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arXiv:cond-mat/9712290 · Physica B Condensed Matter

Symmetry of ‘molecular’ configurations of interacting electrons in a quantum dot in strong magnetic fields

Hiroshi Imamura, Peter A. Maksym, Hideo Aoki

Published Jun 1, 1998• 13 citations
arXivHTMLPDF
DOI
10.1016/s0921-4526(98)00101-x

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Exchange energies and charge densities for few electrons in electrically tunable quantum dot (QD) systems are investigated by using the variational Monte Carlo (VMC) method in the presence of magnetic fields. For N = 2 electrons in double QD, the singlet Coulomb energy decreases in magnetic fields as a consequence of magnetic localization in both strongly and weakly coupled QDs. However, the triplet Coulomb energy reaches a maximum value at intermediate magnetic fields before decreasing. We observe good agreement between the results for VMC with s-p orbital trial wavefunction and exact diagonalization (ED) method in the exchange energies. For N = 2 electrons in triple quantum dot (TQD), we observe a discontinuity in the J-derivative with detuning voltage ( dJdVT ) in triangular TQDs at B = 0 T as crossing of the eigenenergy levels leads to abrupt spatial symmetry change of the triplet densities (density rotation) and relocalization. For B ≠ 0 T, the angular momentum provided to the electrons quenches this effect. The density rotation is absent in collinear TQD for all magnetic fields as the lowest excited state remains the px state and as such, no change in symmetry is possible. By varying the triangular TQD configuration, we show the discontinuity in ( dJdVT ) persists for top angle between 20° and 70°. For N = 3 electrons in symmetric triangular TQD, the monotonicity of the exchange curve from B = 0 to 4 T remains intact for decoupled QDs but not for coupled QDs. Finally, additional energy for the triangular TQD system is computed for up to N = 3 electrons.
The nature of the ground state of a few-electron system in a parabolic twodimensional (2D) quantum dot (QD) is theoretically investigated on the basis of a variational many-body approach within a second quantized formulation. The resulting analytical expressions lead to various phase transitions: maximum density droplet, Wigner phase, etc., in a broad range of magnetic fields. It is observed that in the case of relatively strong QD confinement and weak magnetic fields, a rotationally symmetric spin-singlet state is the ground state of the system. However, in a strong magnetic field and for the same QD confinement, a broken-symmetry spinsinglet state appears to be energetically favoured over the symmetric spin-singlet state. The method developed is generalized for the investigation of possible novel phases for electron-hole interacting systems.
Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.Strongly-correlated phenomena emerging from symmetry breaking include the following.Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices.Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules.At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross-Pitaevskii solutions describing vortex formation.We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.