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Schematic illustration of the device: the 2D Dirac electrons on the surface of a TI are modulated by a periodic exchange field. The latter is generated by an array of FI stripes. The magnetization directions of adjacent FI stripes are parallel in the configuration (a) and antiparallel in the configuration (b). (c) and (d): Profiles of the exchange field due to the proximity effect for the magnetization configuration (a) and (b). Both the FI regions and the spacing regions have the same length . The current flows in the surface of the TI along the direction.
Dispersion relations of the Dirac electrons modulated by the magnetic superlattice with a [(a)–(c)] P and [(d)–(f)] AP configuration. In [(a)–(b)] and [(d)–(e)] the band energy at two values, (solid line) and (dashed line), is plotted as a function of the Bloch wave vector under the magnetization strengths [(a) and (d)] and [(b) and (e)]. In (c) and (f) the variation in with is plotted under two magnetization strengths (circle marks) and (triangular marks).
Contour plot of the transmission as a function of the incident energy and the incident angle . The magnetization strength is fixed at . The number of FI stripes is .
Conductance as a function of the Fermi energy for (a) , (b) , and (c) . The number of FI stripes is .
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