Probing unconventional superconductivity in inversion-symmetric doped Weyl semimetal

Unconventional superconductivity has been predicted to arise in the topologically nontrivial Fermi surface of doped inversion-symmetric Weyl semimetals (WSMs). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion-symmetric doped WSMs. In an effort to resolve the 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 superconductors effectively cancels the momentum carried by FFLO states in doped WSMs. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in $s$-wave superconductors 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 WSMs. We analyze the topological phase transitions induced by nodal pair annihilation in nonequilibrium 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 WSMs.