Spectral properties of hexagonal lattices with the -R coupling

2024/09/05 by Pavel Exner, Exner, Pavel, Jan Pekař +1
Materials Science · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quasicrystal Structures and Properties #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2409.03538

openalex publication_date 2024/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We analyze the spectrum of the hexagonal lattice graph with a vertex coupling which manifestly violates the time reversal invariance and at high energies it asymptotically decouples edges at even degree vertices; a comparison is made to the case when such a decoupling occurs at odd degree vertices. We also show that the spectral character does not change if the equilateral elementary cell of the lattice is dilated to have three different edge lengths, except that flat bands are absent if those are incommensurate.

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