Confined Electrons in Effective Plane Fractals
arXiv:2009.11163 · doi:10.1103/PhysRevB.102.245425
Abstract
As an emerging complex two-dimensional structure, plane fractal has attracted much attention due to its novel dimension-related physical properties. In this paper, we check the feasibility to create an effective Sierpinski carpet (SC), a plane fractal with Hausdorff dimension intermediate between one and two, by applying an external electric field to a square or a honeycomb lattice. The electric field forms a fractal geometry but the atomic structure of the underlying lattice remains the same. By calculating and comparing various electronic properties, we find parts of the electrons can be confined effectively in a fractional dimension with a relatively small field, and representing properties very close to these in a real fractal. In particular, compared to the square lattice, the external field required to effectively confine the electron is smaller in the hexagonal lattice, suggesting that a graphene-like system will be an ideal platform to construct an effective SC experimentally. Our work paves a new way to build fractals from a top-down perspective, and can motivate more studies of fractional dimensions in real systems.
References in corpus (38)
- Kwant: a software package for quantum transport
- Two-dimensional transition metal dichalcogenides under electron irradiation: defect production and doping
- Graphene Antidot Lattices - Designed Defects and Spin Qubits
- Artificial graphene as a tunable Dirac material
- Experimental realization and characterization of an electronic Lieb lattice
- Modeling electronic structure and transport properties of graphene with resonant scattering centers
- Design and characterization of electronic fractals
- Fractal Conductance Fluctuations in Generic Chaotic Cavities
- Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
- Electronic properties of graphene antidot lattices
- Fractal Conductance Fluctuations in a Soft Wall Stadium and a Sinai Billiard
- Weak Localization and Transport Gap in Graphene Antidot Lattices
- Thermoelectric properties of finite graphene antidot lattices
- Imaging Fractal Conductance Fluctuations and Scarred Wave Functions in a Quantum Billiard
- Optical properties of graphene antidot lattices
- Transport and optical properties of an electron gas in a Sierpinski carpet
- Topological states on fractal lattices
- Topology in the Sierpiński-Hofstadter problem
- Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice
- Flat bands in fractal-like geometry
- The existence of robust edge currents in Sierpinsky Fractals
- Hall conductivity of Sierpinski carpet
- From laterally modulated two-dimensional electron gas towards artificial graphene
- Fractal Conductance Fluctuations in Gold--Nanowires
- Gate-tunable two-dimensional superlattices in graphene
- Electronic Properties of Disordered Graphene Antidot Lattices
- Plasmon confinement in fractal quantum systems
- Delocalized-localized transition in a semiconductor two-dimensional honeycomb lattice
- Anyons and Fractional Quantum Hall Effect in Fractal Dimensions
- Optical conductivity of a quantum electron gas in a Sierpinski carpet
- Engineering flat electronic bands in quasiperiodic and fractal loop geometries
- Electrostatic Superlattices on Scaled Graphene Lattices
- Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks
- Power-law energy level-spacing distributions in fractals
- Universal quantum transport and impurity band super metallicity in self-similar graphene carpets
- Fractal Dynamics in Chaotic Quantum Transport
- Fractal fluctuations in quantum integrable scattering
- Fabrication of Artificial Graphene in a GaAs Quantum Heterostructure
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- Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
- Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals
- Haldane model on the Sierpiński gasket
- Level-spectra Statistics in Planar Fractal Tight-Binding Models
- Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
- A fractal geometry immersed in a hierarchical magnetic flux distribution