Properties of the superconducting condensate and the quasiparticles are central to the understanding of superconducting systems. The condensate can be directly probed by the Josephson effect while the quasiparticles can be investigated with transport and spectroscopic methods. We study the Berry curvature effects of the superconducting quasiparticles and investigate the Berry curvature induced thermal Hall effect and the density of state modulation. We also study the Josephson effect in mesoscopic junctions, where the nontrivial Cooper pair splitting effect or the embedded Majorana qubit induces novel transport signatures.
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