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Topological Proximity Effects

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We discuss the induction of new topological band structures from proximity effects and entanglement. We present how to engineer a p+ip topological superconductor in quantum wires with spin-orbit coupling from the vicinity of a reservoir with s-wave Cooper pairing. Topological properties of energy bands associated with a spin-1/2 representation can be characterized from the reciprocal space and the Bloch sphere. The topological Chern number of one spin-1/2 model is known to be an integer. We highlight how to realize fractional topological phases directly from the reciprocal space, through the proximity effect and entanglement between two Bloch spheres. We show the applicability of these rational-valued Chern numbers in quantum circuits and a correspondence with honeycomb bilayer systems developing a nodal semimetallic ring at one Dirac point only.

This talk is part of the Theory of Condensed Matter series.

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