Pseudomagnetic fields in graphene nanobubbles of constrained geometry: A molecular dynamics study

Abstract

Analysis of the strain-induced pseudomagnetic fields generated in graphene nanobulges under three different substrate scenarios shows that, in addition to the shape, the graphene-substrate interaction can crucially determine the overall distribution and magnitude of strain and those fields, in and outside the bulge region. We utilize a combination of classical molecular dynamics, continuum mechanics, and tight-binding electronic structure calculations as an unbiased means of studying pressure-induced deformations and the resulting pseudomagnetic field distribution in graphene nanobubbles of various geometries. The geometry is defined by inflating graphene against a rigid aperture of a specified shape in the substrate. The interplay among substrate aperture geometry, lattice orientation, internal gas pressure, and substrate type is analyzed in view of the prospect of using strain-engineered graphene nanostructures capable of confining and/or guiding electrons at low energies. Except in highly anisotropic geometries, the magnitude of the pseudomagnetic field is generally significant only near the boundaries of the aperture and rapidly decays towards the center of the bubble because under gas pressure at the scales considered here there is considerable bending at the edges and the central region of the nanobubble displays nearly isotropic strain. When the deflection conditions lead to sharp bends at the edges of the bubble, curvature and the tilting of the ${p}_{z}$ orbitals cannot be ignored and contributes substantially to the total field. The strong and localized nature of the pseudomagnetic field at the boundaries and its polarity-changing profile can be exploited as a means of trapping electrons inside the bubble region or of guiding them in channellike geometries defined by nanoblister edges. However, we establish that slippage of graphene against the substrate is an important factor in determining the degree of concentration of pseudomagnetic fields in or around the bulge since it can lead to considerable softening of the strain gradients there. The nature of the substrate emerges thus as a decisive factor determining the effectiveness of nanoscale pseudomagnetic field tailoring in graphene.