相关论文: Topology in the Sierpi\'nski-Hofstadter problem
Fractal lattices, with their self-similar and intricate structures, offer potential platforms for engineering physical properties on the nanoscale and also for realizing and manipulating high order topological insulator states in novel…
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 phases when defined on a Sierpinski gasket. While the…
Topological excitations in periodic magnetic crystals have received significant recent attention. However, it is an open question on their fate once the lattice periodicity is broken. In this work, we theoretically study the topological…
We investigate the topological phases of the Haldane model on the Sierpi\'nski gasket. As a consequence of the fractal geometry, multiple fractal gaps arise. Additionally, a flat band appears, and due to a complex next-nearest neighbour…
There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. It has previously been shown that the Laughlin state can be…
We study the spectral properties and local topology of the Kane-Mele-Rashba model on a Sierpinski Carpet (SC) fractal, constructed from a rectangular flake with an underlying honeycomb arrangement and open boundary conditions. When the…
Fractal lattices are self-similar structures with repeated patterns on different scales. As in other aperiodic lattices, the absence of translational symmetry can give rise to quantum localization effects. In contrast to low-dimensional…
Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…
The possibility of topological phase transition with or without a magnetic flux trapped in the cells of a class of decorated lattices is explored in details.Using a tight binding Hamiltonian and a real space decimation scheme we…
A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for…
Motivated by recent interests in fracton topological phases, we explore the interplay between gapped 2D $\mathbb{Z}_N$ topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such…
Topological phases have been reported on self-similar structures in the presence of a perpendicular magnetic field. Here, we present an understanding of these phases from a perspective of spectral flow and charge pumping. We study the…
Topologically non-trivial phases have recently been reported on self-similar structures. Here, we investigate the effect of local structure, specifically the role of the coordination number, on the topological phases on self-similar…
We consider an infinite graphene geometry where bonds and sites have been removed selectively to map it onto an effective Sierpinski gasket comprising of hexagons. We show that such a structure is capable of sustaining an infinite number of…
An essential attribute of many fractal structures is self-similarity. A Sierpinski gasket (SPG) triangle is a promising example of a fractal lattice that exhibits localized energy eigenstates. In the present work, for the first time we…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
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…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
Despite intense interest in realizing topological phases across a variety of electronic, photonic and mechanical platforms, the detailed microscopic origin of topological behavior often remains elusive. To bridge this conceptual gap, we…