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Quasiclassical theory for the superconducting proximity effect in Dirac materials

Quasiclassical theory for the superconducting proximity effect in Dirac materials

We derive the quasiclassical nonequilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking $\mathbf{p}\ifmmode\cdot\else\textperiodcentered\fi{}\overline{\mathbf{\ensuremath{\sigma}}}$, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the …