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arXiv:cond-mat/0211308 · Physical review. B, Condensed matter

Strongly correlated quantum dots in weak confinement potentials and magnetic fields

Min-Chul Cha, Shuo Yang

Published May 15, 2003• 9 citations
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Abstract

We explore a strongly correlated quantum dot in the presence of a weak confinement potential and a weak magnetic field. Our exact diagonalization studies show that the ground state property of such a quantum dot is rather sensitive to the magnetic field and the strength of the confinement potential. We have determined rich phase diagrams of these quantum dots. Some experimental consequences of the obtained phase diagrams are discussed.

DOI
10.1103/physrevb.67.205312

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The interplay of confinement and Coulomb interactions in quantum dots can lead to strongly correlated phases differing qualitatively from the Fermi liquid behavior. We explore how the presence of magnetic impurities in quantum dots can provide additional opportunities to study correlation effects and the resulting ordering in carrier and impurity spins. By employing exact diagonalization we reveal that seemingly simple two-carrier quantum dots lead to a rich phase diagram. We propose experiments to verify our predictions; in particular, we discuss interband optical transitions as a function of temperature and magnetic field.
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This thesis investigates the use of wave-function methods for the study of quantum-dot systems. It investigates single dots, using quantum Monte Carlo techniques in a wide range of magnetic field values, and a double-dot system, using the exact-diagonalization method.\n\nThe thesis proposes simple yet accurate many-particle wave functions for various angular-momentum and spin states, for both weak and strong magnetic fields. Using these trial wave functions, it evaluates various properties of dots and studies Wigner crystallization and spin polarization for the weak-field limit. For strong magnetic fields, the thesis investigates ground states of different spin polarizations as a function of the magnetic field and tests the commonly used lowest-Landau-level approximation. The results are compared to calculations from the density-functional theory.\n\nFinally, the thesis presents a method that combines the accuracy of the exact-diagonalization method and the scalability of Monte Carlo methods. The Monte Carlo-based diagonalization is a promising tool for use in situations that cannot be handled with a simple trial wave function, and have too many particles for an exact-diagonalization treatment. For quantum dots, methods for efficiently evaluating the high-magnetic-field basis functions and their gradients are demonstrated.