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Majorana-Anderson Impurity Models
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- Author / Creator
- Ganesh, Sankaranarayanan
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Majorana fermions emerge in topological superconductors as end zero modes in one dimension, and vortex-trapped zero modes or chiral edge modes in two dimensions. A question of much recent interest is the effect of electron-electron interactions on such Majorana fermions. We introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution at finite temperature for a wide range of parameters, including on-site interactions of arbitrary strength. A general model in this class is solved by mapping it via the $\mathbb{Z}_2$ slave-spin method to a non-interacting resonant level model for auxiliary Majorana fermions. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. To demonstrate our results, we study representative systems of a quantum dot coupled to (i) the end mode of a Kitaev chain, and (ii) the chiral edge modes of a Read-Green superconductor. In both cases, we obtain exact expressions for the dot spectral functions and host local density of states at any temperature. In case (i), we also study how the interaction strength and localisation length of the end mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations.
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- Graduation date
- Fall 2019
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.