ﻻ يوجد ملخص باللغة العربية
Using the Sierpinski carpet and gasket, we investigate whether fractal lattices embedded in two-dimensional space can support topological phases when subjected to a homogeneous external magnetic field. To this end, we study the localization property of eigenstates, the Chern number, and the evolution of energy level statistics when disorder is introduced. Combining these theoretical tools, we identify regions in the phase diagram of both the carpet and the gasket, for which the systems exhibit properties normally associated to gapless topological phases with a mobility edge.
We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy gaps as th
In two and three spatial dimensions, the transverse response experienced by a charged particle on a lattice in a uniform magnetic field is proportional to a topological invariant, the first Chern number, characterizing the energy bands of the underly
The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding $sim 10^4$ T magnetic fields to a trivial
We investigate theoretically the spectrum of a graphene-like sample (honeycomb lattice) subjected to a perpendicular magnetic field and irradiated by circularly polarized light. This system is studied using the Floquet formalism, and the resulting Ho
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattices hopping amplitudes can induce a series of bulk energy gap openings in the Hofstadter