Kagome network with vertex coupling of a preferred orientation

0560993 - ÚJF 2023 RIV US eng J - Článek v odborném periodiku
Baradaran, M. - Exner, Pavel
Kagome network with vertex coupling of a preferred orientation.
Journal of Mathematical Physics. Roč. 63, č. 8 (2022), č. článku 083502. ISSN 0022-2488. E-ISSN 1089-7658
Grant CEP: GA ČR(CZ) GA21-07129S
Institucionální podpora: RVO:61389005
Klíčová slova: quantum graphs * triangular lattice * kagome
Obor OECD: Pure mathematics
Impakt faktor: 1.3, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1063/5.0093546

We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of an infinite number of bands, some of which may be flat, the negative one has at most three and two bands, respectively. The kagome lattice example shows that even in graphs with such an uncommon vertex coupling, spectral universality may hold: if its edges are incommensurate, the probability that a randomly chosen positive number is contained in the spectrum is asymptotic to 0.639.
Trvalý link: https://hdl.handle.net/11104/0333751