Renormalization-group approach to the metal-insulator transitions in (DCNQI)_2M (DCNQI is N,N'-dicyanoquinonediimine and M=Ag, Cu)

Abstract

Metal-insulator transitions and different ground-state phases in quasi-one- dimensional materials, (R_1R_2-DCNQI)_2M (R_1=R_2=CH_3, I and M=Ag, Cu), are studied with a renormalization-group method. We use one-dimensional continuum models with backward scatterings, umklapp processes and couplings with 2k_F and 4k_F phonons (not static lattice distortion). We take a quarter- filled band for M=Ag and a sixth-filled band coupled with a third-filled band for M=Cu. Depending on electron-electron and electron-phonon coupling strengths, the ground-state phase becomes a Tomonaga-Luttinger liquid or a state with a gap(s). For M=Ag, there appear a spin-gap state with a dominant 2k_F charge-density-wave correlation, a Mott insulator with a dominant 4k_F charge-density-wave correlation, or a spin-Peierls state with different magnitudes of spin and charge gaps. Three-dimensionality is taken into account by cutting off the logarithmic singularity in either the particle-particle channel or the particle-hole channel. The difference between the ground-state phase of the R_1=R_2=CH_3 salt (spin-Peierls state) and that of the R_1=R_2=I salt (antiferromagnetic state) is qualitatively explained by a difference in the cutoff energy in the particle-particle channel. For M=Cu, there appear a Mott insulator with a charge density wave of period 3 and a Peierls insulator with a charge density wave of period 6. The conditions for the experimentally observed, Mott insulator phase are strong correlation in the sixth-filled band, moderate electron-phonon couplings, and finite electron-4k_F phonon coupling. Resistance is calculated as a function of temperature with a memory-function approximation in both cases above. It qualitatively reproduces the differences among the M=Ag and M=Cu cases as well as the R_1=R_2=CH_3 and R_1=R_2=I cases.