The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Wave Function Methods for Quantum Dots in Magnetic Field

Sami Siljamäki

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium E at Helsinki University of Technology (Espoo, Finland) on the 26th of September, 2003, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-6704-7)   [718 KB]
Dissertation is also available in print (ISBN 951-22-6698-9)


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.

The 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.

Finally, 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.

This thesis consists of an overview and of the following 6 publications:

  1. Harju A., Siljamäki S. and Nieminen R. M., 1999. Wave function for quantum-dot ground states beyond the maximum-density droplet. Physical Review B 60, pages 1807-1810. © 1999 American Physical Society. By permission.
  2. Siljamäki S., Sverdlov V. A., Harju A., Hyvönen P. and Nieminen R. M., 2000. Stability of the maximum-density droplet state in quantum dots: a quantum Monte Carlo study. Physica B 284-288, pages 1776-1777. © 2000 Elsevier Science. By permission.
  3. Harju A., Siljamäki S. and Nieminen R. M., 2002. Two-electron quantum dot molecule: composite particles and the spin phase diagram. Physical Review Letters 88, pages 226804 : 1-4. © 2002 American Physical Society. By permission.
  4. Harju A., Siljamäki S. and Nieminen R. M., 2002. Wigner molecules in quantum dots: a quantum Monte Carlo study. Physical Review B 65, pages 075309 : 1-6. © 2002 American Physical Society. By permission.
  5. Saarikoski H., Räsänen E., Siljamäki S., Harju A., Puska M. J. and Nieminen R. M., 2002. Electronic properties of model quantum-dot structures in zero and finite magnetic fields. The European Physical Journal B 26, pages 241-252.
  6. Siljamäki S., Harju A., Nieminen R. M., Sverdlov V. A. and Hyvönen P., 2002. Various spin-polarization states beyond the maximum-density droplet: a quantum Monte Carlo study. Physical Review B 65, pages 121306 (R) : 1-4. © 2002 American Physical Society. By permission.

Keywords: quantum dot, wave function, magnetic field, quantum Monte Carlo, Monte Carlo diagonalization

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© 2003 Helsinki University of Technology

Last update 2011-05-26