2026/07/29 by Igor Kuzmenko, Y. B. Band, Yshai Avishai
Physics and Astronomy · #cond-mat.str-el
6 pages, 4 eps figures
arxiv created 2026/07/29 · arxiv updated 2026/07/30
The Aharonov-Casher (AC) effect is a quantum mechanical phenomenon in which the wave function of a particle with a magnetic moment moving in a region subject to an electric field develops a phase shift due to spin-orbit interaction, even if no classical force acts on it. This phase also depends on the medium through which the particle moves. Here we focus on the AC phase of an electron moving in twisted bilayer graphene (TBG) lying in the x-y plane, subject to a uniform electric field perpendicular to the plane of the graphene, \bf E=E\bf z. The AC phase is determined by an SU(2) vector potential \bf A from which a phase factor is generated, and used to perform a gauge transformation of the Hamiltonian. We find that the AC phase for a straight line path between two points in the TBG plane is linear with E and exhibits sharp peaks at the magic angles. To help demonstrate an experimental method for determining the AC phase, we examine the probability of polarized electron propagation from a source tip to a drain tip in a double-tip scanning tunneling spectroscopy configuration.