Nanostructures in the quantum Hall regime

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Aalto-yliopiston teknillinen korkeakoulu | Doctoral thesis (article-based)
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Verkkokirja (3150 KB, 38 s.)
Dissertations of Department of Applied Physics, 162
The quantum Hall effect observed in a two-dimensional electron gas exposed to a perpendicular magnetic field is one of the most important modern discoveries in condensed matter physics. Advances in technology have allowed both experimental and computer-based theoretical study of miniature-size counterparts of conventional quantum Hall devices. Due to their versatile tunable electronic and magnetic properties, these systems show great promise for future technological applications. This work investigates two-dimensional semiconductor quantum dots and extended quantum rings in the quantum Hall regime. Besides being interesting on purely theoretical grounds as experimentally reachable extreme quantum-mechanical interacting many-body systems, the systems considered have major applicational interest in the realm of quantum information processing. Our emphasis lies in the strongly correlated regime where the enhanced electron-electron interactions lead to a computationally hard problem. For the systems with a few electrons, we employ the in principle exact configuration interaction method, which allows accurate study of the effects of the confinement potential and the effective form of the electron-electron interaction. Larger systems are modeled by Monte Carlo and density functional based methods. Moreover, we develop a computational method based on the reduced density-matrix functional theory to study the physics at the strongly correlated fractional quantum Hall regime with large particle numbers. The main results are related to the interplay of electron correlation and magnetism as well as the effects of tuning the electron correlation through sample engineering. The results on magnetism may find applications in future spintronics devices and spin qubits. Meanwhile, the results on electron correlation are relevant for the attempts to utilize fractional quantum Hall states in topologically protected quantum computing.
Supervising professor
Nieminen, Risto, Prof.
Thesis advisor
Harju, Ari, Dr.
quantum Hall effect, quantum dot, quantum ring
Other note
  • [Publication 1]: Eero Tölö, Juha Suorsa, and Ari Harju. 2008. Two interacting electrons in a square quantum dot. Physica E, volume 40, number 5, pages 1038-1041. © 2007 Elsevier Science. By permission.
  • [Publication 2]: Y. Hancock, J. Suorsa, E. Tölö, and A. Harju. 2008. Fractional periodicity and magnetism of extended quantum rings. Physical Review B, volume 77, number 15, 155103, 9 pages. © 2008 American Physical Society (APS). By permission.
  • [Publication 3]: H. Saarikoski, E. Tölö, A. Harju, and E. Räsänen. 2008. Pfaffian and fragmented states at ν = 5⁄2 in quantum Hall droplets. Physical Review B, volume 78, number 19, 195321, 8 pages. © 2008 American Physical Society (APS). By permission.
  • [Publication 4]: E. Tölö and A. Harju. 2009. Effects of thickness in quantum dots in strong magnetic fields. Physical Review B, volume 79, number 7, 075301, 5 pages. © 2009 American Physical Society (APS). By permission.
  • [Publication 5]: E. Tölö and A. Harju. 2009. Quantum Hall droplet laterally coupled to a quantum ring. Physical Review B, volume 80, number 4, 045303, 7 pages. © 2009 American Physical Society (APS). By permission.
  • [Publication 6]: G. Bårdsen, E. Tölö, and A. Harju. 2009. Magnetism in tunable quantum rings. Physical Review B, volume 80, number 20, 205308, 5 pages. © 2009 American Physical Society (APS). By permission.
  • [Publication 7]: E. Tölö and A. Harju. 2010. Optimal confinement potential in quantum Hall droplets. Physica E, volume 42, number 4, pages 1050-1053. © 2009 Elsevier Science. By permission.
  • [Publication 8]: E. Tölö and A. Harju. 2010. Reduced density-matrix functional theory in quantum Hall systems. Physical Review B, volume 81, number 7, 075321, 12 pages. © 2010 American Physical Society (APS). By permission.