Phase transitions in a few-electron quantum dot in a magnetic field: Wigner phases and broken-symmetry spin-singlet stat
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ELEMENTARY PARTICLES AND FIELDS
Phase Transitions in a Few-Electron Quantum Dot in a Magnetic Field: Wigner Phases and Broken-Symmetry Spin-Singlet States* A. A. Avetisyan1)** , K. Moulopoulos2)*** , and A. P. Djotyan1)**** Received August 20, 2007
Abstract—We develop a variational many-body approach within a second quantized formulation for a fewelectron system in a parabolic two-dimensional quantum dot (QD). By way of application, the nature of the ground state of a two-electron system in a parabolic QD in a broad range of magnetic fields is theoretically investigated. Various phase transitions on the basis of the resulting analytical expressions for energy of the system have been investigated: First, the well-known transition from a maximum density droplet to a Wigner phase in a magnetic field is obtained, provided that the QD is in conditions of weak confinement. Furthermore, 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 spin-singlet state appears to be energetically favored over the symmetric spin-singlet state. A first investigation of such a broken-symmetry spin-singlet phase in a QD in a magnetic field is shown to be an important application of the proposed technique. PACS numbers: 73.21.La, 73.43.Nq, 71.70.Di, 71.10.-w DOI: 10.1134/S1063778808050050
1. INTRODUCTION Quantum dots (QDs), containing a few electrons, have recently been the subject of intense experimental and theoretical research. The standard theoretical model for a two-dimensional parabolic QD is based on a number of approximations [1]. First, a QD is considered in the two-dimensional limit of a thin disc; this is quite reasonable because in a typical QD the motion in the z direction is always frozen out into the lowest subband, since the corresponding extent of the wave function is much less than the one in the xy plane. Secondly, the confining potential is taken to be cylindrically symmetric and parabolic. The final assumption is that the electrons interact by pure Coulomb interaction [1]. The competition between the repulsive electron interaction, confining potential, spin effects, and the presence of an external magnetic field in QDs leads to rich and interesting physical behaviors: with the increase in the magnetic field, the ground state of the ∗
The text was submitted by the authors in English. Department of Physics, Yerevan State University, Yerevan, Armenia. 2) Department of Physics, University of Cyprus, Nicosia, Cyprus. ** E-mail: [email protected] *** E-mail: [email protected] **** E-mail: [email protected] 1)
electron system in a QD undergoes several transformations. In a weak magnetic field, the spin-singlet state may be the lowest state of the electronic system, while in a strong magnetic field, the system undergoes spin polarization, where the so-called maximum density droplet (MDD) phase prevails [2]. In this phase, the electron density distribution possesses
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