Topological materials may exhibit Hall-like currents flowing transversely to the applied electric field even in the absence of a magnetic field. In graphene superlattices, which have broken inversion symmetry, topological currents originating from gr
aphenes two valleys are predicted to flow in opposite directions and combine to produce long-range charge neutral flow. We observe this effect as a nonlocal voltage at zero magnetic field in a narrow energy range near Dirac points at distances as large as several microns away from the nominal current path. Locally, topological currents are comparable in strength to the applied current, indicating large valley-Hall angles. The long-range character of topological currents and their transistor-like control by gate voltage can be exploited for information processing based on the valley degrees of freedom.
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 t
heir 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.
The next-nearest neighbor hopping term t determines a magnitude and, hence, importance of several phenomena in graphene, which include self-doping due to broken bonds and the Klein tunneling that in the presence of t is no longer perfect. Theoretical
estimates for t vary widely whereas a few existing measurements by using polarization resolved magneto-spectroscopy have found surprisingly large t, close or even exceeding highest theoretical values. Here we report dedicated measurements of the density of states in graphene by using high-quality capacitance devices. The density of states exhibits a pronounced electron-hole asymmetry that increases linearly with energy. This behavior yields t approx -0.30 eV +-15%, in agreement with the high end of theory estimates. We discuss the role of electron-electron interactions in determining t and overview phenomena which can be influenced by such a large value of t.
Capacitance measurements provide a powerful means of probing the density of states. The technique has proved particularly successful in studying 2D electron systems, revealing a number of interesting many-body effects. Here, we use large-area high-qu
ality graphene capacitors to study behavior of the density of states in this material in zero and high magnetic fields. Clear renormalization of the linear spectrum due to electron-electron interactions is observed in zero field. Quantizing fields lead to splitting of the spin- and valley-degenerate Landau levels into quartets separated by interaction-enhanced energy gaps. These many-body states exhibit negative compressibility but the compressibility returns to positive in ultrahigh B. The reentrant behavior is attributed to a competition between field-enhanced interactions and nascent fractional states.
