Exploiting the light-like properties of carriers in graphene could allow extreme non-classical forms of electronic transport to be realized [1][2][3][4][5][6][7][8] . In this vein, finding ways to confine and direct electronic waves through nanoscale streams and streamlets, unimpeded by the presence of other carriers, has remained a grand challenge [9][10][11][12] . Inspired by guiding of light in fibre optics, here we demonstrate a route to engineer such a flow of electrons using a technique for mapping currents at submicron scales. We employ real-space imaging of current flow in graphene to provide direct evidence of the confinement of electron waves at the edges of a graphene crystal near charge neutrality. This is achieved by using superconducting interferometry in a graphene Josephson junction and reconstructing the spatial structure of conducting pathways using Fourier methods 13. The observed edge currents arise from coherent guided-wave states, confined to the edge by band bending and transmitted as plane waves. As an electronic analogue of photon guiding in optical fibres, the observed states a ord non-classical means for information transduction and processing at the nanoscale.

How a many-body quantum system thermalizes -or fails to do so-under its own interaction is a fundamental yet elusive concept. Here we demonstrate nuclear magnetic resonance observation of the emergence of prethermalization by measuring out-of-time ordered correlations. We exploit Hamiltonian engineering techniques to tune the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal outof-time ordered correlations. At large fields, we observe an emergent conserved quantity due to prethermalization, which can be revealed by an early saturation of correlations. Our experiment not only demonstrates a new protocol to measure out-of-time ordered correlations, but also provides new insights in the study of quantum thermodynamics.

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.

In a recent experimental paper [Bid et al., Nature 466, 585 (2010)] a qualitative confirmation of the existence of upstream neutral modes at the ν = 2 3 quantum Hall edge was reported. Using the chiral Luttinger liquid theory of the quantum Hall edge we develop a quantitative model of the experiment of Bid et al. A good quantitative agreement of our theory with the experimental data reinforces the conclusion of the existence of the upstream neutral mode. Our model also enables us to extract important quantitative information about nonequilibrium processes in Ohmic and tunneling contacts from the experimental data. In particular, for ν = 2 3 , we find a power-law dependence of the neutral mode temperature on the charge current injected from the Ohmic contact.