ANNUAL REPORT 2011 - Instituto de Estructura de la Materia

terms and that b) stellar pulsations of objects hovering right outside but extremely close to their gravitational radiuscan result in a mechanism for Hawking-like emission.ELECTRONIC PROPERTIES OF GRAPHENEDuring 2011, we have investigated two different aspects of the electronicproperties of the carbon material, whichhave to do with the electronic confinement in graphene bilayers and the dynamical generation of a gap by manybodyeffects in monolayer graphene.We have studied the possibility of localizing electrons in graphene by means of synthetic gauge fields, created bythe mismatch in the lattice registry of strained or twisted bilayers. It is known that the most favorable regularstructure of graphene bilayers corresponds to the so-called Bernal or AB stacking, in which the carbon atoms in asublattice of one of the layers fall onto the atoms in the complementary sublattice of the other layer. When thelattices are distorted, either by strain, shear or twisting, the perfect registry is lost, and one observes the appearanceof typical Moiré patterns where regions of AB stacking alternate with others realizing AA stacking, in which thecarbon atoms in one of the layers fall onto homologous atoms in the other layer. We have shown that the alternationbetween the two types of stacking produces the same effect as having a non-Abelian SU(2) gauge potential, with theability of confining electrons in those regions of the bilayer where the periodic effective field strength becomesmaximum.By applying uniaxial shear to one of the layers, for instance, we can create a quasi-one-dimensional Moiré patternwith a perfect sequence of AA-AB-BA stacking along one of the directions of the bilayer. In this case, the electronicdensity can be confined into 1D channels corresponding to the regions with AA stacking, or AB-BA stacking,depending on the longitudinal momentum of the electronic states. The band structure becomes strongly reminiscentof that found in thick carbon nanotubes in a real perpendicular magnetic field, where there is also a periodicmodulation of the flux around the section of the tube. The lowest-energy subband becomes extremely flat for largeperiod of the stack modulation, corresponding to states localized in the regions of AB and BA stacking. Beyond acertain value of the longitudinal momentum, the electronic states start to disperse along branches linear in energy.This signals the development of propagating modes along the one-dimensional channels with AA stacking, in closeanalogy with the behavior of the edge states in the quantum Hall effect of a 2D electron liquid in areal magneticfield.We have also applied our gauge field approach to understand the electronic properties of twisted bilayers, where therelative rotation of one layer with respect to the other induces a superlattice with alternating regions of AA, AB andBA stacking. We have seen that the electron system develops an extremely flat lowest-energy subband for certainmagic values of the rotation angle, showing that this feature is a direct consequence of the presence of an effectivenon-Abelian SU(2) gauge field across the bilayer. The lack of dispersion is actually the signature of localized lowenergystates that are bound in this case around the regions of AA stacking, giving rise to a triangular array ofquantum dots. We have found that this pattern of confinement is consistent with the periodicity of the maxima in theeffective field strength, and that the first instance at which the lowest subband becomesflat corresponds to the pointwhere the unit cell of the superlatticeis thread precisely by the quantum of gauge flux.The present approach supports in general the possibility of using the graphene bilayers to realize non-AbelianAharonov-Bohm interferometry, by which the amplitude of electrons injected into one of the layers may oscillateand even become completely transferred to the other layer along their propagation. Furthermore, our study may alsoopen a new route to address the problemof localization of electronic states, which are not effectively constrained byscalar potential barriers in graphene, but may be otherwise confined and manipulated in electronic devices made ofgraphene bilayers.On the other hand, we have continued the investigation of the dynamical generation of a gap in graphene, analyzingin particular the impact that theelectron self-energy corrections may have on the chiral symmetry breaking intheinteracting theory of Dirac fermions. Our starting point has been the ladder approximation for the electron-holevertex appearing in the response function for dynamical gap generation, which we have improved byincludingsystematically the self-energy corrections to electron and hole states in theladder series.In this framework, we have been able to account for the effect of the Fermivelocity renormalization on the criticalcoupling for dynamical gap generation.In this respect, the growth of the Fermi velocity at low energies has beenalready observed in experiments carried out by the group of A. K. Geim with graphene at very low doping levels.Our results have shown actually that the effect of renormalization of the Fermi velocity induces a significantreductionin the strength of the dynamical symmetry breaking. We have found that the dynamical gap generationmay take place above a critical value in the graphene fine structure constant α c ≈ 4.9, in the case of static RPA50