Confinement by umklapp scattering in two coupled chains

The effect of umklapp scattering on two coupled chains with both half-filled and doped band has been examined by renormalization group method. It has been found that electrons are confined to a single chain when the doping rate becomes small and when the correlation gap induced by umklapp scattering becomes larger than the interchain hopping energy. A crossover from an insulating state into a metallic state is discussed for several Bechgaard salts at temperatures above spin density wave state.