-6͔mentioning

confidence: 99%

Density-functional theory of the phase diagram of maximum-density droplets in two-dimensional quantum dots in a magnetic field

Ferconi

Vignale

1997

Phys. Rev. B

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We present a density-functional theory ͑DFT͒ approach to the study of the phase diagram of the maximumdensity droplet ͑MDD͒ in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level ͑LLL͒ approximation, analytical expressions are derived for the values of the parameters N ͑number of electrons͒ and B ͑magnetic field͒ at which the transition from the MDD to a ''reconstructed'' phase takes place. The results are then compared with those of full Kohn-Sham calculations, giving thus information about both correlation and Landau level mixing effects. Our results are also contrasted with those of Hartree-Fock ͑HF͒ calculations, showing that DFT predicts a phase diagram, which is in better agreement with the experimental results and the result of exact diagonalizations in the LLL than the HF calculations. ͓S0163-1829͑97͒06443-6͔Two-dimensional quantum dot systems, at high magnetic fields, have been recently studied by various authors. 1 The theoretical interest in these systems arises largely from the fact that they provide a few-electron realization of physical states that, in the macroscopic limit, are responsible for the occurrence of the quantum Hall effect. 2 The simplest example of such a state is the so-called maximum-density droplet ͑MDD͒, which, in the limit of a high magnetic field, can be written as a Slater determinant of lowest Landau level ͑LLL͒ orbitals with angular momenta 0,1, . . . ,NϪ1, where N is the number of electrons. 3 In the limit of N→ϱ this coincides with the incompressible state of the quantum Hall effect at filling factor ϭ1. Because, within the LLL, the MDD is the only N-electron state of angular momentum N(NϪ1)/2 ͑and there is none with lower angular momentum͒ it follows that it must be an exact eigenstate of the Hamiltonianif the small Coulomb coupling between different Landau levels is neglected. Here 0 is the frequency of the external parabolic potential, A i is the external vector potential, k is the dielectric constant, m* is the electron effective mass, B is the Bohr magneton, g* is the effective g factor for the Zeeman splitting, and i is the spin component along the axis perpendicular to the plane of the electrons. The question is whether this exact eigenstate ͑or rather its continuation to a finite magnetic field͒ can actually be the ground state of the quantum dot in some range of magnetic fields. The basic physics is simple: If the magnetic field is too large, the MDD cannot be the ground state because the compact arrangement of the electrons costs too much electrostatic energy. The electrostatic stress is released through a rearrangement of the electrons leading to a state of higher angular momentum. If, on the other hand, the magnetic field is too weak, the confinement energy will cause the external electrons in the MDD to be transferred to the center of the quantum dot, even though, in so doing, a higher Landau level becomes populated at the center of the dot. The conclusion of these arguments is that there will exist, at most, a ''window'' of magneti...

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Section: ͓S0163-1829͑97͒06443-6͔mentioning

confidence: 99%

Density-functional theory of the phase diagram of maximum-density droplets in two-dimensional quantum dots in a magnetic field

Ferconi

Vignale

1997

Phys. Rev. B

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“…The solution of the Schrödinger equation for an electron confined by a harmonic potential, v c = 1 2 m * ω 0 r 2 in the presence of an external magnetic field, is well established [2,6]. The eigenvalues in this case are given bywhere n, l are the principal and azimuthal quantum numbers respectively, Ω 2 = ω This relation has been verified to great accuracy by a variety of experiments [1,2,5]. Interestingly, however, the observed magnetic field dependent FIR absorption in quantum dots with more than one electron was found to be essentially independent of the number of confined electrons and instead was dominated by the above relation for ∆E ± [3].…”

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confidence: 73%

“…This relation has been verified to great accuracy by a variety of experiments [1,2,5]. Interestingly, however, the observed magnetic field dependent FIR absorption in quantum dots with more than one electron was found to be essentially independent of the number of confined electrons and instead was dominated by the above relation for ∆E ± [3].…”

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confidence: 80%

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Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot

Chakraborty

Pietiläinen

2005

Phys. Rev. Lett.

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We demonstrate here that the dipole-allowed optical absorption spectrum of a parabolic quantum dot subjected to an external magnetic field reflects the inter-electron interaction effects when the spin-orbit interaction is also taken into account. We have investigated the energy spectra and the dipole-allowed transition energies for up to four interacting electrons parabolically confined, and have uncovered several novel features in those spectra that are solely due to the SO interaction.PACS numbers: 71.70. Ej,72.25.Dc, Far-infrared (FIR) optical absorption spectrum of quantum dots, in particular, dots with a parabolic confinement, has a long and colorful history [1,2,3,4,5]. First of all, there is a very good theoretical and experimental understanding of the single-electron states in a quantum dot with parabolic confinement. The solution of the Schrödinger equation for an electron confined by a harmonic potential, v c = 1 2 m * ω 0 r 2 in the presence of an external magnetic field, is well established [2,6]. The eigenvalues in this case are given bywhere n, l are the principal and azimuthal quantum numbers respectively, Ω 2 = ω This relation has been verified to great accuracy by a variety of experiments [1,2,5]. Interestingly, however, the observed magnetic field dependent FIR absorption in quantum dots with more than one electron was found to be essentially independent of the number of confined electrons and instead was dominated by the above relation for ∆E ± [3]. It was a rather puzzling result because according to this, magneto-optics was clearly incapable of providing any relevant information about the effect of mutual interactions of the confined electrons. The puzzle was later resolved by Maksym and Chakraborty [2,4], who pointed out that for a parabolic QD in an external magnetic field, the dipole interaction is a function of the center-of-mass (CM) coordinate alone, and only in a parabolic confinement the CM terms of the Hamiltonian are separable. Since the interaction terms are functions of relative coordinates, the observed absorption frequencies are independent of the number of electrons in the dot. Despite this somewhat disappointing performance of a parabolic dot, FIR spectroscopy of QDs (parabolic or otherwise) has generated enormous interest for over a decade that is yet to subside [5]. In this paper we demonstrate that, in the presence of spin-orbit coupling the situation changes considerably. The energy spectra of a parabolic quantum dot containing up to four interacting electrons exhibit structures that are solely due to the presence of SO interaction. Further, the optical absorption spectra of the spin-orbit coupled QDs, reported here for the first time, also exhibit novel features that are direct reflections of the SO coupling effects.Interest on the role of the spin-orbit coupling in nanostructured systems is now at its peak, due largely to its relevance to spin transport in low-dimensional electron channels [7]. Coherent manipulation of electron spins in low-dimensional systems, in parti...

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“…What is more remarkable is that the electronic states in these systems can be precisely controlled via the external voltages [1]. Magneto-optical studies of parabolic quantum dots (described as artificial atoms [2] by us in 1990) have been intensely explored for more than a decade [2,3,4,5,6] in order to understand its unique electronic and optical properties and as promising candidates for optoelectronic devices, applications in optical quantum information technology, etc. [7,8].…”

Section: Introductionmentioning

confidence: 99%

Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling

Pietiläinen

Chakraborty

2006

Phys. Rev. B

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We report on the electronic properties of few interacting electrons confined in a parabolic quantum dot based on a theoretical approach developed to investigate the influence of Bychkov-Rashba spinorbit (SO) interaction on such a system. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Here we present accurate results for the energy levels and optical-absorption spectra for parabolic quantum dots containing upto four interacting electrons, in the presence of spin-orbit coupling and under the influence of an externally applied, perpendicular magnetic field. We have described in detail about a very accurate numerical scheme to evaluate these quantities. We have evaluated the effects of SO coupling on the FockDarwin spectra for quantum dots made out of three different semiconductor systems, InAs, InSb, and GaAs. The SO coupling on the single-electron spectra manifests itself by primarily lifting of the degeneracy at zero magnetic field, rearrangement of some of the energy levels at small magnetic fields, and level repulsions at high fields. These are explained as due to mixing of different spinor states for increasing strength of SO coupling. As a consequence, the corresponding absorption spectra reveal anticrossing structures in the two main lines of the spectra. For the interacting many-electron systems we observed the appearence of discontinuities, anticrossings, and new modes that appear in conjunction with the two main absorption lines. These additional features arise entirely due to the SO coupling and are a consequence of level crossings and level repulsions in the energy spectra. An intricate interplay between the SO coupling and the Zeeman energies are shown to be responsible for these new features seen in the energy spectra. Optical absorption spectra for all three types of quantum dots studied here show a common feature: new modes appear, mostly near the upper main branch of the spectra around 2 tesla that become stronger with increasing SO coupling strength. Among the three types of systems considered here, optical signatures of the SO interaction is found to be the strongest in the absorption spectra of the GaAs quantum dot, but only at very large values of the SO coupling strength, and appears to be the weakest for the InSb quantum dot. Experimental observation of these new modes that appear solely due to the presence of SO coupling would provide a rare glimpse on the role of SO coupling in nanostructured quantum systems.

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Cited by 23 publications

References 24 publications

Density-functional theory of the phase diagram of maximum-density droplets in two-dimensional quantum dots in a magnetic field

Density-functional theory of the phase diagram of maximum-density droplets in two-dimensional quantum dots in a magnetic field

Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot

Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling

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