Graphene zigzag ribbons: hidden multiferroic order and (spin polarized) transport SPAIN J. Fernández-Rossier, F. Muñoz, J. J. Palacios Electronic structure graphene zigzag ribbons= Magnetic edges, S=0, P=0, spin resolved ferroelectricity H = +

Bands of graphene zigzag ribbons Magnetic edges Non interacting bandsDFT LSDA bands 2 gaps Y. Son, Phys. Rev. Lett. 97, (06) Flat edge bands Joaquín Fernández-Rossier H

DFT results and questions Origin of the 2 gaps? What kind of electronic order? Relation with Spin resolved dipole? H Y. Son, Phys. Rev. Lett. 97, (06) Joaquín Fernández-Rossier H

Methodology: Mean field Hubbard Mean Field Hubbard model M. Fujita et al.,J. Phys. Soc. Jpn., 65, 1920 (1996) K. Wakabayashi, M. Sigrist, M. Fujita, J. Phys. Soc. Jpn. 67, 2089 (1998) JFR, J. J. PalaciosPhys. Rev. Lett. 99, (2007) JFR, Phys. Rev. B. 77, (08) M. Wimmer, I. Adagideli, S. Berber, D. Tomanek, K.Richter, arXiv: Joaquín Fernández-Rossier H

Methodology: Mean field Hubbard vs DFT Mean Field Hubbard model MF Hubbard JFR, PRB. 77, (08) Joaquín Fernández-Rossier H

Crucial remark about mean field Hubbard in ZZ JFR, Phys. Rev. B 77, (2008) Joaquín Fernández-Rossier H

Crucial remark about mean field Hubbard in ZZ JFR, Phys. Rev. B 77, (2008) Joaquín Fernández-Rossier H

Crucial remark about mean field Hubbard in ZZ JFR, Phys. Rev. B 77, (2008) Joaquín Fernández-Rossier H

Crucial remark about mean field Hubbard in ZZ JFR, Phys. Rev. B 77, (2008) Joaquín Fernández-Rossier H

Spontaneous generation of eh pairs Joaquín Fernández-Rossier H Non interacting ground state Interacting ground state

Interband coherence, phase Locking, Spin dipole Excitonic Insulator Joaquín Fernández-Rossier H Spin dipole Phase Locking

Origin of the 2 gaps JFR, Phys. Rev. B 77, (2008) Joaquín Fernández-Rossier H Pairing gap (inter-band exchange) Diagonal exchange BCS dispersion

Origin of the 2 gaps Joaquín Fernández-Rossier H JFR,Phys. Rev. B 77, (2008) Diagonal exchange Magnetism in edges Pairing gap (inter-band exchange)

Spin state vs conduction properties FM: conducting AF: insulator No dipole No pairing gap Joaquín Fernández-Rossier H

Graphene Ribbon Spin Valve (CIP) Armchair conducting Short Zigzag Joaquín Fernández-Rossier H

Graphene Ribbon Spin valve (CIP) Joaquín Fernández-Rossier H

Summary J. Fernandez-Rossier, Phys. Rev. B 77, (2008) JFR, F. Muñoz-Rojas, J. J. Palacios, in preparation. DFT= MF Hubbard MF Hubbard=BCS Excitonic Insulator BCS= Spin Hidden Ferroelectricity BCS: intraband vs interband gapsAll Graphene SPIN VALVE