School Colloquia Series: The hunt for Non-Abelian Statistics
Friday 10th May 2019
G59 Old Main Building
Speaker: Professor Yuli Lyanda-Geller, Purdue University USA
Upon exchange, a wavefunction of bosons does not change, and fermionic wavefunction changes a sign. In the quantum Hall systems quantizing the Hall resistivity, the wavefunction upon exchange of (quasi)particles can acquire a nontrivial quantal phase. For a linear combination of degenerate many-body states, exchanges may transform the system into different linear combinations, resulting in non-Abelian statistics if the result of two exchanges depends on their order. I will review non-Abelions in Condensed Matter systems. I will describe the domain walls formed between spin-polarized and spin-unpolarized phases of the quantum Hall effect. When proximity-coupled to a superconductor, domain walls host non-Abelions called Majorana and parafermion zero modes.