Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices

By G. Yu, R. Gorbachev, J. Tu, A. Kretinin, Y. Cao, R. Jalil, F. Withers, L. Ponomarenko, B. Piot, M. Potemski and 9 more. Nature Physics, 2014

178 citations recorded by the source corpus.

Self-similarity and fractals have fascinated researchers across various disciplines. In graphene placed on boron nitride and subjected to a magnetic field, self-similarity appears in the form of numerous replicas of the original Dirac spectrum, and their quantization gives rise to a fractal pattern of Landau levels, referred to as the Hofstadter butterfly. Here we employ capacitance spectroscopy to probe directly the density of states (DoS) and energy gaps in this spectrum. Without a magnetic field, replica spectra are seen as pronounced DoS minima surrounded by van Hove singularities. The Hofstadter butterfly shows up as recurring Landau fan diagrams in high fields. Electron–electron interactions add another twist to the self-similar behaviour. We observe suppression of quantum Hall ferromagnetism, a reverse Stoner transition at commensurable fluxes and additional ferromagnetism within replica spectra. The strength and variety of the interaction effects indicate a large playground to study many-body physics in fractal Dirac systems. Graphene on boron nitride gives rise to a moiré superlattice displaying the Hofstadter butterfly: a fractal dependence of energy bands on external magnetic fields. Now, by means of capacitance spectroscopy, further aspects of this system are revealed—most notably, suppression of quantum Hall antiferromagnetism at particular commensurate magnetic fluxes.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/181cf6d34dbd8190a3eb8ea3091b472ab0b1d700

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Interlayer interaction in general incommensurate atomic layers (2015, background): “Graphene-hBN composite system has also been intensively studied as another example of incommensurate multilayer system, where the two layers share the same hexagonal lattice structure but with slightly-different lattice constants, leading to the long-period modulation even at zero rotation angle [15”
2D materials and van der Waals heterostructures (2016, background): “periodicity of the moiré structure, as has been observed in scanning tunneling microscopy (5) and, later, in transport (6–8) and capacitance (9) measurements.”