Configuration interaction approach to Fermi liquid–Wigner crystal mixed phases in semiconductor nanodumbbells

Ballester, Ana; Movilla, J. L.; Escartín, José María; Pí, M.; Planelles, Josep

doi:10.1063/1.4737774

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…We also consider the electron kinetic energy to be of the standard parabolic form. We are aware that there is a vast literature on the subject, investigating different aspects of quasi-1D systems using various simulation methods and microscopic calculations [19][20][21][22][23][24][25][26][27]. The smallest possible Wigner crystals consisting just of two electrons, also called Wigner molecules, have also been studied in great details [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

One-dimensional few-electron effective Wigner crystal in quantum and classical regimes

Sarma

2020

Phys. Rev. B

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A system of confined charged electrons interacting via the long-range Coulomb force can form a Wigner crystal due to their mutual repulsion. This happens when the potential energy of the system dominates over its kinetic energy, i.e., at low temperatures for a classical system and at low densities for a quantum one. At T = 0, the system is governed by quantum mechanics, and hence, the spatial density peaks associated with crystalline charge localization are sharpened for a lower average density. Conversely, in the classical limit of high temperatures, the crystalline spatial density peaks are suppressed (recovered) at a lower (higher) average density. In this paper, we study those two limits separately using an exact diagonalization of small one-dimensional (1D) systems containing few (< 10) electrons and propose an approximate method to connect them into a unified effective phase diagram for Wigner few-electron crystallization. The result is a qualitative quantum-classical crossover phase diagram of an effective 1D Wigner crystal. We show that although such a 1D system is at best an effective crystal with no true long-range order (and thus no real phase transition), the spatial density peaks associated with the quasi-crystallization should be experimentally observable in a few-electron 1D system. We find that the effective crystalline structure slowly disappears with both the crossover average density and crossover temperature for crystallization decreasing with increasing particle number, consistent with the absence of any true long-range 1D order. Thus, an effective few-electron 1D Wigner crystal may be construed either as existing at all densities (manifesting short-range order) or as non-existing at all densities (not manifesting any long range order). Within one unified description, we show through exact theoretical calculations how a small 1D system interacting through the long-range Coulomb interaction could manifest effective Wigner solid behavior both in classical and quantum regimes. arXiv:1901.00019v2 [cond-mat.mes-hall]

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Section: Introductionmentioning

confidence: 99%

One-dimensional few-electron effective Wigner crystal in quantum and classical regimes

Sarma

2020

Phys. Rev. B

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“…In order to account for electron-hole and electron-electron correlation in QDs, configuration interaction (CI) methods are arguably the most widely employed models to date. [1,2,3,4,9,10,11,12] These methods are generally built upon a basis set of independent particle or Hartree-Fock states, which has been found to provide an excellent description of repulsions in few-and many-fermion systems. [1,10,12] The description of strong attractions is however more demanding, because the afore mentioned basis functions are less suited to account for short-range interactions.…”

Section: Introductionmentioning

confidence: 99%

“…[1,2,3,4,9,10,11,12] These methods are generally built upon a basis set of independent particle or Hartree-Fock states, which has been found to provide an excellent description of repulsions in few-and many-fermion systems. [1,10,12] The description of strong attractions is however more demanding, because the afore mentioned basis functions are less suited to account for short-range interactions. [13] For the same reason, in charged excitons (trions) and multiexcitons they may not describe attractions and repulsions with comparable accuracy.…”

Section: Introductionmentioning

confidence: 99%

A simple variational quantum Monte Carlo-effective mass approach for excitons and trions in quantum dots

Planelles,

Climente

2020

Preprint

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A computational model is presented to calculate the ground state energy of neutral and charged excitons confined in semiconductor quantum dots. The model is based on the variational Quantum Monte Carlo method and effective mass Hamiltonians. Through an iterative Newton-Rhapson process, minimizing the local energy, and (optional) parallelization of random walkers, fast and accurate estimates of both confinement and Coulomb binding energies can be obtained in standard desktop computers. To illustrate the reach of the model, we provide Fortran programs and illustrative calculations for colloidal CdSe nanoplatelets with large lateral dimensions and dielectric confinement, where electronic correlations are strong. The results compare well with exact variational calculations and largely outperform configuration interaction calculations in computational efficiency.

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“…GKT proves that by means of a spatially homogeneous probe, no many-body effects can be observed in the dipole response. Whereas for nonharmonic traps signatures of particle-particle correlation can be observed in the dipole spectrum [32], in separable systems the probe needs to be non-homogeneous to be able to excite internal transitions [33,34]. We propose to use the spatial inhomogeneity associated with the topological charge l of the TL field to study the internal energy spectrum of the trap.…”

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confidence: 99%

Probing particle-particle correlation in harmonic traps with twisted light

Fuks¹,

Quinteiro²,

Appel³

et al. 2021

Preprint

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We explore the potential of twisted light as a tool to unveil many-body effects in parabolically confined systems. According to the Generalized Kohn Theorem, the dipole response of such a multiparticle system to a spatially homogeneous probe is indistinguishable from the response of a system of non-interacting particles. Twisted light however can excite internal degrees of freedom, resulting in the appearance of new peaks in the even multipole spectrum which are not present when the probe is a plane wave. We also demonstrate the ability of the proposed twisted light probe to capture the transition of interacting fermions into a strongly correlated regime in a one-dimensional harmonic trap. We report that by suitable choice of the probe's parameters, the transition into a strongly correlated phase manifests itself as an approach and ultimate superposition of peaks in the second order quadrupole response. These features, observed in exact calculations for two electrons, are reproduced in adiabatic Time Dependent Density Functional Theory simulations.

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Configuration interaction approach to Fermi liquid–Wigner crystal mixed phases in semiconductor nanodumbbells

Cited by 4 publications

References 21 publications

One-dimensional few-electron effective Wigner crystal in quantum and classical regimes

One-dimensional few-electron effective Wigner crystal in quantum and classical regimes

A simple variational quantum Monte Carlo-effective mass approach for excitons and trions in quantum dots

Probing particle-particle correlation in harmonic traps with twisted light

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