Implications of infrared instability in a two-dimensional electron gas

We consider the tight-binding energy band in sq lattices and determine that in the half-filled case there exists an infrared instability in addition to the 2$k_F$ (nesting)-type instability. In view of the pseudo-two-dimensional band structure of ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Ba}}_{\mathrm{x}}$ ${\mathrm{CuO}}_4$ recently proposed by Jorgensen et al. and by Mattheiss, our conclusions should be relevant to this material at least, one of which demonstrates the remarkable phenomenon of high-$T_c$ superconductivity. To further analyze it, we devise a two-dimensional bosonization scheme. Three-dimensional bosonization is also briefly discussed.