Ballistic semiconductor structures have allowed the realization of optics-like phenomena in electronic systems, including the magnetic focusing1 and electrostatic lensing2 of electrons. An extension that appears unique to graphene is to use both n and p carrier types to create electronic analogues of optical devices with both positive and negative indices of refraction3. Here, we use the gate-controlled density of both p and n carrier types in graphene to demonstrate the electronic analogue of fibre-optic guiding4,5,6,7,8. Two basic effects are investigated: bipolar p–n junction guiding, based on the principle of angle-selective transmission through the interface between the graphene and the p–n junction; and unipolar fibre-optic guiding, using total internal reflection controlled by carrier density. We also demonstrate modulation of the guiding efficiency through gating, and comparison of these data with numerical simulations indicates that guiding performance is limited by the roughness of the interface. The development of p–n and fibre-optic guiding in graphene may lead to electrically reconfigurable wiring in high-mobility devices.
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van Houten, H. et al. Coherent electron focusing with quantum point contacts in a two-dimensional electron gas. Phys. Rev. B 39, 8556–8575 (1989).
Sivan, U., Heiblum, M., Umbach, C. P. & Strickman, H. Electrostatic electron lens in the ballistic regime. Phys. Rev. B 41, 7937–7940 (1990).
Cheianov, V. V., Fal'ko, V. I. & Altshuler, B. L. The focusing of electron flow and a Veselago lens in graphene p–n junctions. Science 315, 1252–1255 (2007).
Beenakker, C. W. J., Sepkhanov, R. A., Akhmerov, A. R. & Tworzydlo, J. Quantum Goos–Hänchen effect in graphene. Phys. Rev. Lett. 102, 146804 (2009).
Zhang, F. -M., He, Y. & Chen, X. Guided modes in graphene waveguides. Appl. Phys. Lett. 94, 212105 (2009).
Villegas, C. E. P. & Tavares, R. S. Comment on ‘Guided modes in graphene waveguides’ [Appl. Phys. Lett. 94, 212105 (2009)]. Appl. Phys. Lett. 96, 186101 (2010).
He, Y., Zhang, F. -M. & Chen, X. Response to “Comment on ‘Guided modes in graphene waveguides’” [Appl. Phys. Lett. 96, 186101 2010]. Appl. Phys. Lett. 96, 186102 (2010).
Wu, Z. Electronic fibre in graphene. Preprint at http://arxiv.org/abs/1008.2495 (2010).
Castro Neto, A. H. et al. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
Beenakker, C. W. J. Colloquium: Andreev reflection and Klein tunneling in graphene. Rev. Mod. Phys. 80, 1337–1354 (2008).
Geim, A. K. Graphene: status and prospects. Science 324, 1530–1534 (2009).
Huard, B. et al. Transport measurements across a tunable potential barrier in graphene. Phys. Rev. Lett. 98, 236803 (2007).
Williams, J. R., DiCarlo, L. & Marcus, C. M. Quantum Hall effect in a gate-controlled p–n junction of graphene. Science 317, 638–641 (2007).
Özyilmaz, B. et al. Electronic transport and quantum Hall effect in bipolar graphene p–n–p junctions. Phys. Rev. Lett. 99, 166804 (2007).
Cheianov, V. V. & Fal'ko, V. I. Selective transmission of Dirac electrons and ballistic magnetoresistance of n–p junctions in graphene. Phys. Rev. B 74, 041403(R) (2006).
Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620–625 (2006).
Low, T., Hong, S., Appenzeller, J., Datta, S. & Lundstrom, M. S. Conductance asymmetry of graphene p–n junction. IEEE Trans. Electron. Dev. 56, 1292–1299 (2009).
Stander, N., Huard, B. & Goldhaber-Gordon, D. Evidence for Klein tunneling in graphene p–n junctions. Phys. Rev. Lett. 102, 026807 (2009).
Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Phys. 5, 222–226 (2009).
Park, C. H., Son, Y. -W., Yang, L., Cohen, M. & Louie, S. G. Electron beam supercollimation in graphene superlattices. Nano Lett. 8, 2920–2924 (2008).
Low, T. & Appenzeller, J. Electronic transport properties of a tilted graphene p–n junction. Phys. Rev. B 80, 155406 (2009).
Hartmann, R. R., Robinson, N. J. & Portnoi, M. E. Smooth electron waveguides in graphene. Phys. Rev. B 81, 245431 (2010).
Mishchenko, E. G., Shytov, A. V. & Silvestrov, P. G. Guided plasmons in graphene p–n junctions. Phys. Rev. Lett. 104, 156806 (2010).
Cesar, E. P., Villegas, M. & Tavares, R. S. Strongly coupled modes in bi-waveguides based on graphene. Solid State Commun. 150, 1350–1354 (2010).
Dragoman, D. & Dragoman, M. Quantum-Classical Analogies (Spinger, 2004).
Wilson, D. W., Glytsis, E. N. & Gaylord, T. K. Electron waveguiding characteristics and ballistic current capacity of semiconductor quantum slabs. IEEE J. Quant. Electron. 29, 1364–1382 (1993).
Zhang, L. M. & Fogler, M. M. Nonlinear screening and ballistic transport in a graphene p–n junction. Phys. Rev. Lett. 100, 116804 (2008).
Rossi, E., Bardarson, J. H., Brouwer, P. W. & Das Sarma, S. Signatures of Klein tunneling in disordered graphene p–n–p junctions. Phys. Rev. B 81, 121408(R) (2010).
Shytov, A., Rudner, M. S. & Levitov, L. S. Klein backscattering and Fabry–Pérot interference in graphene heterojunctions. Phys. Rev. Lett. 101, 156804 (2008).
Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nature Phys. 6, 30–33 (2009).
Levy, N. et al. Strain-induced pseudomagnetic fields greater than 300 tesla in graphene nanobubbles. Science 329, 544–547 (2010).
Device fabrication was carried out using Harvard's Center for Nanoscale Systems, a member of the National Nanotechnology Infrastructure Network under National Science Foundation award ECS-0335765, and was supported in part by the Institute for Nanoelectronics Discovery and Exploration, a Nanoelectronics Research Initiative Center, and the Harvard Nanoscale Science and Engineering Center.
The authors declare no competing financial interests.
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Williams, J., Low, T., Lundstrom, M. et al. Gate-controlled guiding of electrons in graphene. Nature Nanotech 6, 222–225 (2011). https://doi.org/10.1038/nnano.2011.3
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