  Nanostructures exhibit unusual properties due to the dominance of quantum
mechanical effects. In addition, the geometry of a nanostructure can have a
strong influence on its physical properties. Using the tight-binding (TB) and
force-constant (FC) approaches with the help of the non-equilibrium Green's
function (NEGF) method, the transport and thermoelectric properties of
cross-shaped (X-shaped) composite heterostructures are studied in two cases:
Mixed graphene and h-BN (HETX-CBN) and all graphene (HETX-C) cross-shaped
structures. Our numerical results show that an X-shaped structure helps to
manipulate its electronic and phononic properties. The transport energy gap can
be tuned in the range of ~0.8 eV by changing one arm width. Due to the drastic
decrease in the electronic conductance of HETX-CBN and the dominance of the
phononic thermal conductance, the ZT performance is degraded despite the high S
value (in the order of meV). However, HETX-C has better ZT performance due to
better electronic conductance and lower phononic/electronic thermal ratio, it
can enhance the ZT ~2.5 times compared to that of zigzag graphene nanoribbon.
The thermoelectric properties of the system can be tuned by controlling the
size of the arms of the device and the type of its atoms.
