We study the electronic properties of rippled freestanding graphene membranes under central load from a sharp tip. To that end, we develop a gauge field theory on a honeycomb lattice valid beyond the continuum theory. Based on the proper phase conjugation of the tight-binding pseudospin Hamiltonian, we develop a method to determine conditions under which continuum elasticity can be used to extract gauge fields from strain. Along the way, we resolve a recent controversy on the theory of strain engineering in graphene: There are no K-point dependent gauge fields. We combine this lattice gauge field theory with atomistic calculations and find that for moderate load, the rippled graphene membranes conform to the extruding tip without significant increase of elastic energy. Mechanical strain is created on a membrane only after a certain amount of load is exerted. In addition, we find that the deformation potential -even when partially screened-induces qualitative changes on the electronic spectra, with Landau levels giving way to equally-spaced peaks.

Elemental phosphorous is believed to have several stable allotropes that are energetically nearly degenerate, but chemically reactive. These structures may be capped by monolayers of hexagonal boron nitride (h-BN) or graphene to prevent chemical degradation under ambient conditions. We perform ab initio density functional calculations to simulate scanning tunneling microscopy (STM) images of different layered allotropes of phosphorus and study the effect of the capping layers on these images. At scanning energies within its intrinsic conduction gap, protective monolayers of insulating h-BN allow to distinguish between the different structural phases of phosphorus underneath due to the electronic hybridization with orbitals from the upmost phosphorus atoms: h-BN capping monolayers thus provide a promising route to tell few-layer phosphorus allotropes from one another with local probes.

We employ room-temperature ultrahigh vacuum scanning tunneling microscopy (UHV STM) and ab-initio calculations to study graphene flakes that were adsorbed onto the Si(111)−7×7 surface. The characteristic 7×7 reconstruction of this semiconductor substrate can be resolved through graphene at all scanning biases, thus indicating that the atomistic configuration of the semiconducting substrate is not altered upon graphene adsorption. Large-scale ab-initio calculations confirm these experimental observations and point to a lack of chemical bonding among interfacial graphene and silicon atoms. Our work provides insight into atomic-scale chemistry between graphene and highly-reactive surfaces, directing future passivation and chemical interaction work in graphene-based heterostructures.

Mechanical strain creates strong gauge fields in graphene, offering the possibility of controlling its electronic properties. We developed a gauge field theory on a honeycomb lattice valid beyond first-order continuum elasticity. Along the way, we resolve a recent controversy on the theory of strain engineering in graphene: there are no K-point dependent gauge fields.