Two-dimensional quantum dots in high magnetic fields: Rotating-electron-molecule versus composite-fermion approach

Physical Review B - Condensed Matter and Materials Physics

Volumn 68, Issue 3, 2003, Pages 353261-3532611

  Yannouleas, Constantine ^a   Landman, Uzi ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ELECTRON; ELEMENTARY PARTICLE; ENERGY; FERMION; MAGNETIC FIELD; MATHEMATICAL ANALYSIS; QUANTUM DOT; QUANTUM MECHANICS; ROTATION;

EID: 0345169919     PISSN: 10980121     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

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61. Both the finite-size REM molecule and several sophisticated bulk Wigner crystal (BWC) approaches at high B (listed at the end of this footnote) start with a single-determinantal UHF wave function constructed out of the orbitals in Eq. (1), and both do improve it by introducing additional correlations; however, the nature of these correlations is quite different between the REM and BWC approaches. Indeed, due the the finite size of the system, the REM approach includes correlations associated with fluctuations in the azimuthal angle (see Ref. 15 and 40); these correlations arise from the restoration of the circular symmetry and result in states with good total angular momenta (in particular magic angular momenta; see Sec. IV A). Naturally, in the BWC approaches, angular momentum conservation and magic angular momenta are not considered; for example, Lam and Girvin include correlations from vibrational-type fluctuations of the BWC that are more in tune with the expected translational invariance of a bulk system. As a result, the REM exhibits drastically different properties from the properties of an N-electron piece of the bulk Wigner crystal. Rather, the REM wave functions exhibit properties associated with the incompressible magic angular momentum states in the spectra of QD's, which are finite-size precursors to the "correlated-liquid" fractional quantum Hall states of the bulk (see Ref. 18). For sophisticated BWC approaches at high B, see, e.g., P.K. Lam and S.M. Girvin, Phys. Rev. B 30, 473 (1984); H. Yi and H.A. Fertig, ibid. 58, 4019 (1998).
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81. B; see Ref. 50). As was the case with the harmonic external potential, these authors found again that their external confinement influences which magic-L state becomes the ground state of the system. Most importantly, the ground-state wave functions in their exact diagonalization study exhibit strong oscillations in the radial electron density (in an apparent agreement with the classical ring configurations of Wigner molecules) and in disagreement with the CF-JL wave functions. It is interesting to note the coincidence, for all practical purposes, of the exact radial electron density for N = 6 and L = 105 calulated by Wan et al. with that calculated by us [compare Fig. 5(d) in Ref. 50 with the middle panel of Fig. 5 in this paper]. In order to account for the disagreement between the exact and CF-JL wave functions, Wan et al. were led to use the concept of "edge reconstruction." In the case studied by us, however, our exact diagonalization results (and those of Tsiper and Goldman; see Ref. 62) do not include any external confinement, a fact that rules out "edge reconstruction" as the underlying cause for the disagreement between the exact and CF-JL wave functions. As we have pointed out in this paper previously (see Sec. IV E and also Ref. 15), this disagreement arises from the fact that the CF-JL functions do not capture the long-range character of the Coulomb interelectron repulsion. On the contrary the REM wave functions are able to capture the long-range Coulombic correlations and thus are in better agreement with the wave functions from exact diagonalization.