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The graphene edge state has long been predicted to be a zero energy, one-dimensional electronic waveguide mode that dominates transport in neutral graphene nanostructures, with potential application to graphene devices. However, its exceptional properties have been observed in only a few cases, each employing novel fabrication methods without a clear path to large-scale integration. We show here that interconnected edge-state networks can be produced using non-conventional facets of electronics grade silicon carbide wafers and scalable lithography, which cuts the epitaxial graphene and apparently fuses its edge atoms to the silicon carbide substrate. Measured epigraphene edge state (EGES) conduction is ballistic with mean free paths exceeding tens of microns, thousands of times greater than for the diffusive 2D bulk. It is essentially independent of temperature, decoupled from the bulk and substantially immune to disorder. Remarkably, EGES transport involves a non-degenerate conductance channel that is pinned at zero energy, yet it does not generate a Hall voltage, implying balanced electron and hole components. These properties, observed at all tested temperatures, magnetic fields, and charge densities, are not predicted by present theories, and point to a zero-energy spin one-half quasiparticle, composed of half an electron and a half a hole moving in opposite directions.
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We investigate an effective low energy theory of HgTe quantum wells near their mass inversion thickness in a perpendicular magnetic field. By comparison of the effective band structure with a more elaborated and well-established model, the parameter regime and the validity of the effective model is scrutinized. Optical transitions in HgTe quantum wells are analyzed. We find selection rules which we functionalize to optically manipulate edge state transport. Qualitatively, our findings equally apply to optical edge current manipulation in graphene.
We report electrical conductance measurements of Bi nanocontacts created by repeated tip-surface indentation using a scanning tunneling microscope at temperatures of 4 K and 300 K. As a function of the elongation of the nanocontact we measure robust, tens of nanometers long plateaus of conductance G0 = 2e^2/h at room temperature. This observation can be accounted for by the mechanical exfoliation of a Bi(111) bilayer, a predicted QSH insulator, in the retracing process following a tip-surface contact. The formation of the bilayer is further supported by the additional observation of conductance steps below G0 before break-up at both temperatures. Our finding provides the first experimental evidence of the possibility of mechanical exfoliation of Bi bilayers, of the existence of the QSH phase in a two-dimensional crystal, and, most importantly, of the observation of the QSH phase at room temperature.
Topological insulators realized in materials with strong spin-orbit interactions challenged the long-held view that electronic materials are classified as either conductors or insulators. The emergence of controlled, two-dimensional moire patterns has opened new vistas in the topological materials landscape. Here we report on evidence, obtained by combining thermodynamic measurements, local and non-local transport measurements, and theoretical calculations, that robust topologically non-trivial, valley Chern insulators occur at charge neutrality in twisted double-bilayer graphene (TDBG). These time reversal-conserving valley Chern insulators are enabled by valley-number conservation, a symmetry that emerges from the moire pattern. The thermodynamic gap extracted from chemical potential measurements proves that TDBG is a bulk insulator under transverse electric field, while transport measurements confirm the existence of conducting edge states. A Landauer-Buttiker analysis of measurements on multi-terminal samples allows us to quantitatively assess edge state scattering and demonstrate that it does not destroy the edge states, leaving the bulk-boundary correspondence largely intact.
The recent observation of non-classical electron transport regimes in two-dimensional materials has called for new high-resolution non-invasive techniques to locally probe electronic properties. We introduce a novel hybrid scanning probe technique to map the local resistance and electrochemical potential with nm- and $mu$V resolution, and we apply it to study epigraphene nanoribbons grown on the sidewalls of SiC substrate steps. Remarkably, the potential drop is non uniform along the ribbons, and $mu$m-long segments show no potential variation with distance. The potential maps are in excellent agreement with measurements of the local resistance. This reveals ballistic transport in ambient condition, compatible with micrometer-long room-temperature electronic mean free paths.
A two-dimensional topological insulator (2DTI) has an insulating bulk and helical spin-polarised edge modes robust to backscattering by non-magnetic disorder. While ballistic transport has been demonstrated in 2DTIs over short distances, larger samples show significant backscattering and a nearly temperature-independent resistance whose origin is unclear. 2DTI edges have shown a spin polarisation, however the degree of helicity is difficult to quantify from spin measurements. Here, we study 2DTI few-layer Na3Bi on insulating Al2O3. A non-local conductance measurement geometry enables sensitive detection of the edge conductance in the topological regime, with an edge mean free path ~100 nm. Magnetic field suppresses spin-flip scattering in the helical edges, resulting in a giant negative magnetoresistance (GNMR), up to 80% at 0.9 T. Comparison to theory indicates >98% of scattering is helical spin scattering significantly exceeding the maximum (67%) expected for a non-helical metal. GNMR, coupled with non-local measurements demonstrating edge conduction, thus provides an unambiguous experimental signature of helical edges that we expect to be generically useful in understanding 2DTIs.
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