Flat and almost flat bands in the quasi-one-dimensional Josephson junction array

TL;DR

This paper derives the dispersion law for linear waves in a quasi-one-dimensional Josephson junction array, revealing multiple flat and nearly flat bands, and analyzes how bias affects their degeneracy and dispersion.

Contribution

It introduces a detailed analysis of flat and nearly flat Josephson plasmon bands in a multiladder array and how bias influences their degeneracy and dispersion.

Findings

The spectrum has 2N-1 branches with N flat degenerate bands.

Applying bias lifts degeneracy, leaving only one flat band.

Maximal flatness occurs within specific parameter ranges.

Abstract

The dispersion law for the linear waves in the quasi-one-dimensional array of inductively coupled Josephson junctions (JJ) is derived. The array has a multiladder structure that consists of the finite number of rows ($N\ge 2$) in $Y$ direction and is infinite in $X$ direction. The spectrum of the linear waves (Josephson plasmons) consists of $2N-1$ branches. Among these branches there is a $N$-fold completely flat degenerate one that coincides with the Josephson plasma frequency. The remaining $N-1$ branches have a standard Josephson plasmon dispersion law typical for 1D JJ arrays. Application of the uniform dc bias on the top of each vertical column of junctions lifts the degeneracy and only one flat branch remains unchanged. The rest of the previously flat branches become weakly dispersive. The parameter range where the flatness of these branches is maximal has been discussed.