Corner and Edge States in Topological Sierpinski Carpet Systems

Abstract

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 ways. Here we present a theoretical study on localized corner and edge states, emerging from topological phases in Sierpinski Carpet within a $\pi$-flux regime. A topological phase diagram is presented correlating the quadrupole moment with different hopping parameters. Particular localized states are identified following spatial signatures in distinct fractal generations. The specific geometry and scaling properties of the fractal systems can guide the supported topological states types and their associated functionalities. A conductive device is proposed by coupling identical Sierpinski Carpet units providing transport response through projected edge states which carry on the details of the system's topology. Our findings suggest that fractal lattices may also work as alternative routes to tune energy channels in different devices.

References in corpus (34)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Anyons in an exactly solved model and beyond
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• The Quantum-Mechanical Position Operator in Extended Systems
• Mapping topological order in coordinate space
• Design and characterization of electronic fractals
• A fractional corner anomaly reveals higher-order topology
• Observation of an acoustic octupole topological insulator
• Compact localized states and flatband generators in one dimension
• Demonstration of a quantized acoustic octupole topological insulator
• Bound states in the continuum of higher-order topological insulators
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Boundary-obstructed topological phases
• Transport and optical properties of an electron gas in a Sierpinski carpet
• Topological states on fractal lattices
• Topology in the Sierpiński-Hofstadter problem
• Higher-order topological phases on fractal lattices
• The existence of robust edge currents in Sierpinsky Fractals
• Dirac points emerging from flat bands in Lieb-kagomé lattices
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Higher-order topological insulators in hyperbolic lattices
• Topological States in Generalized Electric Quadrupole Insulators
• Quantised Bulk Conductivity as a Local Chern Marker
• Decoding flat bands from compact localized states
• Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals
• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Electronic fractal patterns in building Sierpinski-triangles molecular systems
• Compact Localized States in Engineered Flat-Band $\mathcal{P}\mathcal{T}$ Metamaterials
• Thermodynamics of a Higher-Order Topological Insulator

Cited by in corpus (3)

• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Topological insulators on fractal lattices: A general principle of construction
• Orbital magnetization in Sierpinski fractals