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Register a new userComposite fermion theory of correlated electrons in semiconductor quantum dots in high magnetic fields
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Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on the correlated basis functions of the composite-fermion theory, that allows a systematic improvement of the wave functions and the energies for low-lying eigenstates. For a test of the method, we study systems for which exact results are known, and find that practically exact answers are obtained for the ground state wave function, ground state energy, excitation gap, and the pair correlation function. We show how the perturbative scheme helps resolve the subtle physics of competing orders in certain anomalous cases.
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We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called $Lambda$ levels).
This paper provides a review of developments in the physics of two-dimensional electron systems in perpendicular magnetic fields.
We report transport experiments on graphene quantum dots. We focus on excited state spectra in the near vicinity of the charge neutrality point and signatures of the electron-hole crossover as a function of a perpendicular magnetic field. Coulomb blockade resonances of a 50 nm wide and 80 nm long dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 40 states as a function of the back gate voltage can be interpreted in terms of the unique evolution of the diamagnetic spectrum of a graphene dot including the formation of the E = 0 Landau level, situated in the center of the transport gap, and marking the electron-hole crossover.
Spin properties of two interacting electrons in a quantum dot (QD) embedded in a nanowire with controlled aspect ratio and longitudinal magnetic fields are investigated by using a configuration interaction (CI) method and exact diagonalization (ED) techniques. The developed CI theory based on a three-dimensional (3D) parabolic model provides explicit formulations of the Coulomb matrix elements and allows for straightforward and efficient numerical implementation. Our studies reveal fruitful features of spin singlet-triplet transitions of two electrons confined in a nanowire quantum dot (NWQD), as a consequence of the competing effects of geometry-controlled kinetic energy quantization, the various Coulomb interactions, and spin Zeeman energies. The developed theory is further employed to study the spin phase diagram of two quantum-confined electrons in the regime of cross over dimensionality, from quasi-two-dimensional (disk-like) QDs to finite one-dimensional (rod-like) QDs.
We observe the low-lying excitations of a molecular dimer formed by two electrons in a GaAs semiconductor quantum dot in which the number of confined electrons is tuned by optical illumination. By employing inelastic light scattering we identify the inter-shell excitations in the one-electron regime and the distinct spin and charge modes in the interacting few-body configuration. In the case of two electrons a comparison with configuration-interaction calculations allows us to link the observed excitations with the breathing mode of the molecular dimer and to determine the singlet-triplet energy splitting.
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