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We study Andreev bound states (ABS) and resulting charge transport of Rashbasuperconductor (RSC) where two-dimensional semiconductor (2DSM)heterostructures is sandwiched by spin-singlet s-wave superconductor andferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to thatin spinless chiral p-wave pairing in topological phase (TP). We clarify thattwo types of quantum criticality about the topological change of ABS near aquantum critical point (QCP), whether ABS exists at QCP or not. In the formertype, ABS has a energy gap and does not cross at zero energy in non-topologicalphase (NTP). These complex properties can be detected by tunneling conductancebetween normal metal / RSC junctions.

Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization