Molecular aspects of electron correlation in quantum dots

Maksym, P. A.; Imamura, Hiroshi; Mallon, G.P.; Aoki, Hideo

doi:10.1088/0953-8984/12/22/201

Cited by 138 publications

(203 citation statements)

References 117 publications

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“…The recent experimental discovery 19 that solid 4 He exhibits a nonclassical (nonrigid) rotational inertia (NCRI 18 ) has revived an intense interest 20,21,22,23,24 in the existence and properties of the supersolid phase in this system, as well as in the possible emergence of exotic phases in other systems.…”

Section: B Nonclassical (Non-rigid) Rotational Inertiamentioning

confidence: 99%

“…18; we do not mean to imply the presence of a superfluid component for electrons in quantum dots. In the context of the appearance of supersolid behavior of 4 He under appropriate conditions, formation of a supersolid fraction is often discussed in conjunction with the presence of (i) real defects and (ii) real vacancies. 16,17 Our REM wave function [Eq.…”

Section: Lmmentioning

confidence: 99%

“…4,5,6,7,8,9 Experimentally, the case of parabolic QDs with a small number of electrons (N ≤ 30) has attracted particular attention, as a result of precise control of the number of electrons in the dot that has been demonstrated in several experimental investigations.…”

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confidence: 99%

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From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Yannouleas

Landman

2006

Phys. Rev. B

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Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N -electron parabolic quantum dots in strong magnetic fields in the medium-size range 10 ≤ N ≤ 30. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. An analytic expression for the energetics of such non-rigid multi-ring REMs is derived; it is applicable to arbitrary sizes given the corresponding equilibrium configuration of classical point charges. We show that the rotating electron molecules have a non-rigid (non-classical) rotational inertia exhibiting simultaneous crystalline correlations and liquid-like (non-rigidity) characteristics. This mixed phase appears in high magnetic fields and contrasts with the picture of a classical rigid Wigner crystal in the lowest Landau level.

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Section: B Nonclassical (Non-rigid) Rotational Inertiamentioning

confidence: 99%

Section: Lmmentioning

confidence: 99%

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From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Yannouleas

Landman

2006

Phys. Rev. B

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“…At high magnetic fields the electron systems in circular quantum dots form Wigner molecules [1,2] in the internal structure of the system. Deformation [3,4] of the circular symmetry allows the molecules to appear in the laboratory frame only [4] when the classical counterpart [5] of the quantum system possesses a single lowest-energy configuration.…”

mentioning

confidence: 99%

“…Fig. 2(c) shows the pair correlation function (PCF) [2] for the UHF and the exact BS state corresponding to the charge density of Fig. 2(a) with the position of one of the electrons fixed at two different locations: in the center and on the edge of the central charge puddle.…”

mentioning

confidence: 99%

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Szafran

Peeters

Bednarek

et al. 2005

Physica E: Low-dimensional Systems and Nanostructures

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Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree-Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave function on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated separation of charge islands which are more strongly localized than in the exact broken-symmetry states. We assume a spin-polarization of electrons at high magnetic field (0, 0, B) oriented perpendicular to the quantum dot plane and use the Landau gauge. In the ED, described in detail in Ref.[4], the single electron wave functions used for construction of the Slater determinants are obtained via diagonalization of the single electron Hamiltonian in the multicenter basis [7,8,9] of M displaced lowest Landau level wave functionswhere α is treated as variational parameter. In the present UHF approach the one-electron orbitals (1) are optimized self-consistently. We study up to N = 4 electrons, use the material data of GaAs and a basis of 12 centers (x k , y k ) put on an ellipse with a size determined variationally. Basis (1) Classical system of three electrons in an elliptical confinement potential with hω x = 3 meV andhω y = 4 meV possesses two equivalent lowest-energy configurations [cf. inset of Fig. 1] and the quantum system undergoes parity transformations [4] with the magnetic field [cf. Fig. 1]. Superposition [4] of the two lowest-energy eigenstates2 yields a broken-symmetry (BS) charge density with a distinct electron separation. Fig. 1 shows that in contrast to the exact ground-state energy the UHF energy estimate is a smooth function of the magnetic field.The charge densities of considered states are shown in Figs. 2(a) and 2(b) for two magnetic field values corresponding to the even-odd energy crossing presented in Fig. 1. The phase φ in the BS state is chosen such that the electrons are localized at the classical Wigner molecule positions. Notice that in the UHF the separation of electrons is more pronounced than in the exact BS states. Fig. 2(c) shows the pair correlation function (PCF) [2] for the UHF and the exact BS state corresponding to the charge density of Fig. 2(a) with the position of one of the electrons fixed at two different locations: in the center and on the edge of the central charge puddle. In contrast to the exact BS state in the UHF wave function the two electrons are insensitive to the actual position of the third electron in its charge puddle. This is a consequence of the single-determinantal form of the UHF wave function, and can be easily explained for two electrons. In the spin-polarized two electron Wigner molecule the UHF spatial wave function is given by Ψ α (r 1 )Ψ β (r 2 )−Ψ β ...

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Quantum Dot Applications in Biomolecule Assays

Fang

2009

Biosensing Using Nanomaterials

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Molecular aspects of electron correlation in quantum dots

Cited by 138 publications

References 117 publications

From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Quantum Dot Applications in Biomolecule Assays

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