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, 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.

Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes

“…On the one hand, the configuration interaction (CI) approach, despite being in principle capable of describing any correlation regime, is in practice limited to the study of small systems with only very few particles due to its high computational cost, which scales exponentially with the number of particles N. Such numerical difficulties get even worse in the very strongly correlated limit due to the degeneracy of the different quantum states and the consequent need of considering larger Hilbert spaces in the calculations. Other wave-function methods such as quantum Monte Carlo 7,[18][19][20] (QMC) and density matrix renormalization group (DMRG), 21 which rely to some extent on various approximations, can treat systems larger than the CI approach, but are still computationally expensive and limited to N 10 2 . The much cheaper Kohn-Sham (KS) density functional theory (DFT), 22,23 which can treat thousands of electrons, is the method of choice to study larger quantum systems.…”

Wigner crystallization at graphene edges

“…The two limits, high density Fermi liquid and low density Wigner crystal, are well understood. However, the crossover in between is a complex many-body problem which was previously investigated for various electron gas systems in various dimensions both theoretically [2][3][4][5][6][7][8][9][10][11][12][13] and experimentally [14][15][16][17][18][19]. In particular, it is expected that Wigner crystallization has important implications on the transport properties of two-dimensional [14] and one-dimensional [9,12,[16][17][18][19] systems.…”

Role of confinements on the melting of Wigner molecules in quantum dots

“…This conjecture found support from the tunneling conductance measurements of chaotic dots 26 , and associated Coulomb blockade experiments 27,28 . Although a quantum melting of Wigner-type in a circular trap has been studied extensively 3,4,6,29 , a similar study in the irregular confinement has not yet received as much attention, see however Ref. 30 .…”