U(1)xSU(2) Chern--Simons gauge theory of underdoped cuprate superconductors

Abstract

The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied to 2-D t-J model in the limit t >> J, to study the normal state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average--a coexisting flux phase and s+id-like RVB state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field V, the holon field is a fermion and the spinon field is a hard--core boson. We show that the B field produces a πflux phase for holons, converting them into Dirac--like fermions, while the V field, taking into account the feedback of holons produces a gap for spinons vanishing in zero doping limit. The nonlinear sigma-model with a mass term describes the crossover from short-ranged antiferromagnetic (AF) state in doped samples to long range AF order in reference compounds. Moreover, we derive a low--energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. The gauge fluctuations are not confining due to coupling to holons, but yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalisation effects due to gauge fluctuations give rise to non--Fermi liquid behaviour for the composite electron.This formalism provides a new interpretation of the spin gap in underdoped superconductors (due to short-ranged AF order) and predicts the minimal gap for the physical electron is proportional to the square root of the doping concentration.

31 pages, REVTEX, to be published in Phys. Rev. B