Quantum impurity in the bulk of a topological insulator

Abstract

We investigate physical properties of an Anderson impurity embedded in the bulk of a topological insulator. The slave-boson mean-field approximation is used to account for the strong electron correlation at the impurity. Different from the results of a quantum impurity on the surface of a topological insulator, we find for the band-inverted case that a Kondo resonant peak and in-gap bound states can be produced simultaneously. However, only one of them appears for the normal case. It is shown that the mixed-valence regime is much broader in the band-inverted case, while it shrinks to a very narrow regime in the normal case. Furthermore, a self-screening of the Kondo effect may appear when the interaction between the bound-state spin and impurity spin is taken into account.

Anderson impurity in the bulk of topological insulators

“…[26]. Starting from a Hamiltonian describing an Anderson impurity d in the bulk of a TI, a few manipulations are required to transform it into its workable form, Eq.…”

“…It is seen that when | | < ε q , the expression on the lefthand side of the secular equation (11) is positive when is negative and negative when is positive (V 0 is assumed to be positive here). When | | → ε q , the sum diverges as (ε 2 q − 2 ) −1/2 sign(− ) for energy bands with the "inverted Mexican hat" structure [26]. As a result, the secular equation gives us a midgap energy level f which lies within the interval −ε q < f < 0.…”

“…So far, the main attention has been focused on the surface states [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. It was pointed out recently that impurity scattering may have nontrivial effects in the bulk of TIs due to its peculiar band structure [25][26][27][28]. More concretely, in topological insulators with "inverted-Mexican-hat" band dispersion around the point, in-gap bound states occur due to impurities from which band electrons are scattered (even with arbitrary weak scattering rate) [25].…”

“…In the case of magnetic (Anderson) impurities (forming localized moments) the associated Kondo physics in bulk TIs is profoundly distinct from its metallic analog. Using a slave-boson mean-field theory [26], it was shown that an antiferromagnetic exchange interaction ∼J df S d · S f (with J df > 0) between the spins of the Anderson impurity d and the induced midgap bound state f leads to a self-screened Kondo effect (KE) [26]. In fact, the physics described above is not limited to TIs but is a general consequence of insulators (and semiconductors) with a large electronic density of states at the band edge such that in-gap bound states are easily induced by an Anderson impurity.…”

Spin-spin interaction in the bulk of topological insulators

“…Other than the normal Heisenberg-like interactions, there may exist Ising-like and Dzyaloshinskii-Moriya (DM)-like interactions between magnetic impurities on the surface of TIs. For the bulk-doping 31 , mean-field analysis 32 shows that there may exist ferromagnetic (FM) or antiferromagnetic (AFM) correlation between magnetic impurities. Density functional theory calculations [33][34][35] demonstrate complicated anisotropic spin texture in magnetically doped TIs.…”