Study On The Josephson Effect In Weyl Semimetals

Topological semimetals as a novel phases of matter possess the exotic gapless ex-citations that are governed by relativistic quantum mechanics in the low-energy theory.Due to the growing interests in these phases,the number of the materials predicted or shown to have the topological characters are continuously increasing.An interesting example of a topological semimetal in three dimensions,the Weyl semimetal,can host two or more”weyl nodes”with linear dispersion relation in the bulk and those paired Weyl nodes are connected by unusual surface fermi arc.Not only the unique topologi-cal properties of Weyl semimetals but also the superconducting pairing mechanism has attracted much attention.There may be two different pairing mechanisms for the inver-sion symmetry Weyl semimetal:zero momentum BCS pairing mechanism and finite momentum Fulde-Ferrell-Larkin-Ovchinnikov(FFLO)pairing mechanism.Although there are a lot of attentions on Weyl semimetal superconducting heterojunctions,in-cluding Andreev reflection,Josephson junction and cross Andreev reflection and con-ductance,etc,the research on the Weyl semimetal superconducting junction under the influence of Zeeman field still less involved.In this paper,the scattering matrix formalism is used to discuss the current phase relationship of the Weyl semimetal Josephson junction with inversion symmetry un-der the influence of Zeeman field for both BCS pairing and FFLO pairing.For the BCS pairing,the Andreev reflection and normal reflection coefficients of the Weyl semimetal/Weyl superconductor interface are solved by the Bogoliubov-de Gennes(Bd G)equation,then by constructing scattering matrix and solving Andreev's bound states and supercurrent,it is found that the Zeeman field parallel to the line joining two Weyl points has no affect on supercurrent,while the Zeeman field deviated from the line joining two Weyl points will cause an additional phase difference at the metal region to induce a?₀junction.For the case of FFLO pairing,the josephson current when Zeeman field perpendicular to the line joining two Weyl points is similar to the case of BCS pairing,which also induces the?₀junction.However,due to the different response of the Weyl nodes with different chiralities to the Zeeman field,the Zeeman field parallel to the line joining two Weyl points will induce the 0-?transition.