Non-Abelian Holonomy of BCS and SDW Quasiparticles

Abstract

In this work we investigate properties of fermions in the SO(5) theory of high Tc supercondocutivity. We shos that the adiabatic time evolution of a SO(5) superspin vector leads to a non-Abelian SU(2) holomony of the SO(5) spinor states. Physically, this non-trivial holomony arises from the non-zero overlap between the SDW and BCS quasi-particle states. While the usual Berry's phase of a SO(3) spinor is described by a Dirac magnetic monopole at the degeneracy point, the non-Abelian holomony of a SO(5) spinor is described by a Yang monopole at the degeneracy point, and is deeply related to the existence of the second Hopf map from S7 to S4. We concluded this work by extending the bosonic SO(5) nonlinear [][][][ni] model to include the fermionic states around the gap nodes as 4 component Dirac fermions coupled to SU(2) gauge fields in 2+1 dimensions.