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 superconducting proximity effects in Weyl semimetals (WSM) with broken time-reversal symmetry by tunnel-coupling one of its surfaces to an s-wave superconductor using the Green's function approach. We find that the band structure develops coherence peaks, but despite the presence of metallic states in the bulk, the coherence peaks do not extend far into the bulk and remain confined to a few layers close to the interface, similar to the proximity effect in the topological insulators (TI) which are gapped in the bulk. The Weyl nodes remain unaffected, and in that sense, no true gap develops. We also study the induced pand s-wave pairing amplitudes classified by their symmetries, as a function of the various parameters of the theory, and note the exponential decay of the induced pairings in the bulk both in the TI and the WSM, even at finite chemical potential.

We propose a setup for the experimental realization of anisotropic 0-π transitions of the Josephson current, in a junction whose link is made of irradiated Weyl semi-metal (WSM), due to the presence of chiral nodes. The Josephson current through a time-reversal symmetric WSM has anisotropic (with respect to the orientation of the chiral nodes) periodic oscillations as a function of k0L, where k0 is the (relevant) separation of the chiral nodes and L is the length of the sample. We then show that the effective value of k0 can be tuned with precision by irradiating the sample with linearly polarized light, which does not break time-reversal invariance, resulting in 0-π transitions of the critical current. We also discuss the feasibility and robustness of our setup.

We present the results of three-dimensional simulations of quasar polarizations in the presence of pseudoscalar-photon mixing in the intergalactic medium. The intergalactic magnetic field is assumed to be uncorrelated in wave vector space but correlated in real space. Such a field may be obtained if its origin is primordial. Furthermore we assume that the quasars, located at cosmological distances, have negligible initial polarization. In the presence of pseudoscalar-photon mixing we show, through a direct comparison with observations, that this may explain the observed large scale alignments in quasar polarizations within the framework of big bang cosmology. We find that the simulation results give a reasonably good fit to the observed data.