  Unconventional superconductivity has been predicted to arise in the
topologically non-trivial Fermi surface of doped inversion symmetric Weyl
semimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and
nodal BCS states are theoretically predicted to be possible superconductor
pairing states in inversion symmetric doped WSM. In an effort to resolve
preferred pairing state, we theoretically study two separate four terminal
quantum transport methods that each exhibit a unique electrical signature in
the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a
Josephson junction that consists of a doped WSM and an s-wave superconductor in
which we show that the application of a transverse uniform current in s-wave
superconductor effectively cancels the momentum carried by FFLO states in doped
WSM. From our numerical analysis, we find a peak in Josephson current amplitude
at finite uniform current in s-wave superconductor that serves as an indicator
of FFLO states in doped WSMs. Furthermore, we show using a four terminal
measurement configuration that the nodal points may be shifted by an
application of transverse uniform current in doped WSM. We analyze the
topological phase transitions induced by nodal pair annihilation in
non-equilibrium by constructing the phase diagram and we find a characteristic
decrease in the density of states that serves as a signature of the quantum
critical point in the topological phase transition, thereby identifying nodal
BCS states in doped WSM.
