Hofstadter butterfly as quantum phase diagram
نویسندگان
چکیده
منابع مشابه
Phase Diagram of the Dissipative Hofstadter Model
A quantum particle moving in a uniform magnetic field and periodic potential (the Hofstadter model) has an energy band structure which varies in a discontinuous fashion as a function of the magnetic flux per lattice unit cell. In a real system, randomness of various kinds should “smooth out” this behavior in some way. To explore how this happens, we have studied the dissipative quantum mechanic...
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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...
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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...
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The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moiré superlattice of graphene on a hexagonal crystal substrate, is known to exhibit gapped Dirac cones. We show that the gap can be closed by slightly misaligning the substrate, producing a hierarchy of conical singularities (Dirac points) in the band structure at rational values Φ = (p/q)(h/e) of the magnetic fl...
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Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moiré potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replicas of the original Dirac cone and Hofstadter butterflies....
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2001
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1412464