RKKY/Kondo Transition on Edges of Quantum Spin Hall Samples: the NRG approach

Michael Lichtenegger, LMU

15.03.2019 at 09:00 

We study two Kondo impurities coupled to helical edge modes of 2D topological insulator [1] which is described by using a Kane Mele lattice model [2]. The physics of such a system isdetermined by a competition of two seminal phenomena: The Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect exchange interaction.The Kondo phase is normally suppressed in 1D usual systems, thus the RKKY phase dominatesin a huge range of Kondo couplings and inter-impurity distances. However, the Kondo/RKKYcompetition in a helical system is highly nontrivial [3]: the Kondo effect overwhelms the RKKYinteraction even at small distances in the presence of either the Coulomb interaction or the mag-netic anisotropy.
This behavior can be explained with phenomenological Doniach’s criterion [4]. A detailed analyt-ical theory of RKKY/Kondo transition is still missing.Numerical treatment is needed as a complimentary tool to the existing analytical theory [3] toinvestigate details of the transition in a real lattice model. We have chosen the NRG approachas the appropriate numerical tool. Our results qualitatively confirm predictions of Ref. [3] andreveal several unexpected features of the RKKY/Kondo transition which reflect nontrivial physicsof helical systems.

References

[1] Hasan, M. Zahid and Kane, Charles L., Rev. Mod. Phys. 82, 3045 (2010).
[2] Kane, Charles L. and Mele, Eugene J., Phys. Rev. Lett. 95, 226801 (2005).
[3] Yevtushenko, Oleg M. and Yudson, Vladimir I., Phys. Rev. Lett. 120, 147201 (2018).
[4] Doniach, S., Physica B+C 91, 231-234 (1977)