Fractals are fascinating, not only for their aesthetic appeal but also for allowing the
investigation of physical properties in non-integer dimensions. In these unconventional …

The dimensionality of an electronic quantum system is decisive for its properties. In one
dimension, electrons form a Luttinger liquid, and in two dimensions, they exhibit the …

The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity)
and the notion of a fractal dimension D which exceeds the topological dimension d. In this …

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 investigate the fate of topological states on fractal lattices. Focusing on a spinless chiral
p-wave paired superconductor, we find that this model supports two qualitatively distinct …

Deposition of Bi on InSb (111) B reveals a striking Sierpiński-triangle (ST)-like structure in Bi
thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic …

Ultracold quantum gases serve as ideal models for the characterization of universal
properties of a variety of phenomena in quantum systems. In a formal analogy to …

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 …

Electronic materials harbor a plethora of exotic quantum phases, ranging from
unconventional superconductors to non-Fermi liquids and, more recently, topological …

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 …