Electron-Electron Interactions in Isolated and Realistic Quantum Dots: A Density Functional Theory Study

Abstract

We use Kohn-Sham spin-density-functional theory to study the statistics of ground-state spin and the spacing between conductance peaks in the Coulomb blockade regime for both 2D isolated and realistic quantum dots. We make a systematic investigation of the effects of electron-electron interaction strength and electron number on both the peak spacing and spin distributions. A direct comparison between the distributions from isolated and realistic dots shows that, despite the difference in the boundary conditions and confining potential, the statistical properties are qualitatively the same. Strong even/odd pairing in the peak spacing distribution is observed only in the weak e-e interaction regime and vanishes for moderate interactions. The probability of high spin ground states increases for stronger e-e interaction and seems to saturate around $r_s\sim 4$. The saturated value is larger than previous theoretical predictions. Both spin and conductance peak spacing distributions show substantial variation as the electron number increases, not saturating until $N\sim 150$. To interpret our numerical results, we analyze the spin distribution in the even $N$ case using a simple two-level model.

10 pages, 12 figures, submitted to Phys. Rev. B

References in corpus (21)

• The Statistical Theory of Quantum Dots
• Quantum Effects in Coulomb Blockade
• Quantum dot self consistent electronic structure and the Coulomb blockade
• Statistics of Coulomb Blockade Peak Spacings
• Interactions and Interference in Quantum Dots: Kinks in Coulomb Blockade Peak Positions
• Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
• Signatures of spin pairing in a quantum dot in the Coulomb blockade regime
• Absence of bimodal peak spacing distribution in the Coulomb blockade regime
• Ground state spin and Coulomb blockade peak motion in chaotic quantum dots
• Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings
• Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation
• The Addition Spectrum and Koopmans' Theorem for Disordered Quantum Dots
• One-way multigrid method in electronic structure calculations
• Statistics of Hartree-Fock Levels in Small Disordered Systems
• Spin and Conductance-Peak-Spacing Distributions in Large Quantum Dots: A Density Functional Theory Study
• Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects
• Addition Spectra of Chaotic Quantum Dots: Interplay between Interactions and Geometry
• Coulomb Blockade Peak Spacing Distribution: The Interplay of Temperature and Spin
• Ground-state energy and spin in disordered quantum dots
• Even-odd correlations in capacitance fluctuations of quantum dots
• The addition spectrum of interacting electrons: Parametric dependence

Cited by in corpus (9)

• Three real-space discretization techniques in electronic structure calculations
• Geometric and impurity effects on quantum rings in magnetic fields
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots
• Active Brownian Motion in Threshold Distribution of a Coulomb Blockade Model
• Interaction Effects in the Mesoscopic Regime: A Quantum Monte Carlo Study of Irregular Quantum Dots
• Investigating interaction-induced chaos using time-dependent density functional theory
• Scrambling and Gate Effects in Realistic Quantum Dots
• Interactions and Broken Time-Reversal Symmetry in Chaotic Quantum Dots