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The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

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Abstract

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T<T K , is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.

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References

  1. Kondo, J.: Resistance minimum in dilute magnetic alloys. Prog. Theor. Phys. 32, 37 (1964)

    Article  ADS  Google Scholar 

  2. Hewson, A.C.: The Kondo Problem to Heavy Fermions. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  3. Goldhaber-Gordon, D., Shtrikman, H., Mahalu, D., Abusch-Magder, D., Meirav, U., Kastner, M.A.: Kondo effect in a single-electron transistor. Nature 391, 156 (1998)

    Article  ADS  Google Scholar 

  4. Cronenwett, S.M., Oosterkamp, T.H., Kouwenhoven, L.P.: A tunable Kondo effect in quantum dots. Science 281, 540 (1998)

    Article  ADS  Google Scholar 

  5. Li, J., Schneider, W., Berndt, R., Delley, B.: Kondo scattering observed at a single magnetic impurity. Phys. Rev. Lett. 80, 2893 (1998)

    Article  ADS  Google Scholar 

  6. Madhavan, V., Chen, W., Jamneala, T., Crommie, M.F., Wingreen, N.S.: Tunneling into a single magnetic atom: spectroscopic evidence of the Kondo resonance. Science 280, 567 (1998)

    Article  ADS  Google Scholar 

  7. Rashba, E.I., Sheka, V.I.: Fiz. Tverd. Tela (Leningrad) Sb. II, 162 (1959); 3, 1735 (1961). [English translation: Combinational resonance of zonal electrons in crystals having a zinc blende lattice. Sov. Phys. Solid State 3, 1257 (1961)]

    Google Scholar 

  8. Winkler, R.: Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems. Springer, Erlangen (2003)

    Google Scholar 

  9. Hassenkam, T., Pedersen, S., Baklanov, K., Kristensen, A., Sorensen, C.B., Lindelof, P.E., Pikus, F.G., Pikus, G.E.: Spin splitting and weak localization in (110) GaAs/Al x G1−x quantum wells. Phys. Rev. B 55, 9298 (1997) and references therein

    Article  ADS  Google Scholar 

  10. LaShell, S., McDougall, B.A., Jensen, E.: Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy. Phys. Rev. Lett. 77, 3419 (1996)

    Article  ADS  Google Scholar 

  11. Peterson, L., Hedegård, P.: A simple tight-binding model of spin-orbit splitting of sp-derived surface states. Surf. Sci. 459, 49 (2000)

    Article  Google Scholar 

  12. Nicolay, G., Reinart, F., Hüfner, S., Blaha, P.: Spin-orbit splitting of the L-gap surface state on Au(111) and Ag(111). Phys. Rev. B 65, 033407 (2002)

    Article  ADS  Google Scholar 

  13. Meir, Y., Wingreen, N.S.: Spin-orbit scattering and the Kondo effect. Phys. Rev. B 50, 4947 (1994)

    Article  ADS  Google Scholar 

  14. Sun, Q.-F., Wang, J., Guo, H.: Quantum transport theory for nanostructures with Rashba spin-orbital interaction. Phys. Rev. B 71, 165310 (2005)

    Article  ADS  Google Scholar 

  15. Simonin, J.: Kondo quantum dots and the novel Kondo-doublet interaction. Phys. Rev. Lett. 97, 266804 (2006)

    Article  ADS  Google Scholar 

  16. López, R., Sánchez, D., Serra, L.: From Coulomb blockade to the Kondo regime in a Rashba dot. Phys. Rev. B 76, 035307 (2007)

    Article  ADS  Google Scholar 

  17. Ding, G.-H., Dong, B.: Spin-orbit coupling effect on the persistent currents in mesoscopic ring with an Anderson impurity. arXiv:0704.0319 (2007)

  18. Simon, P., Affleck, I.: Kondo screening cloud effects in mesoscopic devices. Phys. Rev. B 68, 115304 (2003)

    Article  ADS  Google Scholar 

  19. Anderson, P.W., Clogston, A.M.: Bull. Am. Phys. Soc. 6, 124 (1961)

    Google Scholar 

  20. Anderson, P.W.: Localized magnetic states in metals. Phys. Rev. 124, 41 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  21. Jusserand, B., Richards, D., Peric, H., Etienne, B.: Zero-magnetic-field spin splitting in the GaAs conduction band from Raman scattering on modulationdoped quantum wells. Phys. Rev. Lett. 69, 848 (1992)

    Article  ADS  Google Scholar 

  22. Jusserand, B., Richards, D., Allan, G., Priester, C., Etienne, B.: Spin orientation at semiconductor heterointerfaces. Phys. Rev. B 51, 4707 (1995)

    Article  ADS  Google Scholar 

  23. Popović, D., Reinert, F., Hüfner, S., Springborg, M., Cercellier, H., Fagot-Revurat, Y., Kierren, B., Malterre, D.: High-resolution photoemission on Ag/Au(111): spin-orbit splitting and electronic localization of the surface state. Phys. Rev. B 72, 045419 (2005)

    Article  ADS  Google Scholar 

  24. Schrieffer, J.R., Wolff, P.A.: Relation between the Anderson and Kondo Hamiltonians. Phys. Rev. 149, 491 (1966)

    Article  ADS  Google Scholar 

  25. Újsághy, O., Zawadowski, A.: Spin-orbit-induced magnetic anisotropy for impurities in metallic samples. I. Surface anisotropy. Phys. Rev. B 57, 11598 (1998)

    Article  ADS  Google Scholar 

  26. Újsághy, O., Zawadowski, A.: Spin-orbit-induced magnetic anisotropy for impurities in metallic samples. II. Finite-size dependence in the Kondo resistivity. Phys. Rev. B 57, 11609 (1998)

    Article  ADS  Google Scholar 

  27. Grundler, D.: Large Rashba splitting in InAs quantum wells due to electron wave function penetration into the barrier layers. Phys. Rev. Lett. 84, 6074 (2000)

    Article  ADS  Google Scholar 

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Correspondence to Justin Malecki.

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Malecki, J. The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling. J Stat Phys 129, 741–757 (2007). https://doi.org/10.1007/s10955-007-9414-x

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