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Magnetic Impurities on the Surface of a Topological Insulator

Qin Liu, Chao-Xing Liu, Cenke Xu, Xiao-Liang Qi, and Shou-Cheng Zhang
Phys. Rev. Lett. 102, 156603 – Published 17 April 2009
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    Abstract

    The surface states of a topological insulator are described by an emergent relativistic massless Dirac equation in 2+1 dimensions. In contrast with graphene, there is an odd number of Dirac points, and the electron spin is directly coupled to the momentum. We show that a magnetic impurity opens up a local gap and suppresses the local density of states. Furthermore, the Dirac electronic states mediate an RKKY interaction among the magnetic impurities which is always ferromagnetic, whenever the chemical potential lies near the Dirac point. Through this exchange mechanism, magnetic atoms uniformly deposited on the surface of a topological insulator could naturally form a ferromagnetically ordered film. These effects can be directly measured in STM experiments. We also study the case of quenched disorder through a renormalization group analysis.

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    • Received 21 August 2008

    DOI:https://doi.org/10.1103/PhysRevLett.102.156603

    ©2009 American Physical Society

    Authors & Affiliations

    Qin Liu1, Chao-Xing Liu2,3, Cenke Xu4, Xiao-Liang Qi3, and Shou-Cheng Zhang3

    • 1Department of Physics, Fudan University, Shanghai 200433, China
    • 2Center for Advanced Study, Tsinghua University, Beijing, 100084, China
    • 3Department of Physics, McCullough Building, Stanford University, Stanford, California 94305-4045, USA
    • 4Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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    Vol. 102, Iss. 15 — 17 April 2009

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    • Figure 1
      Figure 1
      (a) Charge local density of states (LDOS) as a function of the distance r from the magnetic impurity for electron energies E=30  meV (black line) and E=70  meV (blue line). (b) Charge LDOS as a function of electron energy E at positions r=0 (blue line) and r=20  nm (red line). Here we assume a magnetic impurity strength M0=50  meV and a coupling range r0=13  nm. The spin LDOS is plotted as a function of position at E=10  meV for magnetization of the magnetic impurity placed at the origin (0,0) in (c) the z direction and (d) the y direction. Here the arrow indicates the in-plane spin LDOS and the color shows the z direction spin LDOS.Reuse & Permissions
    • Figure 2
      Figure 2
      RKKY interaction versus the distance R between two magnetic impurities. Fermi momentum kF is chosen to be 0.5/a0 for the blue line, 1.0/a0 for the green line and 1.5/a0 for the red line, where a0 is the lattice constant.Reuse & Permissions
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