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Quantum ground states on the non-trivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave superconductivity on a semiconductor platform, which is tuned through a TQCP to a topological superconducting (TS) state by an external Zeeman field. Despite many attractive features of TS states, TQCPs themselves do not break any symmetries, making it impossible to distinguish the TS state from a regular superconductor in conventional bulk measurements. Here we show that for the semiconductor TQCP this problem can be overcome by tracking suitable bulk transport properties across the topological quantum critical regime itself. The universal low-energy effective theory and the scaling form of the relevant susceptibilities also provide a useful theoretical framework in which to understand the topological transitions in semiconductor heterostructures. Based on our theory, specific bulk measurements are proposed here in order to characterize the novel TQCP in semiconductor heterostructures.
A spin-orbit coupled quantum wire, with one end proximate to an s-wave superconductor, can become a topological superconductor, with a Majorana mode localized at each end of the superconducting region. It was recently shown that coupling one end of s
We present a pedagogical review of topological superconductivity and its consequences in spin-orbit coupled semiconductor/superconductor heterostructures. We start by reviewing the historical origins of the notions of Dirac and Majorana fermions in particle physics and discuss how lower dimension
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