Have Mysterious Topological Valley Currents Been Observed in Graphene Superlattices?

We provide a critical discussion concerning the claim of topological valley currents, driven by a global Berry curvature and valley Hall effect proposed in recent litterature. After pointing out a major inconsistency of the theoretical scenario proposed to interpret giant nonlocal resistance, we discuss possible alternative explanations and open directions of research to solve the mystery of nonlocal transport in graphene superlattices.

Low-symmetry nonlocal transport in microstructured squares of delafossite metals

Intense work studying the ballistic regime of electron transport in two-dimensional systems based on semiconductors and graphene had been thought to have established most of the key experimental facts of the field. In recent years, however, additional forms of ballistic transport have become accessible in the quasi–two-dimensional delafossite metals, whose Fermi wavelength is a factor of 100 shorter than those typically studied in the previous work and whose Fermi surfaces are nearly hexagonal in shape and therefore strongly faceted. This has some profound consequences for results obtained from the classic ballistic transport experiment of studying bend and Hall resistances in mesoscopic squares fabricated from delafossite single crystals. We observe pronounced anisotropies in bend resistances and even a Hall voltage that is strongly asymmetric in magnetic field. Although some of our observations are nonintuitive at first sight, we show that they can be understood within a nonlocal Landauer-Büttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of nonlocal transport can be resolved for squares of linear dimension of nearly 100 µm, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated.

Topological valley currents via ballistic edge modes in graphene superlattices near the primary Dirac point

Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance (Rnl) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which Rnl at SDP is negligible, but below 60 K approaches the value of h/2e2 in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 μm. Furthermore, nonlocal transport transmission probabilities based on the Landauer-Büttiker formalism show evidence for spin-degenerate ballistic valley-helical edge modes, which are key for the development of valleytronics.