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A study of topological insulators in three dimensions Rosenberg, Gilad Amir

Abstract

In this work we study four interesting effects in the field of topological insulators: the Witten effect, the Wormhole effect, topological Anderson insulators and the absence of bulk magnetic order in magnetically doped topological insulators. According to the Witten effect, a unit magnetic monopole placed inside a medium with non zero θ is predicted to bind a fractional electric charge. We conduct a first test of the Witten effect based on the recently established fact that the electromagnetic response of a topological insulator is given by the axion term θ(e²/2πh)B·E, and that θ=π for strong topological insulators. We establish the Wormhole effect, in which a strong topological insulator, with an infinitely thin solenoid of magnetic half flux quantum carries protected gapless and spin filtered one-dimensional fermionic modes, which represent a distinct bulk manifestation of the topologically non-trivial insulator. We demonstrate that not only are strong topological insulators robust to disorder but, remarkably, under certain conditions disorder can become fundamentally responsible for their existence. We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological ‘Anderson’ insulator, a new topological phase of matter in three dimensions. Finally, we lay out the hypothesis that a temperature window exists in which the surface of magnetically doped topological insulators is magnetically ordered but the bulk is not. We present a simple and intuitive argument why this is so, and a mean-field calculation for two simple tight binding topological insulator models which shows that indeed a sizeable regime such as described above could exist. This indicates a possible physical explanation for the results seen in recent experiments.

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