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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
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