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Vladimir Falko

Moiré minibands and Hofstadter fractal spectra in van der Waals heterostructures of graphene with hexagonal crystals



Monday 22nd of September




The technological development of graphene has generated new high-quality systems offer access to the earlier inaccessible extremes of quantum physics. When graphene is placed on an atomically flat substrate with hexagonal lattice with a close lattice constant, such as boron nitride (hBN), and their crystalline axes are aligned, a long-wavelength perfectly periodic moiré pattern forms for electrons in graphene. Various regimes of possible moiré minibands at zero magnetic field [Phys. Rev. B 87, 245408 (2013); Phys. Rev. B 88, 205418; Phys. Rev. B 88, 155415 (2013); New J. Phys, 15, 123009 (2013)] and strong magnetic field [Nature 497, 594 (2013), Nature Physics 10, 525 (2014); Phys Rev B 89, 075401 (2014)] will be discussed. Experimentally available magnetic fields are enough to provide flux φ through the moiré superlattice cell comparable to the magnetic flux quantum φ0 and reach the regime of fractal Hofstadter spectra. As a result, a single device can offer a multiplicity of two-dimensional electron systems, realised at rational flux values  φ= φ0, φ0/2, 2φ0/3, etc., each with its own intricate topological properties, including quantum Hall effect physics related to the effective Landau levels emerging from these magnetic minibands at the nearby range of magnetic fields.













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