M. Schmidt, Univ. Basel
We study interfaces between graphene and graphane. These interfaces act
as effective edges for the pi-electrons in graphene. If the interface is
oriented along a zigzag direction, edge states are found that are very
similar to the usual zigzag edge states in graphene nanoribbons. These
interface states have some special properties which, in some respects,
make them superior to usual edge states in pure graphene: (1) Spin-orbit
effects are strongly enhanced at the interface (factors of 100 and
more). (2) Effective edges with 'bearded' boundary conditions are
stable. (3) The bandwidth of the edge state is tunable by electrostatic
gates.
Edge magnetism, well known from graphene edges, is also present at
graphene/graphane interfaces. However, the tunability of the edge state
bandwidth makes it possible to tune through the quantum phase transition
by means of electrostatic gates, i.e. switching edge magnetism on and
off. Near the transition, a regime of one-dimensional itinerant
ferromagnetism exists. In order to better understand the phase
transition, we introduce an effective model for the edge states.
Crucially, the electron-electron interaction becomes velocity-dependent
in this model. This velocity dependence is responsible for the
stabilization of the one-dimensional magnetism.
We incorporate quantum fluctuations around the mean-field theory by
means of the bosonization technique. In the non-magnetic regime the edge
state behaves as an ordinary spinful Luttinger liquid. In the regime of
weak ferromagnetism, the bosonized free Hamiltonian is well behaved only
if the proper mean-field theory is used as a basis for the bosonization.
The backscattering term, which leads to a sine-Gordon action for the
bosonic spin fields, is essentially momentum non-conserving, i.e. not
allowed. As a result, the interaction strength in the spin-sector is not
renormalized to unity and the spin-rotation invariance is broken. Close
to the transition, the usual bosonization technique is not sufficient to
describe the system. We discuss how the description may be extended.