Effective medium approach to electron waves: Graphene superlattices

Effective Medium Approach to Electron Waves: Graphene Superlattices

We develop an effectivemedium approach to characterize the propagation of matterwaves in periodic structures, such as graphene or semiconductor superlattices. It is proven that the time evolution of the states that are not more localized in space than the characteristic period of the structure can be described exactly through an effective Hamiltonian, and that the electronic band structure of t...

Effective magnetic fields in graphene superlattices.

We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We exploit a chiral symmetry in the Dirac Hamiltonian description with a superlattice potent...

Electron interactions and gap opening in graphene superlattices.

We develop a theory of interaction effects in graphene superlattices, where tunable superlattice periodicity can be used as a knob to control the gap at the Dirac point. Applied to graphene on hexa-boron-nitride (G/h-BN), our theory predicts substantial many-body enhancement of this gap. Tunable by the moiré superlattice periodicity, a few orders of magnitude enhancement is reachable under opti...

Twisting bilayer graphene superlattices.

Bilayer graphene is an intriguing material in that its electronic structure can be altered by changing the stacking order or the relative twist angle, yielding a new class of low-dimensional carbon system. Twisted bilayer graphene can be obtained by (i) thermal decomposition of SiC; (ii) chemical vapor deposition (CVD) on metal catalysts; (iii) folding graphene; or (iv) stacking graphene layers...

Chiral Waves in Graphene Medium and Optical Simulation with Metamaterial