Plasmon-polariton fractal spectra in quasiperiodic photonic crystals with graphene

Abstract

In this work we study the plasmon-polariton spectra in one-dimensional photonic crystals based on the Fibonacci, Thue-Morse and double-period sequences, where we have graphene at the interface of one of the constituent building blocks (A = SiO2/graphene, B = SiO2). The dispersion relations for each quasicrystal are numerically calculated by using a transfer-matrix approach. The spectra of these structures are shown to be fractals (for the bulk bands distribution), obeying a power law in a particular frequency region and these are induced specifically by the quasiperiodic ordering in the unit cells of each system studied. We also report a strong dependence of the width of the bulk bands on the wave vector for this particular frequency region, whereas for large wave vectors the fractal properties in these spectra are absent.

Linearized spectral decimation in fractals

“…Recent developments of experimental techniques [1][2][3][4][5][6] open possibilities to study condensed-matter systems with complex geometries (for example, fractals) at the atomic level. Many theoretical and numerical works on fractals appeared recently including the studies on transport and optical properties [7][8][9][10][11], electronic localization [12][13][14][15], topology of fractals [16][17][18][19][20], appearance of flatbands [21][22][23][24], and others [25][26][27][28].…”