We study the stability of the spin gap phase in the U (1) slave-boson theory of the t - J model in connection with the underdoped cuprates. We approach the spin gap phase from the superconducting state and consider the quantum phase transition of the slave bosons at zero temperature by introducing vortices in the boson superfluid. At finite temperatures, the properties of the bosons are different from those in the strange-metal phase and lead to modified gauge field fluctuations. As a result, the spin gap phase can be stabilized in the quantum-critical (QC) and quantum-disordered (QD) regime of the boson system. We also show that the regime of QD bosons with the paired fermions can be regarded as a strong-coupling version of the recently proposed nodal liquid theory.
We have discovered a new example of quantum spin liquid which is a superconducting (SC) phase in 2D electron system close to electronic topological transition. As a quantum spin liquid in low dimensional localized spin systems it is characterized by a resonance spin mode and a well separated two-particle continuum. Application of the theory to the high-T_c cuprates allows to shed light on many observed in the underdoped regime features such as the so called 40 meV resonance peak, incommensurability at lower ω, spin gap etc.
We analyze the phase diagram of single and bi-layer cuprates using the gauge-field description of the t-J model. For
T>TBE the in-plane fermion-pairing order parameter
Δ∥ is eliminated by gauge field fluctuations, leading us to predict the absence of a spin-gap phase in single-layer cuprates. For bi-layer cuprates the inter-layer order parameter
Δ⊥ is enhanced by spin correlations, and is less affected by gauge fluctuations. We believe that the spin gap in bi-layer materials is due to inter-layer fermion pairing, and that for these underdoped samples the superconducting gap may be nodeless.