Wigner crystal physics in quantum wires

Meyer, Jacques; Матвеев, К. А.

doi:10.1088/0953-8984/21/2/023203

Cited by 127 publications

(177 citation statements)

References 81 publications

(269 reference statements)

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“…While the NC wave function remains essentially unaltered by the dielectric confinement, the NR wave function develops a valley in the center of the structure. This is a clear indication that Wigner localization is taking place in the NR, which will have direct implications for transport processes 26 and shell-filling spectroscopy.…”

Section: Electron-electron Interactionmentioning

confidence: 85%

Strong configuration mixing due to dielectric confinement in semiconductor nanorods

et al. 2009

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The interaction between electron-electron and electron-hole pairs in semiconductor nanorods embedded in dielectric media is investigated using a configuration-interaction method. Contrary to spherical quantum dots of similar volume, the dielectric confinement is shown to bring nanorods into a regime of strong configuration mixing. The wave functions are particularly sensitive to such mixing, which leads to qualitative changes in the electronic and optical properties of the rods. DOI: 10.1103/PhysRevB.79.161301 PACS number͑s͒: 73.21.La, 77.22.Ej, 78.67.Hc, 71.27.ϩa Semiconductor quantum rods or nanorods ͑NRs͒ are colloidal quantum dots with strong radial confinement and variable length.1,2 Even though NRs were first synthesized long after spherical nanocrystals ͑NCs͒, it was soon realized that their anisotropic shape posed many benefits for optical and transport applications.3 This prompted a large number of studies, often revealing characteristic physical phenomena which stem from the weak longitudinal confinement, for NRs bridge the gap between zero-dimensional and onedimensional quantum-confined systems. [4][5][6][7][8][9][10] Similar to NCs, NRs are usually embedded in insulating media, whose dielectric constant is much lower than that of the semiconductor structure. This dielectric mismatch gives rise to a so-called dielectric confinement, which greatly enhances the Coulomb interactions inside the semiconductor. 11,12 In spherical NCs, however, owing to the strong quantum confinement, Coulomb interactions are usually a first-order perturbation effect for the low-lying states. 13Furthermore, a strong spatial confinement leads to compensations between electron and hole charge distributions, 14,15 so that the optical properties are barely affected by the dielectric environment.None of these restrictions apply to NRs, where the longitudinal confinement may be fairly weak. Indeed, the dielectric confinement has been held responsible for the large variation in the optical gap of CdSe NRs as compared to the transport one. 7,16 What is more, NRs are the zerodimensional counterpart of quantum wires, where variations in the dielectric confinement have been shown to induce drastic changes in the binding energy and oscillator strength of excitons, thus enabling Coulomb interaction engineering. [17][18][19] One may then wonder to which extent the single-particle and perturbational treatments of Coulomb interactions that dominate the literature of NRs ͑Refs. 6-10͒ provide a valid description of the optoelectronic properties.In this work, we perform a theoretical study of the effect of the dielectric confinement on interacting particles ͑two electrons or one electron and one hole͒ confined in a semiconductor NR. A numerical procedure is used which allows us to estimate the effect of the dielectric environment for arbitrary three-dimensional potentials, thus addressing realistic geometries. Electron correlations are then accounted for exactly using an effective mass-configuration-interaction ͑CI͒ scheme. We go beyond en...

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Section: Electron-electron Interactionmentioning

confidence: 85%

Strong configuration mixing due to dielectric confinement in semiconductor nanorods

et al. 2009

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“…Upon increasing density (and, thus, the interaction energy), or weakening the confining potential, the crystal deviates from its strictly one-dimensional structure. It has been shown that at a critical density, a transition to a zigzag crystal takes place 7,11,23,25,26 . Though not for electrons, this zigzag transition has indeed been observed using 24 Mg + ions in a quadrupole storage ring 27 .…”

Section: Introductionmentioning

confidence: 99%

Formation of defects in multirow Wigner crystals

Klironomos

Meyer

2011

Phys. Rev. B

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We study the structural properties of the ground state of a quasi-one-dimensional classical Wigner crystal, confined in the transverse direction by a parabolic potential. With increasing density, the one-dimensional crystal first splits into a zigzag crystal before progressively more rows appear. While up to four rows the ground state possesses a regular structure, five-row crystals exhibit defects in a certain density regime. We identify two phases with different types of defects. Furthermore, using a simplified model, we show that beyond nine rows no stable regular structures exist.

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“…For example, when d = 1 the system serves as a prototype for ions in electromagnetic traps and when d = 3, as a model of confined dipolar particles. Here we address mainly the limit as g → ∞ in which the perfect linear Wigner molecule is formed [35][36][37], and the harmonic approximation (HA) is valid [11,14,38,39]. Recently, within the framework of this approximation, we have derived when N = 3 and d = 1 an explicit integral representation for the asymptotic occupancies and their natural orbitals [11].…”

Section: Introductionmentioning

confidence: 99%

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

Kościk

2015

Physics Letters A

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We study one-dimensional systems of N particles in a one-dimensional harmonic trap with an inverse power law interaction ∼ |x| −d . Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of N . A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on N is discussed for the systems with d = 1 (charged particles) and with d = 3 (dipolar particles).

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Wigner crystal physics in quantum wires

Cited by 127 publications

References 81 publications

Strong configuration mixing due to dielectric confinement in semiconductor nanorods

Strong configuration mixing due to dielectric confinement in semiconductor nanorods

Formation of defects in multirow Wigner crystals

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

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