▎ 摘　　要

We investigate magnetic, charge, and transport properties of hexagonal graphene nanoflakes (GNFs) connected to two metallic leads by using the functional renormalization group method. The interplay between the on-site and long-range interactions leads to a competition of semimetal (SM), spin-density-wave (SDW), and charge-density-wave (CDW) phases. The ground-state phase diagrams are presented for the GNF systems with as well as uniformly screened long-range Coulomb potential proportional to 1/r. We demonstrate that the realistic screening of Coulomb interaction by sigma bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential. This enhancement gives rise to a wide region of stability of the SM phase for realistic interaction, such that freely suspended GNFs are far from both SM-SDW and SM-CDW phase-transition boundaries and correspond to the SM phase. Close relation between the linear conductance and the magnetic or charge states of the systems is discussed. A comparison of the results with those of other studies on GNF systems and infinite graphene sheets is presented.