2. Chiral P-wave superconductor an example of non-Abelian topological order Ke 2 lack+=(4ic-Kck+ Akde x) △p(k)=△0a( (sin kr+ i sin k) g Strong superconductivity( v=5/2 FQH state): Chemical potential u<o Non-Abelian Topologial order g Weak superconductivity Chemical potential u>0 Z2 topological order
2. Chiral P-wave superconductor an example of non-Abelian topological order ❖ Strong superconductivity( v=5/2 FQH state)： Chemical potential µ<0 Non-Abelian Topologial order ❖ Weak superconductivity ： Chemical potential µ>0 ❖ Z2 topological order
Skyrmion in momentum space 分 glp p Figurc 8: Skyrmion in p-spacc with momcntum spacc topological charge N3=-1. It dcscribcs topologically non-trivial vacua in 2+I systcms with a fully non-singular Grccn function
Skyrmion in momentum space
2 Topological quantum compatation is proposed by Kitaev Application of nonAbelian topological order Quantum Computer De ecoherence Environment If quantum information is cleverly encoded it can be protected from decoherence and other potential sources of error. Intricate quantum ERRORI systems can be accurately controlled
Topological quantum compatation is proposed by Kitaev. Application of nonAbelian topological order
3. Z2 topological orders and spin liquid Z2 charge 人人 Z2 vortex 丌fux Mutual semion statistics
flux Mutual semion statistics Z2 vortex Z2 charge 3. Z2 topological orders and spin liquid
Topological degeneracy for Z2 topological orders: Red line denotes“ half flux tube
Topological degeneracy for Z2 topological orders : Red line denotes “half flux tube