Topological Effects in Tunneling-Coupled Systems of One-Dimensional Quantum Rings [article]

Colin Riggert, Kieran Mullen
2020 arXiv   pre-print
Using a model of idealized, crossed one-dimensional quantum wires we construct a novel model for a single electron on tunneling-coupled systems of one-dimensional quantum rings. We explore and find that topology can affect the energetics of the system, and can introduce frustration in the three ring case. We also study the special cases of an external magnetic field that controls the complex phase of the tunneling matrix element, and introduce the knot theory concept of "writhe" as a new
more » ... ical quantity for distinguishing one hole systems. We find that writhe not only determines the energetic response of the system to magnetic field strength, but is also responsible for a single particle topological quantum phase transition involving the ground state wave function winding number.
arXiv:2007.01967v1 fatcat:avvfbij2crbtrcty2hlnsyacre