  We study the effects of tunnelling on the band structure and Fermi arc of a
time-reversal broken Weyl semimetal (WSM). When coupled to a non-magnetic
parabolic band, the WSM's chiral arc state lowers in energy and forms, together
with a previously extended state, a noticeable spin-dependent asymmetry in the
interface spectrum in the vicinity of the Weyl nodes. We study these effects
with a lattice model which we solve numerically on a finite sample and
analytically through using an ansatz on an infinite sample. Our ansatz agrees
very well with the numerical simulation as it accurately describes the
behaviour of the chiral state, from its energy asymmetry to the spin canting at
the interface. We find that the tunnelling effectively increases the Fermi arc
length, allowing for the presence of interface states beyond the bare Weyl
nodes. These additional states may carry current along the interface and their
contribution can be detected in the conductance. Across the interface, the
spin-independent conductance reproduces the results of an electron tunnelling
experiment to reveal the WSM's density of states. Besides conductivity, the
effect of tunnelling between the WSM and the metallic band can be seen in
quantum oscillations experiments which we briefly comment about.
