Abstract
AbstractIn this chapter, we introduce the Dirac and Weyl equation in solids. We classify the boundary conditions in Weyl materials and show how Fermi arcs naturally follow from the boundary conditions. Then the Green’s function is used to study superconducting proximity in Dirac and Weyl materials. In the case of Dirac materials we find that a novel form of parity breaking superconductivity, \(\Delta _5\), namely the pseudoscalar superconductivity can be induced. We discuss its transport signatures. We further discuss the induction of superconductivity in Fermi arc states. We discuss how the simultaneous presence of pseudoscalar superconductivity, \(\Delta _5\), combined with the conventional superconducting parameter \(\Delta _s\) can give rise to chiral supercurrent.
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