Origin of magic angular momenta in few-electron quantum dots

Ruan, Weidong; Liu, Youyan; Bao, C. G.; Zhang, Zhao-Qing

doi:10.1103/physrevb.51.7942

Cited by 126 publications

(104 citation statements)

References 3 publications

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“…Such studies (both EXD and variational) revealed that, at least for finite systems, the underlying physical picture governing the behavior of strongly-correlated electrons is not that of a "quantum liquid." Instead, the appropriate description is in terms of a "quantum crystal," with the localized electrons arranged in polygonal concentric rings [19,20,21,22,23,25,26,27]. These "crystalline" states lack [21,23] the familiar rigidity of a classical extended crystal, and are better described [19,20,21,22,23,24] as rotating electron ( or Wigner) molecules (REMs or RWMs).…”

Section: Introductionmentioning

confidence: 99%

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

2007

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The Hamiltonian for a small number, N ≤ 11, of bosons in a rapidly rotating harmonic trap, interacting via a short range (contact potential) or a long range (Coulomb) interaction, is studied via an exact diagonalization in the lowest Landau level. Our analysis shows that, for both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. Focusing on systems with the number of trapped atoms sufficiently large to form multi-ring bosonic molecules, we find that, as a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling ν than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions ν < 1/2, we observe well developed crystallinity in the CPDs (twopoint correlation functions). For larger filling fractions ν > 1/2, observation of similar molecular patterns requires consideration of even higher-order correlation functions.

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Section: Introductionmentioning

confidence: 99%

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

2007

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“…Our study leads to the following two main results: (i) in analogy with 3D natural molecules, the WM's can rotate and the restoration of the total-spin and rotational symmetries via projection techniques describes their lowest rotational bands (yrast bands 14,34 ) in addition to the ground state, and (ii) the lowering of the symmetry, which results in the (discrete) point-group symmetry of the UHF wave function, underlies the appearance of the sequences of magic angular momenta (familiar from exact-diagonalization studies [35][36][37][38][39][40] ) in the excitation spectra of single QD's. Since exact-diagonalization methods are typically restricted to small sizes with N ≤ 10, the present two-step method of breakage and subsequent restoration of symmetries offers a promising new avenue for accurately describing larger 2D electronic systems.…”

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confidence: 99%

“…In this section, we will not proceed any further with explicit numerical or analytic derivations of additional RBS wave functions. Instead, we will use the RBS approach to illustrate through a couple of concrete examples how certain universal properties of the exact solutions, i.e., the appearance of magic angular momenta in the exact rotational spectra, [35][36][37][38][39][40] relate to the symmetry broken UHF solutions. Indeed, we will demonstrate that the magic angular momenta are a direct consequence of the symmetry breaking at the UHF level and that they are determined fully by the molecular symmetries of the UHF determinant.…”

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confidence: 99%

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

2003

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We present a group theoretical study of the symmetrybroken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N -electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hückel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N -electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via post-Hartree-Fock projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetrybreaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.

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“…A cyclic coordinate permutation is a π/3 rotation such that Ψ → exp (πiM/3)Ψ. In this case Ψ changes sign [25], and therefore M = 6p + 3 (p integer) and odd parity. Our findings show that an excited magic state can be created adding L quanta of angular momentum to the ground state via the density fluctuation operator ρ † L .…”

mentioning

confidence: 99%

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

Rontani¹,

Goldoni²,

Manghi³

et al. 2002

Europhys. Lett.

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Abstract. -We study electron molecules in realistic vertically coupled quantum dots in a strong magnetic field. Computing the energy spectrum, pair correlation functions, and dynamical form factor as a function of inter-dot coupling via diagonalization of the many-body Hamiltonian, we identify structural transitions between different phases, some of which do not have a classical counterpart. The calculated Raman cross section shows how such phases can be experimentally singled out.Electron systems form a Wigner crystal at sufficiently low density or high magnetic field B [1]. Theoretical [2,3] and experimental [4,5] studies suggest that lowering dimensionality favors localization: in this perspective interacting electrons confined in a quantum dot (QD) [6], sometimes called Wigner molecules [7], are interesting in their own right [8,9], due to the interplay between the electron-electron repulsion and the confining potential. This leads to a complex zero temperature phase diagram [10], as compared to the infinite layer case, as well as to complex melting mechanisms [9]. The formation of coupled QDs (artificial molecules) introduces qualitatively new physics [11]. New energy scales appear -inter-dot tunneling, inter-vs intra-dot Coulomb correlation -, whose balance controls the phase diagram [12]. Significantly, these parameters can be tuned by inter-dot distance d and/or electron density, so that the nature of these few-particle systems and their phases can be explored experimentally.In this Letter we discuss quantum mechanical calculations of N electrons in a coupled QD structure in the strong field regime, where localization is ensured in the parent isolated QDs. Monitoring the spatial correlation functions, we identify different ground states depending on the inter-dot coupling. More interestingly, we find that some of the phases do not have a classical counterpart [13], and are ascribed to a two-three-two dimensional (2D-3D-2D) transition of the electronic system. Such phases were not identified in previous studies of the coupled layer system due to the neglect of tunneling and/or finite width of the layers [14-17], i.e., of the 3D nature of the system, which turns out to be essential for their formation. From the analysis of the dynamical form factor, we associate to each phase peculiar collective charge

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Origin of magic angular momenta in few-electron quantum dots

Cited by 126 publications

References 3 publications

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

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