Kagome network with vertex coupling of a preferred orientation

Abstract

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 the lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of 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 $\approx 0.639$.

arXiv comment29 pages, 11 figures

References in corpus (11)

• Kirchhoff's Rule for Quantum Wires
• Weakly coupled states on branching graphs
• Approximation of a general singular vertex coupling in quantum graphs
• Universality of the momentum band density of periodic networks
• Quantum graphs with vertices of a preferred orientation
• Spectral asymptotics of the Laplacian on Platonic solids graphs
• PT-symmetric quantum graphs
• Quantum Graphs: $\mathcal{P}\mathcal{T}$-symmetry and reflection symmetry of the spectrum
• Ring chains with vertex coupling of a preferred orientation
• Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{P}\mathcal{T}$-symmetry
• Magnetic ring chains with vertex coupling of a preferred orientation

Cited by in corpus (2)

• Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
• Magnetic square lattice with vertex coupling of a preferred orientation