We study magnetoconductance, weak localization, and topological protection in weakly and strongly dis- ordered 3-D TIs. For single wires in a longitudinal magnetic field we that experimental Aharonov-Bohm and Altshuler-Aronov-Spivak signals are substantially different from the ensemble averaged signal, which requires reinterpretation of many previous experiments. We also predict the experimental signature of the Perfectly Conducting Channel, a single topologically protected conductance quantum that occurs in long TI wires. We also propose a practical technique for patterning controlling and directing electron flow on the surface of a TI.
1. Royal Holloway University of London 2. ETH Zurich, and Station Q Microsoft 3. University of Texas Austin 4. Sophia University 5. Institute for Materials Research, Tohoku University, and Frontier Research Institute for Interdisciplinary Sciences, Tohoku University