Aharonov-Bohm and Relativistic Corbino Effects in Graphene: A Comparative Study of Two Quantum Interference Phenomena

• Authors: A. Rycerz
• Languages of publication: EN

Abstracts

EN

This is an analytical study of magnetic fields effects on the conductance, the shot noise power, and the third charge-transfer cumulant for the Aharonov-Bohm rings and the Corbino disks in graphene. The two distinct physical mechanisms lead to very similar magnetotransport behaviors. Differences are unveiled when discussing the third-cumulant dependence on magnetic fields.

Keywords

EN

72.80.Vp; 73.43.Qt; 73.63.-b

Discipline

• 73.63.-b: Electronic transport in nanoscale materials and structures(see also 73.23.-b Electronic transport in mesoscopic systems)
• 72.80.Vp: Electronic transport in graphene
• 73.43.Qt: Magnetoresistance(see also 75.47.-m Magnetotransport phenomena; materials for magnetotransport in magnetic properties and materials)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 5-6
• Pages: 1242-1245

Dates

published

2012-05

Contributors

author

A. Rycerz

• Instytut Fizyki im. Mariana Smoluchowskiego, Uniwersytet Jagielloński, W.S. Reymonta 4, PL-30-059 Kraków, Poland

References

• 1. G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984)
• 2. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Y. Zhang, Nature 438, 197 (2005)
• 3. Yu.V. Nazarov, Ya.M. Blanter, Quantum Transport: Introduction to Nanoscience, Cambridge University Press, Cambridge 2009
• 4. Y. Imry, R.A. Webb, Sci. Am. 260, 36 (1989)
• 5. K. Popper, The Logic of Scientific Discovery, Routledge Classics, New York 2002, Appendix V
• 6. P. Recher, B. Trauzettel, A. Rycerz, Ya.M. Blanter, C.W.J. Beenakker, A.F. Morpurgo, Phys. Rev. B 76, 235404 (2007); M. Zarenia, J.M. Pereira Jr., A. Chaves, F.M. Peeters, G.A. Farias, ibid., 81, 045431 (2010)
• 7. S. Russo, J.B. Oostinga, D. Wehenkel, H.B. Heersche, S.S. Sobhani, L.M.K. Vandersypen, A.F. Morpurgo, Phys. Rev. B 77, 085413 (2008); C. Stampfer, E. Schurtenberger, F. Molitor, J. Guettinger, T. Ihn, K. Ensslin, Int. J. Mod. Phys. 23, 2647 (2009)
• 8. A. Rycerz, Acta Phys. Pol. A 115, 322 (2009); J. Wurm, M. Wimmer, H.U. Baranger, K. Richter, Semicond. Sci. Technol. 25, 034003 (2010); J. Schelter, D. Bohr, B. Trauzettel, Phys. Rev. B 81, 195441 (2010)
• 9. A. Rycerz, Phys. Rev. B 81, 121404(R) (2010)
• 10. M.I. Katsnelson, Europhys. Lett. 89, 17001 (2010); M.I. Katsnelson, J. Comput. Theor. Nanosci. 8, 912 (2011)
• 11. B. Reulet, J. Senzier, D.E. Prober, Phys. Rev. Lett. 91, 196601 (2003); Y. Bomze, G. Gershon, D. Shovkun, L.S. Levitov, M. Reznikov, Phys. Rev. Lett. 95, 176601 (2005)
• 12. C.W.J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008)
• 13. Yu.V. Nazarov, Phys. Rev. B 47, 2768 (1993)
• 14. Typically, Γp ≪ 1 as for graphene rings with irregular edges there are only evenascent modes present in each of the ring arms at zero and weak dopings, see Refs. [7, 8]
• 15. More generally, for centrosymmetric field $B = B(r)ê_z$, the parameter $ϕ= Φ_{12}/Φ_0$ in Eq. (7) is replaced by [10]: $ϕ' ≡ Φ_1/Φ_{AB} + 4π/Φ_0 ∫_{r_1}^{r_2} dr/r ∫_{r_1}^{r} dr'r'B (r)$, where $Φ_1$ is flux through the inner ring ($r<r_1$). In particular, if B(r)=0 for $r>r_1$, the Aharonov-Bohm-like oscillations occur when varying $Φ_1$

Identifiers

DOI

10.12693/APhysPolA.121.1242