Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _x (Bi _0.1 Sb _0.9 ) _2-x Te ₃

Abstract

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking timereversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr 0.08 (Bi 0.1 Sb 0.9 ) 1.92 Te 3 . Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r) ∝ n(r) is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm 2 . These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.ferromagnetic topological insulator | Dirac-mass gapmap | Dirac-mass disorder | magnetic dopant atoms T hat the surface states of 3D topological insulators (TIs) exhibit a "massless" Dirac spectrum EðkÞ = Zvk · σ with spinmomentum locking and protected by time-reversal symmetry is now firmly established. Opening a gap in this spectrum is key to the realization of several extraordinary new types of electronic phenomena. The prevalent approach to opening this "Dirac-mass gap" is to dope the materials with magnetic atoms (1-6). A plethora of new physics is then predicted, including σ xy = ±e 2 =h quantum anomalous Hall effects (QAHE) (7, 8), topological surface-state magneto-electric effects (9-12), related magneto-optical Kerr and Faraday rotations (10, 13, 14), axionic-like electrodynamics (15, 16), and even E-field induced magnetic monopoles (17,18). As yet, none of these phenomena except the QAHE (19-22) have been detected, and the QAHE itself is poorly understood because σ xy = ±e 2 =h is observed only at temperatures far below 1 K.Interactions between the TI surface electrons and the magnetic dopant atoms at random surface locations r i can be represented theoretically by a Hamiltonian of the type H DA = −J p P S i · sδðr − r i Þ. Here S i (s) is the spin of each dopant (surfacestate carrier) measured in units of Z, and J p is their exchangeinteraction energy scale. In the simple case of a homogenous ferromagnetic state with magnetization parallel to the surface normal z, the Hamiltonian becomes H = −J p n 0...

Breaking time-reversal symmetry at the topological insulator surface by metal-organic coordination networks

“…Due to the rectangular symmetry of the FM MOCNs under consideration they could create quasi-one-dimensional regions (stripes) of the gapped Dirac state at the TI surface. This is somewhat similar to the spatially dependent DP gap opening in the case of Cr x (Bi 0.1 Sb 0.9 ) 2−x Te 3 stemming from the inhomogeneous distribution of Cr dopants [87].…”

Emergent functions of quantum materials

“…109), while the mass gap is estimated as large as about 50 meV (ref. 110). However, the QAHE has currently been realized only at very low temperature (<100 mK) for homogeneously doped thin films.…”

Filling of magnetic-impurity-induced gap in topological insulators by potential scattering

“…A gap in the TI surface states can be generated by timereversal breaking perturbations and one of the currently most discussed approaches for engineering a gap is magnetic doping [11][12][13][14] . The idea is that ferromagnetically ordered impurities will produce a net magnetic field, which then gaps the TI surface states 15,16 .…”