Oscillating Bloembergen-Rowland interaction in three-dimensional topological insulators

Magnetic impurities deposited on the surface of a thin film experience oscillating-in-space indirect exchange interaction even if the chemical potential is pinned to a middle gap position in the surface electron spectrum, preventing free electrons and holes to exist in the ground state. Oscillating interaction mediated by massive Dirac fermions is a signature of the topologically nontrivial state.

Figure 1

Surface electron spectrum in topological phase.

Figure 2

Spatial distribution of the exchange interaction along the direction normal to the plane: top $\left(Z_{1,2}=-20\AA \right)$ to bottom $\left(Z_{1,2}=20\AA \right)$ axis, (a) $C_1\left(Z_1,Z_2\right)$ and (b) $C_2\left(Z_1,Z_2\right)$.

Figure 3

Function $F_2\left(r\right)\left(\mathrm{a}.\mathrm{u}.\right)$: (a) $R_0=5\AA$, solid line - $k_M=0.8{\AA }^{-1}$, dashed line - $k_M=1.6{\AA }^{-1}$; (b) $k_M=0.8{\AA }^{-1},$ solid line - $R_0=5\AA$, dashed line - $R_0=10\AA$.

Figure 4

Oscillating Bloembergen-Rowland interaction. Effective spin-orbit parameter $A\left[\mathrm{eV}\AA \right]$: solid line, $0.7$; dashed line, $0.5;$ dotted line, $0.2$.