Superparamagnetism-induced mesoscopic electron focusing in topological insulators

Recently it has been shown that surface magnetic doping of topological insulators induces backscattering of Dirac states which are usually protected by time-reversal symmetry [Sessi et al., Nat. Commun. 5, 5349 (2014)]. Here we report on quasiparticle interference measurements where, by improved Fermi level tuning, strongly focused interference patterns on surface Mn-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ could be directly observed by means of scanning tunneling microscopy at 4 K. Ab initio and model calculations reveal that their mesoscopic coherence relies on two prerequisites: (i) a hexagonal Fermi surface with large parallel segments (nesting) and (ii) magnetic dopants which couple to a high-spin state. Indeed, x-ray magnetic circular dichroism shows superparamagnetism even at very dilute Mn concentrations. Our findings provide evidence of strongly anisotropic Dirac-fermion-mediated interactions and demonstrate how spin information can be transmitted over long distances, allowing the design of experiments and devices based on coherent quantum effects in topological insulators.

Figure 1

(a) Topographic STM image of 0.01 ML Mn on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ $(I=35$ pA; $U=150$ mV). (b) Schematic dispersion above the Dirac point and (c)–(e) constant-energy contours with in-plane/out-of-plane spin polarization at selected energies. Green and red arrows indicate preferred scattering vectors ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$ along the $\overline{\mathrm{\Gamma }K}$ and $\overline{\mathrm{\Gamma }M}$ directions, respectively. Corresponding quasiparticle interference maps measured at energies that mark the transition from convex to concave constant-energy cuts are shown in (f) $E-E_{\mathrm{F}}=+70$ meV, (g) $-10$ meV, and (h) $-70$ meV. Line sections measured between the arrows are plotted in panels (i)–(k). Insets show the corresponding Fourier-transformed $dI/dU$ maps (top, raw data).

Figure 2

Simulated exJDOS images for energies (a),(c),(e) $E=E_F+50\text{meV}$ and (b),(d),(f) $E=E_F$ as generated by a Te vacancy (top row), a single Mn atom at a Te vacancy site (middle), and a Mn trimer (bottom). With the exception of (a) (contrast tenfold magnified), the color scale is the same in all panels. Red $(\overline{\mathrm{\Gamma }M}$ direction) and green $(\overline{\mathrm{\Gamma }K}$ direction) ellipses highlight exJDOS features associated to conventional scattering and backscattering, respectively. Insets in (c) and (d) show isoenergy contours for the different energies color coded by the states' surface localization (yellow: $>80\%$ in first QL; dark blue: $\sim 60\%$ in first QL). In the inset in (f), the relative magnitude of the backscattering signal is compared for five different impurity and spin configurations.

Figure 3

(a) Mn $L_{2,3}$-edges x-ray absorption spectra (XAS; top panel) and x-ray magnetic circular dichroism (XMCD; bottom panel) signal of 0.016 ML Mn on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, obtained at normal and grazing incidence, with $B=6$ T and $T=2.5$ K. (b) Corresponding magnetization cycles, recorded at the XMCD maximum at the Mn $L_3$ edge. (c) Mn-coverage dependence of the saturation magnetization extracted from the recorded magnetization cycles.