Higher-order topological phases in crystalline and non-crystalline systems: a review Page 1
Journal of Physics: Condensed Matter ACCEPTED MANUSCRIPT • OPEN ACCESS Higher-order …

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 …

The first quantum fractal discovered in physics is the Hofstadter butterfly. It stems from large
external magnetic fields. We discover instead a class of non-Hermitian quantum fractals …

High-order topological insulators can be realized via two-dimensional photonic crystals
(PCs) with different lattices including honeycomb, square and kagome lattices. In this paper …

The search for novel topological quantum states has recently moved beyond naturally
occurring crystalline materials to complex and engineered systems. In this work we …

Abstract Non-Hermitian (NH) crystals, quasicrystals, and amorphous network display an
accumulation of a macroscopic number of states near one of its specific interfaces with …

We propose the c-function as a new and accurate probe to detect the location of topological
quantum critical points. As a direct application, we consider a holographic model which …

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

Topological insulators, featuring bulk-boundary correspondence, have been realized on a
large number of noncrystalline materials, among which amorphous network, quasicrystals …