  We study theoretically electron interference in a Mach--Zehnder-like geometry
formed by four zigzag graphene nanoribbons (ZGNRs) arranged in parallel pairs,
one on top of the other, such that they form intersection angles of 60$^\circ$.
Depending on the interribbon separation, each intersection can be tuned to act
either as an electron beam splitter or as a mirror, enabling tuneable circuitry
with interfering pathways. Based on the mean-field Hubbard model and Green's
function techniques, we evaluate the electron transport properties of such
8-terminal devices and identify pairs of terminals that are subject to
self-interference. We further show that the scattering matrix formalism in the
approximation of independent scattering at the four individual junctions
provides accurate results as compared with the Green's function description,
allowing for a simple interpretation of the interference process between two
dominant pathways. This enables us to characterize the device sensitivity to
phase shifts from an external magnetic flux according to the Aharonov--Bohm
effect as well as from small geometric variations in the two path lengths. The
proposed devices could find applications as magnetic field sensors and as
detectors of phase shifts induced by local scatterers on the different
segments, such as adsorbates, impurities or defects. The setup could also be
used to create and study quantum entanglement.
