Deformations in two-dimensional materials

Two dimensional (2d) materials not only possess an intrinsic tendency to deformation not found in 3d materials, but also a geometry that more naturally allows for imposed deformations, for example via a vicinal substrate. In graphene, state-of-the-art theory based on encoding deformation through gauge potentials in the Dirac-Weyl equation neglects the role of the sub-lattice degrees of freedom, and thus only considers homogeneous (Cauchy-Born) deformation. We have generalized this theory to account for both acoustic and optical deformation fields [1], finding that non-Cauchy-Born gauges behave very differently and, in principle, allow for the long distance transport of valley charge. Our approach is based on formulating a general operator equivalence between the Slater-Koster tight-binding method and a general continuum effective Hamiltonian [2], an approach which captures both perturbative and non-perturbative deformation (such as interlayer twists). This methodology allows for the treatment of deformation via effective Hamiltonians in general 2d materials, and we demonstrate this via a discussion of deformations in the semi-metallic graphynes and stanene. Despite their complex structure, the graphynes show a remarkable closeness to the physics of deformation in graphene. Stanene, on the other hand, due to its intrinsic buckling and hence broken mirror symmetry behaves rather differently. Finally I will also examine the role of interlayer deformations, in particular a local twist to create a small angle moire, and partial dislocation networks [3], [4].

• [1] R. Gupta et al., arXiv:1810.04775 (to appear in Phys. Rev. B)
• [2] F. Rost, R. Gupta et al., arXiv:1901.04535.
• [3] M. Fleischmann et al., arXiv1901.04679.
• [4] D. Weckbecker et al. arXiv:1812.03343.