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 Bi₂Te₃ 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.