The separation of the Weyl nodes in a broken time-reversal symmetric Weyl semimetal leads to helical quasi-particle excitations at the Weyl nodes, which, when coupled with overall spin conservation allows only inter-nodal transport at the junction of the Weyl semimetal with a superconductor. This leads to an unusual periodic oscillation in the Josephson current as a function of k0L, where L is the length of the Weyl semimetal and 2k0 is the inter-nodal distance. This oscillation is robust and should be experimentally measurable, providing a direct path to confirming the existence of chiral nodes in the Weyl semimetal. PACS numbers: 74.45.+c, 74.50.+r, Introduction.-Weyl semimetals (WSM), which have received much interest recently due to their non-trivial transport characteristics, are 3D topological systems where conduction and valence bands touch at two or more 'Weyl' points 1-5 . According to a no-go theorem 6 , gapless Weyl nodes in a WSM appear as pairs in momentum space with each of the nodes having a definite 'chirality', a quantum number that depends on the Berry flux enclosed by a closed surface around the node. Gauss law prevents the annihilation of the nodes unless two of them with opposite chirality are brought together, which provides the 'topological' protection of the Weyl nodes 7 . A WSM phase requires broken time-reversal and/or inversion symmetry and a growing number of systems has been put forward which realize the WSM phase 8-10 .The separation of the chiral nodes, allows charge pumping between the nodes in the presence of parallel electric and magnetic fields, as a consequence of the chiral anomaly 11 , and this has led to detailed studies of transport in Weyl semi-metals in several recent papers .In this paper we study the current in a simple Josephson junction setup, depicted in Fig. 1(a). The helical quasi-particle excitations at the Weyl nodes, due to the overall spin conserving processes at a WSMsuperconductor (SC) junction, allow only inter-nodal transport 33 . Further, we show, unlike in a normal metal-SC interface, the inter-nodal 'normal' (electron to electron) reflection process in a WSM-SC interface is not suppressed even for energies close to Fermi-energy, due to the broken time-reversal symmetry separating the Weyl nodes. The Josephson current, flowing through the bound levels formed by multiple inter-nodal 'normal' and Andreev (electron to hole) processes in a SC-WSM-SC system, consequently, acquires a specific periodicity as a function of the length of the WSM which depends only on the separation of the Weyl nodes in the momentum space (see Fig. 1(b)). We argue that both of these features are robust because they are not only bulk effects, but they are also protected by the robustness of the Weyl nodes. We also discuss the feasibility of experimental observations of this transition in our system, which can confirm the presence of chiral nodes in WSM.
We study transport through a Weyl semimetal quantum dot sandwiched between an s-wave superconductor and a normal lead. The conductance peaks at regular intervals and exhibits double periodicity with respect to two characteristic frequencies of the system, one that originates from Klein tunneling in the system and the other coming from the chiral nature of the excitations. Using a scattering matrix approach as well as a lattice simulation, we demonstrate the universal features of the conductance through the system and discuss the feasibility of observing them in experiments.
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