Long-range ballistic transport of Brown-Zak fermions in graphene superlattices

Barrier, Julien and Kumaravadivel, Piranavan and Kumar, Roshan Krishna and Ponomarenko, Leonid and Xin, Na and Holwill, Matthew and Mullan, Ciaran and Kim, Minsoo and Gorbachev, R. V. and Thompson, Michael and Prance, Jonathan and Taniguchi, T. and Watanabe, K. and Grigorieva, I. V. and Novoselov, K. S. and Mishchenko, Artem and Fal'ko, V. I. and Geim, A. K. and Berdyugin, A. I. (2020) Long-range ballistic transport of Brown-Zak fermions in graphene superlattices. Nature Communications, 11: 5756. ISSN 2041-1723

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Abstract

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational (p/q) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 106 cm2 V−1 s−1 and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are 4q times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1 K. We also found negative bend resistance at 1/q fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field.