Chiral nodes and oscillations in the Josephson current in Weyl semimetals

Abstract

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.

0−π transitions in a Josephson junction of an irradiated Weyl semimetal

“…Note that the 0-π transition or change in sign of the critical current is expected [44][45][46][47] in time-reversal broken systems, like the SC-ferromagnet-SC junction and has even been observed experimentally 48 . The transition was also shown earlier in a time-reversal breaking WSM 22 , but, motivated by the fact that almost all experimentally discovered WSMs 31-36 break inversion symmetry instead of time-reversal symmetry, in this paper, we show that it occurs in a time-reversal invariant setup, using linearly polarized light.…”

“…As shown, for T broken systems, in Ref. 22 , such momentum separation of the chiral nodes, 2k 0 contributes to transfer of momentum at the superconducting interface each time a reflection/Andreev reflection process takes place. As a result, the energies of the bound-states between the two superconductors oscillate as a function of k 0 L with oscillation frequency of π.…”

“…This extra transfer of momentum gives rise to an unusual oscillation 22 of Josephson current in a SC-WSM-SC setup with the period being proportional to both the distance between the two nodes in momentum space and the length of the WSM sample. The observation of such oscillations could be a direct proof of the existence of the chiral nodes, but since the momentum separation of the chiral nodes remains fixed for a given material, it is not likely to be usable as a tuning parameter.…”

“…If there was no chirality associated with the nodes, one would naively expect pairing between nodes α +(−) to β +(−) , which are the zero-momentum pairings. But, due to the overall spin conserving processes at a WSM-superconductor (SC) junction 14,22 , the helical quasiparticle excitations at the Weyl nodes allow only transport between nodes of opposite chirality. This implies that inter-nodal scattering can occur, say, from node α + to node α − (an inter-nodal distance of 2k 0 ) or from node α + to β − , (an inter-nodal distance of π).…”

“…We model the coupling with the superconductor by adding a self-energyΣ(ω) 15,22 to the first and last sites of the bare Green's function G R 0 .Σ accounts for tunnelling processes between the WSM and superconductor at the boundaries. The total retarded Green's function of the SWS device is…”