Abstract

Graphene, an atomically-thin sheet of carbon atoms, is elastically stiff, extremely flexible, and has a number of exciting electronic properties. Among these is the so-called pseudomagnetic field, which arises when the sheet is stretched inhomogeneously and can be interpreted classically through the deflection of electrons’ paths as they traverse the deformed crystal lattice.

While these pseudomagnetic fields do not correspond to real magnetic fields, their effect can be measured at hundreds of Tesla, far beyond that of conventional magnets. As such this phenomenon has been studied widely for potential use in nanodevices.

In this talk I will discuss the origin of this field, and its dependence on the strain field in the graphene sheet. This then leads naturally to a constrained optimization problem, where the control variables necessary to produce a pseudomagnetic field of a given pattern is sought. Two particular applications are discussed: graphene atop an undulating substrate, where the control variables describe the elevation of the surface; and a Corbino device, where the control variables describe an annular region of non-circular boundary which is pressurized to deform a superimposed graphene sheet.