U(1)XSU(2) CHERN-SIMONS GAUGE-THEORY OF UNDERDOPED CUPRATE SUPERCONDUCTORS

The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied t o the two-dimensional t-J model in the limit t much greater than J, to study the normal-state properties of underdoped cuprate superconducto rs. We prove the existence of an upper bound on the partition function for holons in a spinon background and we find the optimal spinon conf iguration saturating the upper bound on average-a coexisting flux phas e and s+id-like resonating-valence-bond state. After neglecting the fe edback of holon fluctuations on the U(1) field B and spinon fluctuatio ns on the SU(2) field V, the holon field is a fermion and the spinon f ield is a hard-core boson. Within this approximation we show that the B field produces a rr flux phase for the holons, converting them into Dirac-like fermions, while the V field, taking into account the feedba ck of holons produces a gap for the spinons vanishing in the zero-dopi ng limit. The nonlinear-a model with a mass term describes the crossov er from the 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-gen erated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi-liquid theory with a Fermi surface consist ing of four ''half-pockets'' centered at (+/-pi/2,+/-pi/2) and one rep roduces the results for the electron spectral function obtained in the mean-field approximation, in agreement with the photoemission data on underdoped cuprates: The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction b etween spinons and holons leading to a bound state with electron quant um numbers. The renormalization effects due to gauge fluctuations give rise to non-Fermi-liquid behavior for the composite electron, in cert ain temperature range showing the linear in T resistivity. This formal ism provides a new interpretation of the spin gap in the underdoped su perconductors (mainly due to the short-ranged AF order) and predicts t hat the minimal gap for the physical electron is proportional to the s quare root of the doping concentration. Therefore the gap does not van ish in any direction. All these predictions can be checked explicitly in experiment.