A quantum graph approach to metamaterial design

This structure is characterized by a material of one type connected in a different dimension. The dispersion curve exhibits maximum and minimum values, influenced by the nearest neighbor coupling. However, our focus here is solely on the interface, rather than the material as a whole.

By removing the material on the left and right, we concentrate on the interface, which I will label as M. The parameter μ represents the coupling of the M cell to the M plus μ-th cell, where μ is an integer. The standard unit in this context is the length between these vertices or connectors.

Additionally, when we eliminate the bond, we can emphasize the interface further, introducing an extra parameter that denotes the length of the connector, which I refer to as μ.