Visualization of charge transport through Landau levels in graphene

Abstract

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 scattering 1 . Recent progress in understanding such effects in low-dimensional carrier gases in conventional semiconductors has been achieved by realspace 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.Since the demonstration of the unusual half-integer QHE in graphene 4,5 , many related QHE experiments have been interpreted within the framework of edge-state transport [6][7][8] , that is, the backscattering-free flow of charge through edge states 9 bounded by insulating barriers with incompressible electron densities 10 . Although compressible and incompressible electron densities have recently been observed in graphene 11 , their role in shaping the QHE in graphene remains to be explained. Spatially inhomogeneous charge distributions owing to adsorbate-induced surface doping 12 are expected to be particularly pronounced in graphene and could cause deviations from pure edge-state transport. Here, we use scanning photocurrent microscopy to explore these effects by mapping carrier propagation through graphene Landau levels in the QHE regime.The experiments were carried out on two-terminal monolayer graphene field-effect devices at 4.2 K and in magnetic fields B up to ±9 T (Fig. 1a,b). In these conditions, the conductance of our devices (Fig. 1c) shows series of local extrema 6,8,11,13,14 associated with individual Landau levels 13,15 , with maxima predicted to occur at quantized Hall conductances of 2, 4, 6, 10 and 14 e 2 /h (refs 13,15). The observed maxima are higher owing to an inhomogeneous filling-factor distribution across the device, as shown below.Photocurrent maps were obtained by scanning a focused laser across the graphene channel, and recording the two-terminal photocurrent signal as a function of beam position. Previously, a similar approach has been used to investigate contact-induced band bending [16][17][18][19] and the photo-thermoelectric effect 20 in graphene at B = 0, as well as the electrostatics of the QHE in conventional semiconductor devices [21][22][23] . We observe that the gate-voltagedependent photocurrent at fixed locations is oscillatory, with polarity determined by the direction of the magnetic field (Fig. 1d). Such local oscillations are due to a recurring global photocurrent distribution across the device, sy...

Shockley-Ramo theorem and long-range photocurrent response in gapless materials

“…In general, α is finite in all materials, whereas β is only non-zero in chiral systems where edge-state transport allows j ph to be directed along the contours of n(r). This is the case in chiral materials such as topological insulators due to coupling between orbital motion and spin 4,5,16 , or in non-chiral materials in the presence of a magnetic field 14 . The effects of spatial inhomogeneity are illustrated in Fig.3 for the chiral response (a) and the nonchiral response (b).…”

“…ized near current-collecting contacts, the photocurrent hot spots feature complex spatial patterns spanning the entire system area, typically separated by many microns from the contacts [11][12][13][14][15] . These large length scales may seem hard to reconcile with the short picosecond-scale recombination times over which the photoexcited carriers lose their energy and become part of the thermal distribution, traversing distances much less than system size.…”

“…Recently, however, a long-range photocurrent response was reported in systems where carrier recombination is fast on the carrier diffusion timescales. Notably, this is the case in scanning photocurrent experiments that probe new gapless materials, such as graphene and topological insulators [10][11][12][13][14][15][16] . Photoresponse in these systems is of a distinctly global character: rather than being local-…”

Photo-Nernst current in graphene

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Photocurrent measurements provide a powerful means of studying the spatially resolved optoelectronic and electrical properties of a material or device [1][2][3][4][5][6][7] . Generally speaking there are two classes of mechanism for photocurrent generation: those involving separation of electrons and holes, and thermoelectric e ects driven by electron temperature gradients.

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“…In contrast, in a gapless material such as graphene the full electron distribution rapidly thermalizes, eliminating the distinction between electrons and holes. Nevertheless, photocurrent is readily produced when light is focused on inhomogeneous regions or junctions in graphene devices 6,7,[13][14][15][16][17][18][19][20] . Detailed measurements of the dependence on gate voltage and time delay have shown that it is primarily of a thermoelectric nature 6,11,13,17,19 , and that the heating of the electrons is sometimes enhanced by slow energy transfer to the lattice due to the large optical phonon energy and high electron velocity 14,[21][22][23][24][25][26] .…”