Strain Modulated Superlattices in Graphene

Abstract

Strain engineering of graphene takes advantage of one of the most dramatic responses of Dirac electrons enabling their manipulation via strain-induced pseudo-magnetic fields. Numerous theoretically proposed devices, such as resonant cavities and valley filters, as well as novel phenomena, such as snake states, could potentially be enabled via this effect. These proposals, however, require strong, spatially oscillating magnetic fields while to date only the generation and effects of pseudo-gauge fields which vary at a length scale much larger than the magnetic length have been reported. Here we create a periodic pseudo-gauge field profile using periodic strain that varies at the length scale comparable to the magnetic length and study its effects on Dirac electrons. A periodic strain profile is achieved by pulling on graphene with extreme (>10%) strain and forming nanoscale ripples, akin to a plastic wrap pulled taut at its edges. Combining scanning tunneling microscopy and atomistic calculations, we find that spatially oscillating strain results in a new quantization different from the familiar Landau quantization observed in previous studies. We also find that graphene ripples are characterized by large variations in carbon-carbon bond length, directly impacting the electronic coupling between atoms, which within a single ripple can be as different as in two different materials. The result is a single graphene sheet that effectively acts as an electronic superlattice. Our results thus also establish a novel approach to synthesize an effective 2D lateral heterostructure -by periodic modulation of lattice strain. Main Text:Due to its high electronic mobility, optical transparency, mechanical strength and flexibility, graphene is attractive for electronic applications 1,2 . However, several factors prevent the realization of common electronic applications. For example, the lack of a band gap prevents an effective off-state in graphene transistors. Furthermore, Klein tunneling 3 , in which electrons pass through an electrostatic barrier with perfect transmission, prevents electron confinement by traditional gating methods. Figure 1. Engineering periodic pseudo electric and magnetic fields at strained interfaces: (a)High(low) density of carbon atoms and hence electrons are created in regions marked by lightblue (yellow) regions due to a strain gradient. This inhomogeneous charge distribution results in an electric field (green arrows). (b) Stretching of bonds cause the Dirac cones at K and K' points to shift symmetrically (yellow) from their original unstrained positions (light-blue) in the reciprocal space. As a momentum shift can be interpreted as generating a pseudo-vector potential term eA/c 15 , (where is the electronic charge and is the velocity of light) this creates pseudo-magnetic fields with opposite signs at the two valleys. (c) The strain associated with rippling creates rare (yellow) and dense (turquoise) regions in the graphene, effectively acting as two different materials in a superlattice. (d) Pseudo...

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