We show, analytically, that vacancies in an half-filled honeycomb lattice induce the formation of quasi-localized electronic states. If particle-hole symmetry is broken, these states become resonances close to the Fermi level. We also calculate numerically the electronic density of states for a finite density of vacancies, and discuss the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductor.
*Acknowledgements: C. Mudry for discussions, the Quantum Condensed Matter Visitor's Program at Boston University; FCT, Portugal, grant SFRH/BD/4655/2001; NSF grant DMR-0343790; FCT and EU through POCTI (QCAIII).
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Authors
J.M.B. Lopes dos Santos
CFP and Departamento de F\'{i}sica, Faculdade de Ci\^{e}ncias Universidade do Porto
CFP and Departamento de F{\'\i}sica, Faculdade de Ci{\^e}ncias Universidade do Porto, 4169-007 Porto, Portugal
Vitor M. Pereira
CFP and Departamento de F{\'\i}sica, Faculdade de Ci\^encias , Universidade de Porto
Francisco Guinea
Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco E28049 Madrid, Spain
Inst de Ciencia de Materiales de Madrid (CSIC) Cantoblanco 28049 MADRID
Instituto de Ciencia de Materiales de Madrid, Spain
Nuno M.R. Peres
Center of Physics and Departamento de F{\'\i}sica, Universidade do Minho, P-4710-057, Braga, Portugal
Universidade do Minho. Portugal
Antonio H. Casto Neto
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA
Boston University
Department of Physics, Boston University
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
