Coherent Oscillations and Giant Edge Magnetoresistance in Singly Connected Topological Insulators

The topological insulators have a gap in the bulk but extended states at the edge that can carry current. We study a geometry in which such edge states will manifest themselves through periodic oscillations in the magnetoconductance of a singly connected sample coupled to leads through narrow point contacts. The oscillations occur due to quantum interference of helical edge states of electrons traveling along the circumference of the sample, and have a period of B_0=h/eA_{eff}, where A_{eff} is the effective area enclosed by the edge states of the sample. Our calculation indicates the possibility of a large change in the magnetoresistance at small B, termed giant edge magnetoresistance, which can have potential for application. The zero field conductance also exhibits oscillations as a function of the Fermi energy due to interference between edge states. The amplitude of the oscillations is governed by, and therefore can be used to investigate, the transverse width of the edge channels.