Electronic states in quantum wires on the Möbius strip

J. J. L. R. Pinto, J. E. G. Silva, C. A. S. Almeida

Published 2023-03-10Version 1

In this work, we study the properties of an electron constrained on wires along the M\"{o}bius strip. We considered wires around the strip and along the transverse direction, across the width of the strip. For each direction, we investigate how the curvature modifies the electronic states and their corresponding energy spectrum. At the center of the strip, the wires around the surface form quantum rings whose spectrum depends on the strip radius $a$. For wires at the edge of the strip, the inner edge turns into the outer edge. Accordingly, the curvature yields localized states in the middle of the wire. Along the strip width, the effective potential exhibits a parity symmetry breaking leading to the localization of the bound state on one side of the strip.