21-23 December 2020
Online meeting
Europe/Kiev timezone

Flat bands in quasi-one-dimensional Josephson junction arrays

21 Dec 2020, 17:20
Online meeting

Online meeting

Oral talk Condensed Matter Physics Condensed Matter Physics


Daryna Bukatova (Kyiv Academic University)


We study quasi-one-dimensional arrays of inductively coupled Josephson junctions with only self-inductance of a cell taken into account. A 2-row anisotropic Josephson junction ladder (JJL) has a flat band in the linear electromagnetic wave spectrum [1]. We derive the equations of motion for a 3-row anisotropic JJL and generalise them for a ladder with an arbitrary number of rows $ \kappa \geq 3 $. In the case of weak damping we obtain the spectrum of linear electromagnetic waves in these arrays. A $ \kappa $-row JJL has 3 bands in the spectrum, two of them are dispersive: the upper band consists of $ (\kappa-1) $ branches, the lower one of 2 branches, the band in the middle of the spectrum is dispersionless (flat) and is $ (\kappa - 2) $-fold degenerate. At zero external dc bias current the two lower branches become flat, resulting in $ \kappa $-fold degeneracy of the flat band.

The Authors acknowledge the support by the National Research Foundation of Ukraine grant ”Topological phases of matter and excitations in Dirac materials, Josephson junctions and magnets” (No. 2020.02.0051).

  1. A. E. Miroshnichenko, S. Flach, M.V. Fistul, Y. Zolotaryuk, J. B. Page. Breathers in Josephson junction ladders: Resonances and electromagnetic wave spectroscopy. $-$ PHYSICAL REVIEW E, VOLUME 64, 066601. $-$ 2001.

Primary authors

Daryna Bukatova (Kyiv Academic University) Dr Yaroslav Zolotaryuk (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

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