Electron-electron interaction and instabilities in one-dimensional metals

Abstract

The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interaction V(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x≲ (2k_F )^-1) part of the interaction is greatly reduced or is made attractive, V(x) is non-monotonic, V_q (q≅ 2k_F ) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [V _q (0<q<k_F )+Vq (q≃2k_F )] <0.