Related papers: Corner and Edge States in Topological Sierpinski C…
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…
Using the Sierpi\'nski 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…
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…
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…
Fractal is an intriguing geometry with self-similarity and non-integer dimensions, the elastic-wave topological phase based on fractal structures has not been revealed up to now. In this work, elastic-wave higher-order topological states in…
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new…
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well…
Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d$th-order topology of a $d$-dimension system. In this work, we…
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied…
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…
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…
Topological insulators are a new phase of matter with the distinctive characteristics of an insulating bulk and conducting edge states. Recent theories indicate there even exist topological edge states in the fractal-dimensional lattices,…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
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…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
Higher-order topological phase as a generalization of Berry phase attracts an enormous amount of research. The current theoretical models supporting higher-order topological phases, however, cannot give the connection between lower and…
Time-periodic modulation of a static system is a powerful method for realizing robust unidirectional topological states. So far, all such realizations have been based on interactions among $s$ orbitals, without incorporating inter-orbital…
The search for artificial structure with tunable topological properties is an interesting research direction of today's topological physics. Here, we introduce a scheme to realize `topological semimetal states' with a three-dimensional…
In recent years, synthesis and experimental research of fractalized materials has evolved in a paradigmatic crossover with topological phases of matter. We present here a theoretical investigation of the helical edge transport in Sierpinski…
Using the Sierpinski gasket (triangle) and carpet (square) lattices as examples, we theoretically study the properties of fractal superconductors. For that, we focus on the phenomenon of $s$-wave superconductivity in the Hubbard model with…