Coulomb interaction in the layered electron gas

We discuss interplane attraction between electrons in the layered interacting two-dimensional electron gas. For small electron density, N 2 < N 2c (N 2c is the critical density), anomalous many-body effects lead to an instability of the superlattice. It is found that in the regime of the instability the screened interplane electron-electron interaction potential is attractive. We suggest that for N 2 < N 2c the electron system breaks up into a confined Fermi liquid (electrons) and a gas of paired electrons (bosons). We calculate the density of bosons N 2B as a function of the electron density and find N 2B ∝ N 2/N 2c [1 - (N 2/N 2c) ½]. The specific heat and the importance of correlation effects are discussed.