Parafermions and domain walls in 2D electron and hole systems

Abstract

Search for Non-Abelions - particles whose exchange transforms the quantum state of a system noncommutatively- is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. Examples of non-Abelions are Majorana and parafermion zero modes. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. To demonstrate new examples of such experimentally feasible systems, we will describe the domain walls formed in spin transitions in the integer and fractional quantum Hall effects between spin- polarized and spin-unpolarized phases. We show that superconducting proximity coupling to domain walls between two topologically distinct fractional quantum Hall liquids leads to emergence of parafermions. While Majorana zero modes form a double degenerate state, parafermions emerge as a six-fold degenerate state. Emergence of parafermions in electron and hole systems is discussed.