Trial wave functions with long-range Coulomb correlations for two-dimensional<i>N</i>-electron systems in high magnetic fields

Yannouleas, Constantine; Landman, Uzi

doi:10.1103/physrevb.66.115315

Cited by 71 publications

(168 citation statements)

References 29 publications

Supporting

Mentioning

160

Contrasting

Order By: Relevance

“…Such studies (both EXD and variational) revealed that, at least for finite systems, the underlying physical picture governing the behavior of strongly-correlated electrons is not that of a "quantum liquid." Instead, the appropriate description is in terms of a "quantum crystal," with the localized electrons arranged in polygonal concentric rings [19,20,21,22,23,25,26,27]. These "crystalline" states lack [21,23] the familiar rigidity of a classical extended crystal, and are better described [19,20,21,22,23,24] as rotating electron ( or Wigner) molecules (REMs or RWMs).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the "quantum-liquid" picture for a small number of trapped electrons in the FQHE regime has been challenged in a series of extensive studies [19,20,21,22,23,24] of electrons in 2D quantum dots under high magnetic fields (B). Such studies (both EXD and variational) revealed that, at least for finite systems, the underlying physical picture governing the behavior of strongly-correlated electrons is not that of a "quantum liquid."…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

2007

Self Cite

View full text Add to dashboard Cite

The Hamiltonian for a small number, N ≤ 11, of bosons in a rapidly rotating harmonic trap, interacting via a short range (contact potential) or a long range (Coulomb) interaction, is studied via an exact diagonalization in the lowest Landau level. Our analysis shows that, for both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. Focusing on systems with the number of trapped atoms sufficiently large to form multi-ring bosonic molecules, we find that, as a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling ν than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions ν < 1/2, we observe well developed crystallinity in the CPDs (twopoint correlation functions). For larger filling fractions ν > 1/2, observation of similar molecular patterns requires consideration of even higher-order correlation functions.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to obtain strongly correlated ground states the Coulomb interaction has to dominate over the other energy scale, namely the shell structure of the single particle spectrum determined by the confinement. This is typically achieved by either using strong magnetic fields 17,18 , so that the single particle levels form highly degenerate Landau levels, or using rather weak confinement. 16 Interestingly, strongly correlated states naturally arise already in small graphene quantum dots even without magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Electron-electron interactions and charging effects in graphene quantum dots

2008

View full text Add to dashboard Cite

We analyze charging effects in graphene quantum dots. Using a simple model, we show that, when the Fermi level is far from the neutrality point, charging effects lead to a shift in the electrostatic potential and the dot shows standard Coulomb blockade features. Near the neutrality point, surface states are partially occupied and the Coulomb interaction leads to a strongly correlated ground state which can be approximated by either a Wigner crystal or a Laughlin like wave function. The existence of strong correlations modify the transport properties which show non equilibrium effects, similar to those predicted for tunneling into other strongly correlated systems.

show abstract

“…[4], the single electron wave functions used for construction of the Slater determinants are obtained via diagonalization of the single electron Hamiltonian in the multicenter basis [7,8,9] of M displaced lowest Landau level wave functions…”

Section: Introductionmentioning

confidence: 99%

“…We assume a spin-polarization of electrons at high magnetic field (0, 0, B) oriented perpendicular to the quantum dot plane and use the Landau gauge. In the ED, described in detail in Ref.[4], the single electron wave functions used for construction of the Slater determinants are obtained via diagonalization of the single electron Hamiltonian in the multicenter basis [7,8,9] of M displaced lowest Landau level wave functionswhere α is treated as variational parameter. In the present UHF approach the one-electron orbitals (1) are optimized self-consistently.…”

mentioning

confidence: 99%

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Szafran

Peeters

Bednarek

et al. 2005

Physica E: Low-dimensional Systems and Nanostructures

View full text Add to dashboard Cite

Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree-Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave function on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated separation of charge islands which are more strongly localized than in the exact broken-symmetry states. We assume a spin-polarization of electrons at high magnetic field (0, 0, B) oriented perpendicular to the quantum dot plane and use the Landau gauge. In the ED, described in detail in Ref.[4], the single electron wave functions used for construction of the Slater determinants are obtained via diagonalization of the single electron Hamiltonian in the multicenter basis [7,8,9] of M displaced lowest Landau level wave functionswhere α is treated as variational parameter. In the present UHF approach the one-electron orbitals (1) are optimized self-consistently. We study up to N = 4 electrons, use the material data of GaAs and a basis of 12 centers (x k , y k ) put on an ellipse with a size determined variationally. Basis (1) Classical system of three electrons in an elliptical confinement potential with hω x = 3 meV andhω y = 4 meV possesses two equivalent lowest-energy configurations [cf. inset of Fig. 1] and the quantum system undergoes parity transformations [4] with the magnetic field [cf. Fig. 1]. Superposition [4] of the two lowest-energy eigenstates2 yields a broken-symmetry (BS) charge density with a distinct electron separation. Fig. 1 shows that in contrast to the exact ground-state energy the UHF energy estimate is a smooth function of the magnetic field.The charge densities of considered states are shown in Figs. 2(a) and 2(b) for two magnetic field values corresponding to the even-odd energy crossing presented in Fig. 1. The phase φ in the BS state is chosen such that the electrons are localized at the classical Wigner molecule positions. Notice that in the UHF the separation of electrons is more pronounced than in the exact BS states. Fig. 2(c) shows the pair correlation function (PCF) [2] for the UHF and the exact BS state corresponding to the charge density of Fig. 2(a) with the position of one of the electrons fixed at two different locations: in the center and on the edge of the central charge puddle. In contrast to the exact BS state in the UHF wave function the two electrons are insensitive to the actual position of the third electron in its charge puddle. This is a consequence of the single-determinantal form of the UHF wave function, and can be easily explained for two electrons. In the spin-polarized two electron Wigner molecule the UHF spatial wave function is given by Ψ α (r 1 )Ψ β (r 2 )−Ψ β ...

show abstract

Trial wave functions with long-range Coulomb correlations for two-dimensionalN-electron systems in high magnetic fields

Cited by 71 publications

References 29 publications

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

Electron-electron interactions and charging effects in graphene quantum dots

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Contact Info

Product

Resources

About