منابع مشابه
Hofstadter Butterfly and a Hidden Apollonian Gasket
The Hofstadter butterfly, a quantum fractal made up of integers describing quantum Hall states, is shown to be related to an integral Apollonian gasket with D3 symmetry. This mapping unfolds as the self-similar butterfly landscape is found to describe a close packing of (Ford) circles that represent rational flux values and is characterized in terms of an old ((300BC) problem of mutually tangen...
متن کاملEffects of screening on the Hofstadter butterfly.
We study, within the Hartree approximation, the effects of the electronelectron interaction on the energy spectrum of a two-dimensional electron gas in a perpendicular homogeneous magnetic field and a lateral superlattice potential with square symmetry. Due to the strong screening effects, the bandwidth of the Landau bands oscillates strongly with their filling. For short enough periods and str...
متن کاملAcoustic characterization of Hofstadter butterfly with resonant scatterers
We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the st...
متن کاملDetection of a Landau band-coupling-induced rearrangement of the Hofstadter butterfly.
The spectrum of 2D electrons subjected to a weak 2D potential and a perpendicular magnetic field is composed of Landau bands with a fractal internal pattern of subbands and minigaps referred to as Hofstadter's butterfly. The Hall conductance may serve as a spectroscopic tool as each filled subband contributes a specific quantized value. Advances in sample fabrication now finally offer access to...
متن کاملMassive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure.
van der Waals heterostructures constitute a new class of artificial materials formed by stacking atomically thin planar crystals. We demonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking...
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2016
ISSN: 2469-9950,2469-9969
DOI: 10.1103/physrevb.94.205437