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We find that the vortex bound states in superconducting topologicalsemimetals are gapless owing to topological massless excitations in theirnormal states. We demonstrate this universal result in a variety of semimetalsincluding Dirac and Weyl semimetals, threefold degenerate spin-1 fermions,spin-3/2 Rarita-Schwinger-Weyl fermion semimetals and other exotic fermionsemimetals. The formation of these gapless bound states are closely related totheir Andreev specular reflection and propagating Andreev modes in $\pi$ phasesuperconductor-normal metal-superconductor (SNS) junctions. We furtherdemonstrate that these gapless states are topologically protected and can bederived from a topological pumping process.

Gapless vortex bound states in superconducting topological semimetals