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A remarkable property of intrinsic graphene is that upon doping, electronsand holes travel through the monolayer thick material with constant velocitywhich does not depend on energy up to about $0.3$ eV (Dirac fermions), asthough the electrons and holes are massless particles and antiparticles whichmove at the Fermi velocity $v_F$. Consequently, there is Klein tunneling at a$p-n$ junction, in which there is no backscattering at normal incidence ofmassless Dirac fermions. However, this process yielding perfect transmission atnormal incidence is expected to be affected when the group velocity of thecharge carriers is energy dependent and there is non-zero effective mass forthe target particle. We investigate how away from normal incidence the combinedeffect of incident electron energy $\epsilon$ and band gap parameter $\Delta$can determine whether a $p-n$ junction would allow focusing of an electron beamby behaving like a Veselago lens with negative refractive index. We demonstratethat there is a specific region in $\epsilon-\Delta$ space where the index ofrefraction is negative, i.e., where monolayer graphene behaves as ametamaterial. Outside this region, the refractive index may be positive orthere may be no refraction at all. We compute the ballistic conductance acrossa $p-n$ junction as a function of $\Delta$ and $\epsilon$ and compare ourresults with those for a single electrostatic potential barrier and multiplebarriers.

Effect of Energy Band Gap in Graphene on Negative Refraction through the Veselago Lens and Electron Conductance