TBPLaS is an open-source software package for the accurate simulation of physical systems
with arbitrary geometry and dimensionality utilizing the tight-binding (TB) theory. It has an …

We calculate the Hall conductivity of a Sierpiński carpet using Kubo-Bastin formula. The
quantization of Hall conductivity disappears when we increase the depth of the fractal, and …

We investigate the Hall conductivity in a Sierpiński carpet, a fractal of Hausdorff dimension
df= ln (8)/ln (3)≈ 1.893, subject to a perpendicular magnetic field. We compute the Hall …

Using the Sierpiński carpet and gasket, we investigate whether fractal lattices embedded in
two-dimensional space can support topological phases when subjected to a homogeneous …

The fractional quantum Hall effect is a paradigm of topological order and has been studied
thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall …

Disorder effects on topological materials in integer dimensions have been extensively
explored in recent years. However, its influence on topological systems in fractional …

Here, we investigate the fractal-lattice Hubbard model using various numerical methods:
exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock …

In this paper we investigate the energy spectrum statistics of fractals at the quantum level.
We show that the energy level distribution of a fractal follows a power-law behavior, if its …

In this Letter, we study two-dimensional Floquet conformal field theory, where the external
periodic driving is described by iterated logistic or tent maps. These maps are known to be …

Fractals, a fascinating mathematical concept made popular in the 1980s, has remained for
decades mainly a beautiful scientific curiosity. With the tremendous advances in …