Plasmon generation through electron tunneling in twisted double-layer graphene and metal-insulator-graphene systems

Abstract

The generation of highly-confined plasmons through far-field optical illumination appears to be impractical for technological applications due to their large energy-momentum mismatch with external light. Electrical generation of plasmons offers a possible solution to this problem, although its performance depends on a careful choice of material and geometrical parameters. Here we theoretically investigate graphene-based structures and show in particular the very different performance between (i) two layers of graphene separated by a dielectric and (ii) metal$|$insulator$|$graphene sandwiches as generators of propagating plasmons assisted by inelastic electron tunneling. For double-layer graphene, we study the dependence on the relative tilt angle between the two sheets and show that the plasmon generation efficiency for $4^\circ$ twist angle drops to $\sim20$\% of its maximum for perfect stacking. For metal$|$insulator$|$graphene sandwiches, the inelastic tunneling efficiency drops by several orders of magnitude relative to double-layer graphene, regardless of doping level, metal$|$graphene separation, choice of metal, and direction of tunneling (metal to or from graphene), a result that we attribute to the small fraction of the surface-projected metal Brillouin zone covered by the graphene Dirac cone. Our results reveal a reasonable tolerance to graphene lattice misalignment and a poor performance of structures involving metals, thus supporting the use of double-layer graphene as an optimum choice for electrical plasmon generation in tunneling devices.