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Graphene pn -junctions and their ”applications”

Graphene Journal Club. Graphene pn -junctions and their ”applications”. 6 th of June 2007. Romain Danneau Nano Group r.danneau@boojum.hut.fi. Outline. Reminder on pn -junctions What is interesting in graphene pn -junctions? Theoretical work:

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Graphene pn -junctions and their ”applications”

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  1. Graphene Journal Club Graphene pn-junctions and their ”applications” 6th of June 2007 Romain Danneau Nano Group r.danneau@boojum.hut.fi

  2. Outline • Reminder on pn-junctions • What is interesting in graphene pn-junctions? • Theoretical work: - V.V. Cheianov and V.I. Fal’ko, PRB 74, 041403(R) (2006) - J. Tworzydło et al., cond-mat/0705.3763v1 - D.A. Abanin and L.S. Levitov, cond-mat/0704.3608v2 - A. Ossipov, M.Titov and C.W.J. Beenakker, PRB 75, 241401(R) (2007) - V.V. Cheianov, V.I. Fal’ko and B.L. Altshuler, Science 315, 1252 (2007) • Experimental work: - B. Huard et al., cond-mat/0704.2626v1, PRL (in press) - J.R. Williams, L. DiCarlo and C.M. Marcus, cond-mat/0407.3487v1 - B. Özilmaz et al., cond-mat/0705.3044v1

  3. Back to basics...pn-junctions in semiconductors pn junctions:building blocks formicroelectronics

  4. Graphene pn junctions from V.Y. Cheianov et al. Science 315, 1252 (2007)

  5. Massless particles in 2D: NEVER LOCALIZED -k k -  Absence of Localization (Klein paradox) Massive particles in 2D: always localized Klein paradox (propagation of relativistic particles through a barrier) O. Klein, Z. Phys53,157 (1929); 41, 407 (1927) Consequence of pseudo-spin conservation M.I. Katsnelson et al. Nature Physics 2, 660 (2006)

  6. 1- Magnetoresistance in graphenepn-junctions Conductance maximised for small angles Shot noise Electrostatic potential Transmission probability

  7. Magnetoresistance for three geometries for the Corbino geometry

  8. 2- Reentrance effect in graphene pn-junctions Reentrance in SN junctions:Conductance in a diffusive conductors increases if one contact is a superconductor(phase coherence of h-e pairs).Not valid at low T:h-e thermal coherence length exceeds the sample size

  9. 3 - Quantum Hall effect in graphene pn-junctions Φ the angle between the valley isospins at the two edges of the nanoribbon.

  10. 4 - Quantum Hall effect in graphene pn-junctions Fano Factor Conductance

  11. 5 - Quantum Hall effect in graphene pn-junctions non-convalent functionalization layer (NCFL) and Al2O3 grown by atomic layer deposition (ALD) between the top gate and graphene layer

  12. 5 - Quantum Hall effect in graphene pn-junctions B = 4 T, T = 250 mK B = 0 T, T = 4 K

  13. 6 - Quantum Hall effect in graphene pnp-junctions Hafnium oxide between top gate and graphene.

  14. 6 - Quantum Hall effect in graphene pnp-junctions QH im pnp-junctions: Even more steps... Graphene nanoribbon transistor made With local gate has a better ON/OFF ratio than with an overall back gate.

  15. 7 - Transport in graphene pnp-(or npn)-junctions

  16. 7 - Transport in graphene pnp-(or npn)-junctions T = 4 K Modeling of R is better in the ballistic regime pn-junctions=ballistic npn-junctions = far from ballistic

  17. 7 – Electronic lens with pn-junctions

  18. 7 – Electronic lens with pn-junctions The straight interface is able to focus electric current, whereas a ballistic stripe of p-type graphene separating two n-type regions acts as a lens.

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