Bag Boundaries for Quasispinor Confinement Within Nanolanes on a Graphene Sheet

Abstract

AbstractThe problem of bag boundary conditions within a field‐theoretic approach is revisited to study confinement of massless Dirac quasispinors in monolayer graphene. While no‐flux bag boundaries have previously been used to model lattice termination sites in graphene nanoribbons, a generalized setting is considered in which the confining boundaries are envisaged as arbitrary straight lines drawn across a graphene sheet and the quasispinor currents are allowed to partially permeate (leak) through such boundaries. Specifically focus is on rectangular nanolanes defined as areas confined between a pair of parallel lines at arbitrary separation on an unbounded lattice. It is shown that such nanolanes exhibit a considerable range of bandgap tunability depending on their widths and armchair, zigzag, or intermediate orientation. The case of nanoribbons can be derived as a special limit from the nanolane model. In this case, certain inconsistencies are clarified in previous implementations of no‐flux bag boundaries and show that the continuum approach reproduces the tight‐binding bandgaps accurately (within just a few percent in relative deviation) even as the nanoribbon width is decreased to just a couple of lattice spacings. This accentuates the proper use of boundary conditions when field‐theoretic approaches are applied to graphene systems.