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The semiconductors InSb, InAs, and InGaAs, and the semimetal Bi have substantial spin-orbit interaction (SOI). We discuss spin-dependent quantum transport experiments performed on these materials, particularly on mesoscopic geometries on thin films and heterostructures, where SOI and quantum coherence determine the properties. SOI results in anti-localization, which is sensitive to spin- and quantum phase coherence lengths. Using anti-localization we determine the dependence of spin coherence lengths on the wire width in narrow nanolithographic ballistic InSb wires, ballistic InAs wires, and diffusive Bi wires. The three systems differ in several aspects, but in all we find that the spin coherence lengths increase with decreasing wire widths if other parameters stay constant. The experiments also indicate that Bi has surface states with strong Rashba-like SOI. In InAs heterostructures patterned into ring arrays, we observe coexisting Aharonov-Bohm oscillations due to spatial quantum interference and Altshuler-Aronov-Spivak oscillations due to time-reversed paths. A quantum coherent network formalism shows that the quantum phase coherence lengths coincide for both spatial- and temporal-loop quantum interference, indicating a fundamentally similar origin. We also describe experiments, in InGaAs heterostructures, on the duality between the Aharonov-Bohm and the Aharonov-Casher phase, the latter due to confinement-induced SOI in mesoscopic structures. Here our experiments search for evidence of edge states, dual to quantum Hall edge states. Host: Avadh Saxena |