Purdue University Graduate School
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Parafermion Excitations in Hole Systems in the ν=1/3 Filled Fractional Quantum Hall State

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posted on 2019-08-12, 18:46 authored by Ian Asher ArnoldIan Asher Arnold
Non-Abelian excitations, including Majorana fermions, parafermions, and Fibonacci anyons, provide potential new settings for realizations of topological quantum computation operations. Topological quantum systems have the advantage of being protected against some types of entanglement with the surrounding environment, but their elusive nature has inspired many to pursue rare systems in which they may be physically realized. In this work we present a new platform for production of parafermions in the ν=1/3 fractional quantum hall effect regime in a two-dimensional hole gas in a Gallium Arsenide quantum well, where spin transitions in the rich Γ8 Luttinger ground state can be manipulated by gate-controlled electric fields. When numerical and analytical calculations of many-particle interactions combine with a proximity-induced superconducting pairing potential in this system, the spin transition we observe gives rise to a superconducting gap with an onset of six-fold degenerate ground state which disappears at critical values of the gap parameter Δk, the energetic signature associated with parafermion production.


Degree Type

  • Doctor of Philosophy


  • Physics and Astronomy

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Yuli Lyanda-Geller

Additional Committee Member 2

Andrew Hirsch

Additional Committee Member 3

Ephraim Fischbach

Additional Committee Member 4

Leonid Rokhinson