Instabilities of interacting electrons on the triangular lattice

Abstract

Motivated by the recent finding of superconductivity in layered ${\mathrm{CoO}}_2$ compounds, we investigate superconducting and magnetic instabilities of interacting electrons on the two-dimensional triangular lattice. Using a one-loop renormalization-group scheme for weak- to moderate-coupling strengths, we find that for purely local interactions $U>\mathrm{}0\mathrm{}$ and small Fermi surfaces the renormalization-group flow remains bounded down to very low scales and no superconducting or other instabilities can be detected. Antiferromagnetic exchange interactions J generate a wide density region with a $d_{x^2-y^2}{+id}_{\mathrm{xy}}-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}$ superconducting instability similar to recent proposals for the strongly correlated $t-J$ model. For larger Fermi-surface volumes the interactions flow to strong coupling also for purely local interactions $U>\mathrm{}0.\mathrm{}$ We find a singlet-pairing instability in the vicinity of strong magnetic ordering tendencies at three wave vectors for the Van Hove filling.