Reentrant metallicity in the Hubbard model: the case of honeycomb nanoribbons

Abstract

Based on the Cluster Perturbation solution of the Hubbard hamiltonian for a 2-D honeycomb lattice we present quasiparticle band structures of nanoribbons at half filling as a function of the on-site electron-electron repulsion. We show that at moderate values of e-e interaction ribbons with armachair shaped edges exhibit an unexpected semimetallic behavior, recovering the original insulating character only at larger values of U .The repulsive interaction among electrons is responsible of the failure of single particle picture and of the opening/widening of energy gaps in solids. The Hubbard model is the paradigm to describe this phenomenon: sufficiently large values of the on-site e-e repulsion inhibit the inter-site hopping favoring in this way an insulating behaviour. The 1-atom thick 2D honeycomb lattice (graphene) does not contradict this picture: many body effects due to on-site Coulomb repulsion have been shown to lead, for sufficiently strong interactions, to semimetalto-insulator transition 1,2 as well as to other deviations from Fermi-liquid behavior such as unconventional quasiparticle lifetimes 3 , long range antiferromagnetic order 4 and spin liquid phase 5 .In this paper we show that for honeycomb nanoribbons the repulsive e-e interaction may be responsible of a metallic phase in ribbons that in the single particle picture are semiconducting. This appears to be another extraordinary property of the 2-D honeycomb lattice.It is well known that honeycomb nanoribbons manifest peculiar properties related to the topology of their edges 6 : according to single-particle theory ribbons with armchair shaped edges may exhibit a finite energy gap depending on their width 7-9 , while ribbons with zigzag edges are metallic and become insulating only after the inclusion of an antiferromagnetic order 10,11 . The modifications of the single particle band structure of zigzag graphene ribbons due to e-e interaction has been investigated within a mean field solution of the Hubbard model 12,13 , showing spin polarization of edge states and gap opening at the Fermi level. How the single particle band picture evolves to a quasi-particle one and how the electronic states of both armchair and zigzag honeycomb ribbons are modified by on-site Coulomb repulsion described as a true many body term is the question we address in this paper.We have adopted a many body approach based on the Cluster Perturbation Theory 14 (CPT). CPT belongs to the class of Quantum Cluster theories 15 that solve the problem of many interacting electrons in an extended lattice by a divide-and-conquer strategy, namely solving first the many body problem in a subsystem of finite size and then embedding it within the infinite medium.Quantum Cluster theories represent some of the most powerful tools for the numerical investigation of strongly correlated many-body systems. They include Dynamical Cluster Approach 16 , Cellular Dynamical Mean Field Theory 17 as well as CPT and have found an unified language within the variational scheme 18 based on the the Sel...