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

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.

Out-of-equilibrium criticalities in graphene superlattices

“…Next, assuming that different electronic minibands did not overlap so that nS should be zero at NPs, we calculated nS around them as nS = Cg(Vg -VNP)/e. The resulting linear dependences nS(Vg) were separated by VHS where nS abruptly changed its sign (42). The found vd are shown in figs.…”

“…1A-C of the main text). To find nS, we followed the procedure described in (42). Briefly, we first used Hall measurements in small magnetic fields (section #2) to extract the geometrical capacitance Cg to the back gate and to find gate voltages Vg for NPs and VHS (VNP and VVHS, respectively).…”

New Class of Landau Levels and Hall Phases in a 2D Electron Gas Subject to an Inhomogeneous Magnetic Field: An Analytic Solution

“…Further, in the presence of a periodic potential, the Landau levels develop mini-gaps and for the energy spectrum a self-similar fractal pattern emerges, known as the Hofstadter butterfly, 6 which has become experimentally accessible via magnetotransprot measurements in Moiré materials. [7][8][9][10] The study of Landau levels and topological edge states is still very actively pursued and is currently even considered in quantum optics and cavity quantum electrodynamics (QED), where ultra-strong coupling of the Landau levels to the quantum vacuum fluctuations and the control of conduction properties have been achieved experimentally in a cavity, [11][12][13][14] with several theoretical studies and proposals accompanying these developments. [15][16][17][18][19] In parallel to the fundamental investigation of quantum systems exposed to magentic fields, the study of impurity models has a long lasting tradition in solid state physics.…”

Effect of boron nitride defects and charge inhomogeneity on 1/f noise in encapsulated graphene

“…7 This has opened a new field of moir e physics. [8][9][10] Moreover, hBN is being used as an encapsulating layer in various twodimensional (2D) materials, such as semiconductor transition metal dichalcogenides (TMDs), superconductor NBSe 2 , semimetal black phosphorous, and ferromagnet CRI 3 . [11][12][13][14] Encapsulating these materials with hBN leads to a reduction in charge inhomogeneity and also protects the material from degradation.…”