Spatial ordering of charge and spin in quasi-one-dimensional Wigner molecules

Abstract

Few-electron systems confined in quasi one-dimensional quantum dots are studied by the configuration interaction approach. We consider the parity symmetry of states forming Wigner molecules in large quantum dots and find that for the spin-polarized Wigner molecules it strictly depends on the number of electrons. We investigate the spatial spin-ordering in the inner coordinates of the quantum system and conclude that for small dots it has a short-range character and results mainly from the Pauli exclusion principle while the Wigner crystallization in large dots is accompanied by spin ordering over the entire length of the dot.

Spectra and correlated wave functions of two electrons confined in a quasi-one-dimensional nanostructure

“…1 are doubly degenerate, respectively, as well as the apparent doublets at E = 0.173 and 0.263. A similar doublet structure was reported previously for two electrons confined in a quasione-dimensional rectangular potential well of large size [16,46] as a precursor of the Wigner lattice [47]. Therefore, the observed doublet energy-level structure can be a general trend for weakly confined two electron systems.…”

Mixed correlation phases in elongated quantum dots

“…On the one hand, Wigner crystallization in the presence of an attractive defect was considered, albeit briefly, by Szafran et al 14 They studied a quasi-onedimensional QD populated with N = 2 and N = 3 electrons and perturbed by a steplike defect potential localized at the center of the system. In the absence of the defect, their configuration-interaction ͑CI͒ study reveals that the number of maxima equals the number N of electrons, as corresponds to Wigner molecules.…”

Semiconducting carbon nanotube quantum dots: Calculation of the interacting electron states by exact diagonalisation

“…One dimensional nanotube (NT) dots are, however, very different to the 2D semiconductor dots that have been used to study effects such as the formation of all electron (Wigner) molecules [2,3] and electronic shell filling analogous to that observed in atoms [4]. The reduced dimensionality of NT dots alters the form of the effective Coulomb interaction [5], it affects the allowed symmetries of the states [6] and the types of confinement that can be engineered.In particular, NT dots can be used to fabricate room temperature single electron transistors because of the large single particle level spacings which can be engineered [7]. They are promising candidates for spin qubits [8] and also exhibit interesting shell filling effects due to the approximately degenerate [8] K, K ′ sub-bands.…”

“…One dimensional nanotube (NT) dots are, however, very different to the 2D semiconductor dots that have been used to study effects such as the formation of all electron (Wigner) molecules [2,3] and electronic shell filling analogous to that observed in atoms [4]. The reduced dimensionality of NT dots alters the form of the effective Coulomb interaction [5], it affects the allowed symmetries of the states [6] and the types of confinement that can be engineered.…”