We propose a general capacitive model for an antidot, which has two localized edge states with different spins in the quantum Hall regime. The capacitive coupling of localized excess charges, which are generated around the antidot due to magnetic flux quantization, and their effective spin fluctuation can result in Coulomb blockade, h/(2e) Aharonov-Bohm oscillations, and the Kondo effect. The resultant conductance is in qualitative agreement with recent experimental data.PACS numbers: 73.23. Hk, 72.15.Qm, The Kondo effect arises due to many-body interactions between a localized spin and free electrons [1,2]. Recently, there has been renewed interest in the effect as it was predicted [3,4] and observed [5,6,7] in quantum dots. In a quantum dot, the localized spin is naturally provided when the dot has an odd number of electrons.Quantum antidots in the integer quantum Hall regime have attracted recent interest in connection with experimental observations of the charging effect [8], h/(2e) Aharonov-Bohm (AB) oscillations [8,9], and Kondo-like signatures [10]. In these systems, localized quantum Hall edge states are formed along an equipotential line of a "potential hill" which defines the antidot. As in quantum dots, electrostatic interaction of the localized antidot states may give rise to the charging effect. However, the magnetic flux quantization makes the antidots rather intriguing. When magnetic field B changes adiabatically, each single-particle state encircling the antidot moves with respect to the antidot potential, adjusting the enclosed antidot area S in order to keep the flux BS constant [ Fig. 1(b)]. This electron displacement results in charge imbalance around the antidot, i.e., local accumulation of excess charge δq(B) [9], which is the source of the charging effect [8]. The accumulated δq(B) is relaxed via single electron resonant tunnelings [11]. These tunneling events occur ν c times within one AB period ∆B(= h/eS) when the antidot has ν c localized edge states [12]. Also δq(B) is periodic with the period ∆B.The origin of the Kondo-like signature in the antidots is not understood yet. One may naively consider that the spin-split single-particle antidot states support a localized spin. However, their SU(2) spin symmetry may be broken by the Zeeman energy and thus they can not cause the signature. Rather, many-body antidot states may play an important role.In this Letter, we provide a theoretical model for the Kondo effect in a quantum Hall antidot system. As a natural way to incorporate the charging effect, capacitive interactions of excess charges with different spins are adopted, and the source-drain conductance G(B) is computed within the model. We find that the effective spin flips of the excess charges can cause the Kondo effect. Within one AB period ∆B, G(B) can show approximately two normal resonances and one Kondo resonance, consistent with experimental data [10]. The two normal resonant tunneling events, involving spin-down electrons, are evenly spaced with varying B, constituting h/(2e) A...

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetry in the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.

We investigate a quantum antidot in the integer quantum Hall regime (the filling factor is two) by using a Hartree-Fock approach and by transforming the electron antidot into a system which confines holes via an electron-hole transformation. We find that its ground state is the maximum density droplet of holes in certain parameter ranges. The competition between electron-electron interactions and the confinement potential governs the properties of the hole droplet such as its spin configuration. The ground-state transitions between the droplets with different spin configurations occur as magnetic field varies. For a bell-shape antidot containing about 300 holes, the features of the transitions are in good agreement with the predictions of a recently proposed capacitive interaction model for antidots as well as recent experimental observations. We show this agreement by obtaining the parameters of the capacitive interaction model from the Hartree-Fock results. An inverse parabolic antidot is also studied. Its ground-state transitions, however, display different magnetic-field dependence from that of a bell-shape antidot. Our study demonstrates that the shape of antidot potential affects its physical properties significantly.

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We have investigated pumping in quantum dots from the perspective of non-Abelian (matrix) Berry phases by solving the time dependent Schr{\"o}dinger equation exactly for adiabatic changes. Our results demonstrate that a pumped charge is related to the presence of a finite matrix Berry phase. When consecutive adiabatic cycles are performed the pumped charge of each cycle is different from the previous ones