Visualizing the edge states in graphene

(1) Band bending and the associated spatially inhomogeneous population of Landau levels play a central role in the physics of the quantum Hall effect (QHE) by constraining the pathways for charge-carrier transport and scattering¹. Recent progress in understanding such effects in low-dimensional carrier gases in conventional semiconductors has been achieved by real-space mapping using local probes^{2, 3}. Here, we use spatially resolved photocurrent measurements in the QHE regime to study the correlation between the distribution of Landau levels and the macroscopic transport characteristics in graphene. Spatial maps show that the net photocurrent is determined by hot carriers transported to the periphery of the graphene channel, where QHE edge states provide efficient pathways for their extraction to the contacts. The photocurrent is sensitive to the local filling factor, which allows us to reconstruct the local charge density in the entire conducting channel of a graphene device. [doi:10.1038/nphys1745]

(2) Spintronics, where the spin of electrons is used to carry information, is a rapidly growing area of research^{1, 2}. There are several techniques for generating pure spin currents^{3, 4, 5, 6, 7, 8, 9, 10}; however, there is no method that can directly detect them, largely because they carry no net charge current and no net magnetization. At present, studies of pure spin currents rely on measuring the induced spin accumulation with either optical techniques^{5, 11, 12, 13} or spin-valve configurations^{14, 15, 16, 17}. However, spin accumulation does not directly reflect the spatial distribution or temporal dynamics of the pure spin current, and therefore does not give a real-time or real-space measurement. Here we demonstrate a second-order nonlinear optical effect of the pure spin current that has never been explored before, and show that it can be used for the non-invasive, non-destructive and real-time imaging of pure spin currents. The detection scheme can be applied in a wide range of materials with different electronic band structures because it does not rely on optical resonances. Furthermore, the control of nonlinear optical properties of materials with pure spin currents may have potential applications in photonics integrated with spintronics. [doi:10.1038/nphys1742]