  We revisit the problem of bag boundary conditions within a field-theoretic
approach 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, we consider a generalized
setting 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. We specifically focus on
rectangular nanolanes defined as areas confined between a pair of parallel
lines at arbitrary separation on an unbounded lattice. We show 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, we clarify certain inconsistencies 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.
