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Unconventional superconductivity has been predicted to arise in thetopologically non-trivial Fermi surface of doped inversion symmetric Weylsemimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) andnodal BCS states are theoretically predicted to be possible superconductorpairing states in inversion symmetric doped WSM. In an effort to resolvepreferred pairing state, we theoretically study two separate four terminalquantum transport methods that each exhibit a unique electrical signature inthe presence of FFLO and nodal BCS states in doped WSMs. We first introduce aJosephson junction that consists of a doped WSM and an s-wave superconductor inwhich we show that the application of a transverse uniform current in s-wavesuperconductor effectively cancels the momentum carried by FFLO states in dopedWSM. From our numerical analysis, we find a peak in Josephson current amplitudeat finite uniform current in s-wave superconductor that serves as an indicatorof FFLO states in doped WSMs. Furthermore, we show using a four terminalmeasurement configuration that the nodal points may be shifted by anapplication of transverse uniform current in doped WSM. We analyze thetopological phase transitions induced by nodal pair annihilation innon-equilibrium by constructing the phase diagram and we find a characteristicdecrease in the density of states that serves as a signature of the quantumcritical point in the topological phase transition, thereby identifying nodalBCS states in doped WSM.

Probing unconventional superconductivity in inversion symmetric doped Weyl semimetal