Vortex Fractionalization in a Josephson Ladder

TL;DR

This paper demonstrates through numerical simulations that vortices in a Josephson ladder can fractionalize into multiple smaller fluxons under specific magnetic fields, revealing new excitations and dynamic behaviors.

Contribution

It introduces the concept of vortex fractionalization in Josephson ladders and characterizes the conditions and properties of fractional fluxons.

Findings

Fractional fluxons carry 1/q units of vorticity.

Fractional fluxons depin and move collectively under applied current.

Time-averaged voltage relates to the ac voltage frequency in fractional fluxon states.

Abstract

We show numerically that, in a Josephson ladder with periodic boundary conditions and subject to a suitable transverse magnetic field, a vortex excitation can spontaneously break up into two or more fractional excitations. If the ladder has N plaquettes, and N is divisible by an integer q, then in an applied transverse field of 1/q flux quanta per plaquette the ground state is a regular pattern of one fluxon every q plaquettes. When one additional fluxon is added to the ladder, it breaks up into q fractional fluxons, each carrying 1/q units of vorticity. The fractional fluxons are basically walls between different domains of the ground state of the underlying 1/q lattice. The fractional fluxons are all depinned at the same applied current and move as a unit. For certain applied fields and ladder lengths, we show that there are isolated fractional fluxons. It is shown that the fractional fluxons would produce a time-averaged voltage related in a characteristic way to the ac voltage frequency.