Theoretical Study On Artificial Electronic Metamaterials In Graphene

Graphene is a unique quantum material in which low-energy excited electrons near the Dirac point behave as massless relativistic Dirac fermions with linear energy dispersion.The analogies between optics and low-energy electronics in graphene inspires us to explore the possibilities of controling graphene ballistic electrons like photons.A series of unique phenomena in optics can also occur in graphene massless charge carriers.Typical discoveries include self-collimation,whispering gallery mode and negative refraction.However,controlling electron wave propagation in graphene at this stage is not as easy as controlling light waves.One of the reasons is the lack of relevant control mechanism that can cause the sudden change of the transmission direction for the electron wave.The abrupt change mechanism of the transmission direction is the theoretical basis for realizing the curved electron waveguide suitable for high-density integration.At present,Several waveguide schemes that change the transmission direction of the electron wave at a large angle in the existing stage need a large turning radius,and the device size cannot be further reduced.Graphene is a zero band gap semiconductor material.The existing methods of opening the full band gap can not ensure that the electrons still have high mobility.Without opening the full band gap,Klein tunneling effect will cause the nearly normal incident electrons in graphene completely pass through the barrier,so that the near 180° change of the electron transmission direction cannot be achieved.To solve these problems,we have mainly carried out the following theoretical work:Firstly,we have developed the electron scattering theory of multiple quantum dot(QD)system in graphene,that is,the multiple scattering theory for graphene electron waves.Quantum dot is the circular npn(or pnp)junction with adjustable gate-defined bias.We have further developed the band calculation method for the periodic quantum dot arrays.Based on the multiple scattering theory and Floquet’s theorem,we derive the expression of the transmissivity / reflectivity for each order diffracted wave after the plane electron wave is scattered by a single-layer quantum dot array.And we regard the 2D quantum dot array as the stack of single-layer quantum dot array,and further develop the layer KKR(Korringa-Kohn-Rostoker)method to calculate the transmissivity / reflectivity of 2D quantum dot array.Secondly,based on the transmissivity and reflectivity of the single-layer quantum dot array we derived,we have designed the single-layer periodic quantum dot array into a metagrating similar to optics,so as to steer electron beams toward the(0)-1st order(total reflection)transmission direction with unity efficiency.Equivalently,electron waves are deflected by an arbitrary angle ranging from 90° to 180° by controlling the bias.This effect is independent of the band gap,so the advantage of high mobility of graphene will not be destroyed.The sudden change of propagation direction occurs at a distance smaller than the electron wavelength,so a large transition distance is not required.Moreover,this sudden change in direction does not need to work in low temperature environment,which provides the possibility of developing compact integrated circuits in graphene electronic technology.The concept of Dirac fermion metagrating opens up a new paradigm in electron beam steering and could be applied to achieve two-dimensional electronic holography.Thirdly,we periodically arrange quantum dots(QDs)into a square array.Based on the equivalent medium theory(EMT),we find that quantum dot array behaves as the metamaterial with equivalent zero refractive index.We further demonstrate various typical applications of the electron metamaterials(quantum dot array)with effective zero refractive index on graphene.