Fractional ac Josephson effect as evidence of topological hinge states in a Dirac semimetal NiTe2

Abstract: We experimentally investigate Josephson current between two 5~$\mu$m spaced superconducting indium leads, coupled to a NiTe$_2$ single crystal flake, which is a type-II Dirac semimetal. Under microwave irradiation, we demonstrate a.c. Josephson effect at millikelvin temperatures as a number of Shapiro steps. In addition to the integer ($n=1,2,3,4...$) steps, we observe fractional ones at half-integer values $n=1/2,3/2,5/2$ and 7/2, which corresponds to $\pi$ periodicity of current-phase relationship. In contrast to previous investigations, we do not observe $4\pi$ periodicity (disappearance of the odd $n=1,3,5...$ Shapiro steps), while the latter is usually considered as a fingerprint of helical surface states in Dirac semimetals and topological insulators. We argue, that our experiment confirms Josephson current through the topological hinge states in NiTe$_2$: since one can exclude bulk supercurrent in 5~$\mu$m long Josephson junctions, interference of the hinge modes is responsible for the $\pi$ periodicity, while stable odd Shapiro steps reflect chiral character of the topological hinge states.