LOW-TEMPERATURE PROPERTIES OF THE METALLIC PHASE OF THE T-J MODEL IN 2 DIMENSIONS

The low-temperature properties of the fluxless metallic phase of the t-J model in two dimensions are calculated using a large-N slave-boson formulation, with explicit fermion-boson decoupling of the correlated electron in the large-N limit. We find that although this metal possesses both a large Fermi-surface and Fermi-Thomas screening corresponding to a system of free electrons near half filling, both the square of the plasma frequency and the Hall conductance of this phase scale with the doping concentration. This qualitatively accounts for the observed doping dependence of the Hall constant in high-temperature superconductors. A slow zero-sound mode arising out of the bare-electron-slave-boson quasiparticle liquid is also found in the low-temperature regime of this phase. We predict that the density-density correlation function should have a pole at this resonance, and we suggest that this pole has already been observed in recent electron-energy-loss experiments on high-T(c) materials. In addition, resonant coupling of this zero-sound mode to acoustic longitudinal phonons via the electron-phonon interaction results in an electronically driven lattice instability at a critical doping concentration. We suggest that such a mechanism is responsible for the tetragonal-to-orthorhombic crystallographic transitions generally observed in high-T(c) materials.