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Supersymmetry Method for Network Models of Quantum Hall Transitions and Hybrid Structures

Davis, Alexander Michael
http://rave.ohiolink.edu/etdc/view?acc_num=osu1566157715556164

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Physics.
Despite nearly forty years of investigation, the theoretical understanding of the nature of the quantum Hall transition remains largely inadequate in its explanatory power of the critical and universal behavior of the transition. The nonperturbative nature of the transition, along with the difficultly of theoretically handling disorder makes it one of the most challenging problems in condensed matter physics. Two of the best tools for investigating the quantum Hall transition are network models, such as the Chalker-Coddington (CC) network model, and supersymmetry (SUSY) to handle the disorder averages. Despite assuming a particular model for the disorder, necessary for a quantum Hall state to be achieved, namely weak smoothly varying disorder, the effective field theory obtained in the limit of large conductivity is the same nonlinear $\sigma$ model (NL$\sigma$M) that Pruisken derived for short ranged, Gaussian white noise disorder, implying some universality with respect to the model of disorder. Furthermore, the CC network model is easily modified to accommodate other types of quantum Hall effects, the spin and thermal Hall effects. In this thesis we will use the CC network and supersymmetry to derive the NL$\sigma$M for a variety of quantum Hall transitions. Chapter two takes a bit of a pedagogical approach to the standard CC model and subsequent derivation of the NL$\sigma$M using supersymmetry. Chapter three justifies the necessary changes to the CC model so that it can model the spin and thermal Hall effects. We then use supersymmetry to derive the NL$\sigma$M for the spin and thermal Hall effects. Finally, in chapter four we will look at a hybrid network that describes a standard Hall insulator in contact with a spin Hall insulator on the other side. Again, we will use SUSY to derive the NL$\sigma$M that describes the quantum Hall transition
Ilya Gruzberg (Advisor)
Yuanming Lu (Committee Member)
Chris Hirata (Committee Member)
Lemberger Tom (Committee Member)
101 p.
Physics
Quantum Hall Transition; Spin Quantum Hall; Thermal Quantum Hall; Chalker-Coddington Model; Supersymmetry

Recommended Citations

Citations

  • Davis, A. M. (2019). Supersymmetry Method for Network Models of Quantum Hall Transitions and Hybrid Structures [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1566157715556164

    APA Style (7th edition)

  • Davis, Alexander. Supersymmetry Method for Network Models of Quantum Hall Transitions and Hybrid Structures. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1566157715556164.

    MLA Style (8th edition)

  • Davis, Alexander. "Supersymmetry Method for Network Models of Quantum Hall Transitions and Hybrid Structures." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1566157715556164

    Chicago Manual of Style (17th edition)

osu1566157715556164
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© 2019, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.