Purdue University Graduate School
TQIM_Guangjie_Li_Purdue_Dissertation.pdf (3.14 MB)

Topological Quantum Impurity Models

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posted on 2024-04-22, 21:27 authored by Guangjie LiGuangjie Li

A bath of free electrons interacting with a local quantum impurity leads to various exotic non-Fermi liquid behaviors, such as the non-integer effective ground state degeneracy of the impurity and the correction to the zero temperature conductance, which is temperature to the power of a fractional number. The former indicates emergent anyons, which are the key ingredients for achieving topological protected quantum computations. The latter can be used for experimentally probing non-Fermi liquid physics. It was recently proposed that a Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO(M). Inspired by the multichannel generalization of the original Kondo model, we introduce a physically motivated N-channel generalization of this topological Kondo model whose impurity spin stems from the non-local topological ground state degeneracy of the island. This multichannel topological Kondo model supports Z3 parafermion and Fibonacci anyon (not supported by one-channel topological Kondo model) but may be limited to experiments because it is unstable to channel anisotropy. Therefore, we propose a Majorana-free meso- scopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and Z3 parafermions) even in the absence of perfect channel symmetry. Besides, I comment on the future work such as the strong tunneling case that is beyond the topological Kondo regime and the two-impurity Kondo physics.


Degree Type

  • Doctor of Philosophy


  • Physics and Astronomy

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Dr. Jukka Vayrynen

Additional Committee Member 2

Dr. Martin Kruczenski

Additional Committee Member 3

Dr. Xingshan Cui

Additional Committee Member 4

Dr. Yong P. Chen