$U(1)\times SU(2)$ gauge theory of underdoped cuprate superconductors

Abstract

The $U(1)\times SU(2)$ Chern-Simons gauge theory is applied to study the 2-D $t-J$ model describing the normal state of underdoped cuprate superconductors. The U(1) field produces a flux phase for holons converting them into Dirac-like fermions, while the SU(2) field, due to the coupling to holons gives rise to a gap for spinons. An effective low-energy action involving holons, spinons and a self-generated U(1) gauge field is derived. The Fermi surface and electron spectral function obtained are consistent with photoemission experiments. The theory predicts a minimal gap proportional to doping concentration. It also explains anomalous transport properties including linear $T$ dependence of the in-plane resistivity.