Persistent current in quantum torus knots

TL;DR

This paper investigates how electrons moving along knotted paths in a quantum torus knot generate persistent currents, revealing their dependence on knot geometry and magnetic field orientation, with implications for quantum interference phenomena.

Contribution

It introduces a formulation of persistent current in quantum torus knots based on knot geometry parameters, highlighting the effects of geometric distortion and field direction.

Findings

Persistent current exhibits periodic oscillations influenced by knot class and magnetic field direction.

Oscillation period is sensitive to geometric distortions of the knot.

The study provides a geometric framework for understanding quantum interference in knotted trajectories.

Abstract

I consider the quantum interference of electrons moving along knotted trajectories under external magnetic field. The induced persistent current is formulated in terms of characteristic parameters that classify the torus knot geometry. The current is found to show a periodic oscillation whose period depends strongly both on the knot's class and the field direction. The shift in the oscillation period caused by geometric distortion is also discussed.