Robustness of chiral edge modes in fractals below two dimensions: A case study
Journal Club
2021.05.03.
Zoltán Tajkov
https://arxiv.org/pdf/2104.11533.pdf
Colorful and fragrant
is there any practical use?
Everything is fractal
Everything is fractal
Sierpinski carpet
Sierpinski triangle
d_\mathrm{H}=\log(3)/\log(2) \approx 1.58
d_\mathrm{H}=\log(8)/\log(3) \approx 1.89
Considered fractals
Everything is fractal
Sierpinski carpet
Sierpinski triangle
Lattice implementations
Everything is fractal
A Haldane type Chern insulator
The Hofstadter model
Considered models
H_\mathcal{L}=-t \sum_{\left< i,j \right> \in \mathcal{L}} \left( a_i^{\dag} a_j \mathrm{e}^{i A_{i,j}} +\mathrm{h.c.} \right)
A_{i,j}=\frac{e}{h}\int_{\mathbf{r}_i}^{\mathbf{r}_j} \overrightarrow{A}\mathrm{d}\overrightarrow{l}
Everything is fractal
The Hofstadter model on a Sierpinski carpet
Generation 5 fractal, full depth
Everything is fractal
The Hofstadter model on a Sierpinski carpet
Everything is fractal
The Hofstadter model on a Sierpinski carpet
Everything is fractal
The Haldane Chern insulator on a Sierpinski carpet
Everything is fractal
The Haldane Chern insulator on a Sierpinski carpet
