Incipient Wigner Localization in Circular Quantum Dots

Abstract

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, r_s<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 r_s 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 r_s) side of our regime.

14 pages, 12 figures

References in corpus (42)

• Metallic behavior and related phenomena in two dimensions
• Correlation energy and spin polarization in the 2D electron gas
• Metal-insulator transition in two-dimensional electron systems
• Wigner Crystallization in mesoscopic 2D electron systems
• Crossover from Fermi liquid to Wigner molecule behavior in quantum dots
• Energy and variance optimization of many body wave functions
• Full configuration interaction approach to the few-electron problem in artificial atoms
• Spin-density-functional theory of circular and elliptical quantum dots
• Universal Aspects of Coulomb Frustrated Phase Separation
• On the formation of Wigner molecules in small quantum dots
• 2D Metal-Insulator transition as a percolation transition
• Spin Polarization of the Low Density 3D Electron Gas
• Diffusion Monte Carlo study of circular quantum dots
• Wigner Glass, Spin-liquids, and the Metal-Insulator Transition
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Phase separation in the two-dimensional electron liquid in MOSFETs
• Correlation Induced Inhomogeneity in Circular Quantum Dots
• Wigner molecules in quantum dots: a quantum Monte Carlo study
• Thermodynamic density of states of two-dimensional GaAs systems near the apparent metal-insulator transition
• Group theoretical analysis of symmetry breaking in two-dimensional quantum dots
• Spontaneous Spin Polarization in Quantum Wires
• Path-integral Monte Carlo simulations for interacting few-electron quantum dots with spin-orbit coupling
• The interplay between shell effects and electron correlations in quantum dots
• Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots
• Hybrid phase at the quantum melting of the Wigner crystal
• Unrestricted Hartree-Fock for Quantum Dots
• Multiparticle ring exchange in the Wigner glass and its possible relevance to strongly interacting two-dimensional electron systems in the presence of disorder
• Anatomy of the quantum melting of the two dimensional Wigner crystal
• Unified description of floppy and rigid rotating Wigner molecules formed in quantum dots
• Crystalline character of high-magnetic-field cusp states in quantum dots
• Spontaneous symmetry breaking in single and molecular quantum dots
• Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime
• Erratum: Diffusion Monte Carlo study of circular quantum dots
• Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases
• From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings
• Linear temperature dependence of conductivity in Si two-dimensional electrons near the apparent metal-to-insulator transition
• Ground-state energy and spin in disordered quantum dots
• Ground-state densities and pair correlation functions in parabolic quantum dots
• Floating Wigner molecules and possible phase transitions in quantum dots
• Symmetry breaking and Wigner molecules in few-electron quantum dots
• Interaction Correction to the Longitudinal Conductivity and Hall Resistivity in High Quality Two-Dimensional GaAs Electron and Hole Systems
• Interaction Effects in the Mesoscopic Regime: A Quantum Monte Carlo Study of Irregular Quantum Dots

Cited by in corpus (34)

• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Strong correlation in Kohn-Sham density functional theory
• Effects of symmetry breaking in finite quantum systems
• Electron-electron interaction and charging effects in graphene quantum dots
• Wigner islands with electrons over helium
• Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
• Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking
• Localization in an Inhomogeneous Quantum Wire
• Coherent control and spectroscopy of a semiconductor quantum dot Wigner molecule
• Transport properties of quantum dots in the Wigner molecule regime
• High-order Path Integral Monte Carlo methods for solving quantum dot problems
• Spin projected unrestricted Hartree-Fock ground states for harmonic quantum dots
• Wigner crystallization in topological flat bands
• Interaction-Induced Strong Localization in Quantum Dots
• Ab initio computation of circular quantum dots
• Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters
• Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases
• Quantum Wigner molecules in moiré materials
• Wigner-molecule supercrystal in transition-metal dichalcogenide moiré superlattices: Lessons from the bottom-up approach
• Nodal Variational Principle for Excited States
• Universality of Many-Body States in Rotating Bose and Fermi Systems
• Efficient Solutions of Fermionic Systems using Artificial Neural Networks
• Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer
• Influence of the nature of confinement on the melting of Wigner molecules in quantum dots
• Crystal-field effects in the formation of Wigner-molecule supercrystals in moiré TMD superlattices
• Wigner crystallization at graphene edges
• Microscopic theory on magnetic-field-tuned sweet spot of exchange interactions in multielectron quantum-dot systems
• The Wigner localization of interacting electrons in a one-dimensional harmonic potential
• Solving fermion problems without solving the sign problem: symmetry-breaking wave functions from similarity-transformed propagators for solving 2D quantum dots
• Kinetic correlation functionals from the entropic regularisation of the strictly-correlated electrons problem
• Simple Impurity Embedded in a Spherical Jellium: Approximations of Density Functional Theory compared to Quantum Monte Carlo Benchmarks
• Chiral Spin Textures of Strongly Interacting Particles in Quantum Dots
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• Energy spectrum and structure of one-dimensional few-electron Wigner crystals with and without coupling to light in cavity