Strain-engineering of graphene's electronic structure beyond continuum elasticity

Abstract

We present a new first-order approach to strain-engineering of graphene's electronic structure where no continuous displacement field u(x, y) is required. The approach is valid for negligible curvature. The theory is directly expressed in terms of atomic displacements under mechanical load, such that one can determine if mechanical strain is varying smoothly at each unit cell, and the extent to which sublattice symmetry holds. Since strain deforms lattice vectors at each unit cell, orthogonality between lattice and reciprocal lattice vectors leads to renormalization of the reciprocal lattice vectors as well, making the K and K points shift in opposite directions. From this observation we conclude that no K−dependent gauges enter on a first-order theory. In this formulation of the theory the deformation potential and pseudo-magnetic field take discrete values at each graphene unit cell. We illustrate the formalism by providing strain-generated fields and local density of electronic states on graphene membranes with large numbers of atoms. The present method complements and goes beyond the prevalent approach, where strain engineering in graphene is based upon first-order continuum elasticity.

Large intravalley scattering due to pseudo-magnetic fields in crumpled graphene

“…This model reproduces the magnitude of B ps measured via scanning tunneling microscopy [48,13,49]. Computing B ps , directly from the modulation of the atomic positions [50] we find a maximum B ps of 20 T in the single fold, and as expected from the difference in strain, the double fold shows a B ps in the 200 T range (Fig. 4e,f).…”

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

“…In those cases, such as in the next section or in appendix C, that will be explicitly stated. We wish to note also that, as this manuscript was being prepared, we became aware of a recent proposal to connect structure and electronic properties of two-dimensional crystals based on concepts from discrete geometry that allows yet another efficient alternative to obtain the strain and PMF at discrete lattice points without the need, for example, to perform numerical derivatives upon the displacement fields or vector potentials extracted from the MD data 53,54 .…”

Discrete differential geometry and the properties of conformal two-dimensional materials

“…These Equations thus provide an original, discrete, viewpoint -in which one retains atomic positions-to the issue of gauge fields in two-dimensional materials [3,4,6].…”

“…The degree of sensitivity of MBL with respect to fluctuations on interatomic distances makes a direct correlation difficult [46,6,4]. In Figures 5(a-c) we contrast MBL with T r(g) and det(g) (we will not display the determinant of the metric tensor in further figures).…”

“…We identify two-dimensional materials with meshes, and apply precepts from a branch of Mathematics [2] that deals with discrete surfaces. We have presented a number of results in linking this geometry to materials properties already [3,4,5,6,7]. This subject has contributions from other teams as well [8,9,10].…”