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Kondo effect in bilayer graphene

Kondo effect in bilayer graphene. Diego Mastrogiuseppe , Sergio Ulloa & Nancy Sandler. Department of Physics & Astronomy Ohio University , Athens, OH. Kondo effect in a simple metal. Anderson model. Schrieffer-Wolff transformation. Kondo model.

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Kondo effect in bilayer graphene

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  1. Kondo effect in bilayergraphene Diego Mastrogiuseppe, Sergio Ulloa & Nancy Sandler Department of Physics & Astronomy Ohio University, Athens, OH

  2. Kondo effect in a simple metal Anderson model Schrieffer-Wolff transformation Kondo model Crossover between free spin behavior and entanglement between impurity spin and conduction electrons

  3. Motivation Kondo effect in single layergraphene Pseudogap needed for Kondo regime D. Withoff and E. Fradkin, PRL 64, 1835 (1990) K. Ingersent, PRB 54, 11936 (1996) Image: A. Castro Neto et al, RMP 81,109 (2009) Kondo in graphene M. HentschelM. and F. Guinea, PRB, 76 (2007) B. Dora and P. Thalmeier, PRB 76, 115435 (2007) K. Sengupta and G. Baskaran, PRB 77, 045417 (2008) P. Cornaglia et al, PRL 102, 046801 (2009) Z-G Zhu et al, EPL 90, 67001 (2010) T. O. Wehling et al, PRB 81, 115427 (2010) B. Uchoa et al, PRL 106, 016801 (2011)

  4. Motivation Kondo effect in bilayergraphene Kondo effect in single layergraphene (unpublished)

  5. Bilayer graphene – band structure Bernal stacking A2 B2 A1 B1 Feature in DOS at

  6. Addition of theimpurity

  7. Schrieffer-Wolff transformation band electrons impurity Anderson modelforbilayer hybridization With a suitablechoice of S tofirstorder in V Kondo model

  8. Results Diagonalizing (and for ) twoeigenvalues are 0 and Two effective channels coupled to the impurity, but no possibility of 2-channel Kondo We are goingtoconcentrate in

  9. Half filling Reduces toeffective single layerproblem Theresultisinsensitiveto therelationship in Fortheimpurity in themiddle of thehexagon, J = 0 • T. O. Wehling et al, PRB 81, 115427 (2010) • B. Uchoa et al, PRL 106, 016801 (2011)

  10. Away from half-filling Problemwith SW tranformation Possibleissues(work in progress): Wegetclosertothejump in DOS Interbandscatteringinducedbyimpurity (ischargewelldefined?) Mayhigherordercommutators in SW regularizethedivergences?

  11. Conclusions • Two effective channels coupled to the impurity (FM, AFM). No possibility of two-channel Kondo. • Quadratic bands at half filling, no need of a critical J for having Kondo. • At half-fillingtheresults reduce toaneffective single layerproblem. • Awayfromhalffilling, problemwith SW transformation(jump in DOS, interbandscattering, higherorderterms in SW).

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