Superparamagnetism-induced mesoscopic electron focusing in topological insulators

Abstract

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.