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

Area of Science:

• Condensed Matter Physics
• Solid State Physics
• Quantum Electronics

Background:

• Josephson junctions (JJs) are crucial in quantum electronics.
• Understanding wave propagation in JJ arrays is key for device applications.
• Quasi-one-dimensional multiladder structures offer unique electronic properties.

Purpose of the Study:

• Derive the dispersion law for linear waves in a quasi-one-dimensional multiladder JJ array.
• Analyze the spectrum of Josephson plasmons in this specific geometry.
• Investigate the effect of uniform DC bias on wave dispersion and degeneracy.

Main Methods:

• Theoretical derivation of the dispersion law for linear waves.
• Analysis of the 2N-1 spectral branches in the multiladder JJ array.
• Mathematical modeling of DC bias effects on wave degeneracy.

Main Results:

• Identified an N-fold degenerate flat band coinciding with the Josephson plasma frequency.
• Observed N-1 branches with standard 1D JJ array dispersion.
• Demonstrated that DC bias lifts degeneracy, leaving one flat branch and making others weakly dispersive.

Conclusions:

• The multiladder JJ array exhibits unique flat band characteristics.
• DC bias provides a mechanism to control and tune the dispersion of Josephson plasmons.
• The study offers insights into designing JJ-based devices with specific wave propagation properties.