Erratum: Crossover from Fermi Liquid to Wigner Molecule Behavior in Quantum Dots [Phys. Rev. Lett. 82, 3320 (1999)]

Egger, Reinhold; Häusler, Wolfgang; Mak, C. H.; Grabert, Hermann

doi:10.1103/physrevlett.83.462

Cited by 75 publications

(147 citation statements)

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“…We believe the lack of sufficient statistical accuracy in Ref. 38 led to that erroneous conclusion. Note, for instance, that the statistical error in the PIMC energies is often larger than the energy differences between different S states that we find.…”

Section: E Reordering Of States In Energymentioning

confidence: 83%

“…23,27,36,38,42 We do find many violations of Hund's second rule -the value of the orbital angular momentum is not necessarily a maximum -but a modified second rule holds for small r s . (iv) The addition energy curve first becomes smoother as interactions strengthen -the mesoscopic fluctuations are damped by correlation -and then starts to show features characteristic of the classical addition energy, indicating incipient Wigner crystallization.…”

Section: Introductionmentioning

confidence: 99%

“…Path Integral Monte Carlo (PIMC) has also been applied to large r s circular dots. 38,39,40,41,42 One study 38 found a crossover from Fermi liquid to Wigner molecule behavior at r s ≈ 4, a value significantly smaller than the bulk r c,2D s . Another, 40 using different criteria for the transition, found a two-stage transition for r s larger than r c,2D s .…”

Section: Introductionmentioning

confidence: 99%

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Incipient Wigner localization in circular quantum dots

et al. 2007

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We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N ≤ 20, and electron gas parameter, rs < ∼ 18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of "incipient" Wigner crystallization in these quantum dots. Our specific conclusions are: (i) The density develops sharp rings while the pair density shows both radial and angular inhomogeneity. (ii) The spin of the ground state is consistent with Hund's (first) rule throughout our entire range of rs for all 4 ≤ N ≤ 20. (iii) The addition energy curve first becomes smoother as interactions strengthen -the mesoscopic fluctuations are damped by correlation -and then starts to show features characteristic of the classical addition energy. (iv) Localization effects are stronger for a smaller number of electrons. (v) Finally, the gap to certain spin excitations becomes small at the strong interaction (large rs) side of our regime.

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Section: E Reordering Of States In Energymentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Incipient Wigner localization in circular quantum dots

et al. 2007

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“…For instance, for two electrons and S = 0, PIMC predicts E clean = 4.893(7), while the T = 0 result is E = 4.848. Such differences arise because PIMC proceeds at fixed total z-component of the spin and therefore receives contributions from higher spin states [7]. Note that this effect is rather tiny and does neither affect the (finite-temperature) addition energies (1) nor the prediction of ground-state spins.…”

mentioning

confidence: 99%

“…A particularly interesting aspect of such artificial atoms is the wide experimental tunability of the electron number N and the Brueckner interaction strength parameter r s in high-quality semiconductor dots [3,4,6]. In particular, it has been established both theoretically [1,7] and experimentally [8,9] that a "Wigner molecule" of crystallized electrons forms already at surprisingly high densities corresponding to r s > ∼ 2 [10]. In this paper, we present numerically exact path-integral Monte Carlo (PIMC) [11] simulation results for N ≤ 10 electrons in the most challenging incipient Wigner molecule regime, choosing r s ≈ 4.…”

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confidence: 99%

Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime

Reusch

Egger

2003

Europhys. Lett.

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Abstract. -Numerically exact path-integral Monte Carlo data are presented for N ≤ 10 strongly interacting electrons confined in a 2D parabolic quantum dot, including a defect to break rotational symmetry. Low densities are studied, where an incipient Wigner molecule forms. A single impurity is found to cause drastic effects: (1) The standard shell-filling sequence with magic numbers N = 4, 6, 9, corresponding to peaks in the addition energy ∆(N ), is destroyed, with a new peak at N = 8, (2) spin gaps decrease, (3) for N = 8, sub-Hund's rule spin S = 0 is induced, and (4) spatial ordering of the electrons becomes rather sensitive to spin. We also comment on the recently observed bunching phenomenon.During the past few years, the electronic properties of 2D quantum dots have been the subject of intense theoretical studies [1,2]. A particularly interesting aspect of such artificial atoms is the wide experimental tunability of the electron number N and the Brueckner interaction strength parameter r s in high-quality semiconductor dots [3,4,6]. In particular, it has been established both theoretically [1,7] and experimentally [8,9] that a "Wigner molecule" of crystallized electrons forms already at surprisingly high densities corresponding to r s > ∼ 2 [10]. In this paper, we present numerically exact path-integral Monte Carlo (PIMC) [11] simulation results for N ≤ 10 electrons in the most challenging incipient Wigner molecule regime, choosing r s ≈ 4. Due to the breakdown of effective single-particle descriptions, this parameter regime is notoriously difficult to treat within approximation schemes such as Hartree-Fock theory [1], density functional theory [1,12,13], semiclassical [14] or classical [15] approaches. Especially concerning disordered dots, in the absence of benchmark calculations, their accuracy has so far been largely unclear.The incipient Wigner molecule regime also exhibits unexpected and interesting physics, in particular rather dramatic effects when including just one impurity in order to break rotational symmetry. Below we shall demonstrate this in three different ways. First, despite the presence of strong interactions, the clean system still exhibits shell structure, with exceptional stability of the dot for "magic numbers" N = 4, 6, and 9. The stability is reflected in peaks in the corresponding addition energy, ∆(N ) = E(N + 1) − 2E(N ) + E(N − 1),c EDP Sciences

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