1 research outputs found
Graphene zigzag ribbons, square lattice models and quantum spin chains
We present an extended study of finite-width zigzag graphene ribbons (ZGRs)
based on a tight-binding model with hard-wall boundary conditions. We provide
an exact analytic solution that clarifies the origin of the predicted width
dependence on the conductance through junctions of ribbons with different
widths. An analysis of the obtained solutions suggests a new description of
ZGRs in terms of coupled chains. We pursue these ideas further by introducing a
mapping between the ZGR model and the Hamiltonian for N-coupled quantum chains
as described in terms of 2N Majorana fermions. The proposed mapping preserves
the dependence of ribbon properties on its width thus rendering metallic
ribbons for N odd and zero-gap semiconductor ribbons for N even. Furthermore,
it reveals a close connection between the low-energy properties of the ZGR
model and a continuous family of square lattice model Hamiltonians with similar
width-dependent properties that includes the flux and the trivial square
lattice models. As a further extension, we show that this new description makes
it possible to identify various aspects of the physics of graphene ribbons with
those predicted by models of quantum spin chains (QSCs)