Fig. 1: Magnetoresistances (MRs) of InAs/(Ga,Fe)Sb bilayer heterostructures.

a Schematic illustration of the InAs/(Ga,Fe)Sb heterostructure with 1D transport channels at the side edges. We applied an electric current I parallel to the x-axis and an external magnetic field B parallel to the z-axis. Because (Ga,Fe)Sb is insulating, electron carriers flow only in the InAs QW layer, both in the 2D channel and the 1D channels at the edges. The triangular potentials at the side surfaces create static electric fields E_sur parallel to the y-axis at the side edges of the InAs QW. b Optical microscopy top view image of the device. The terminals are labeled “1”–“6”, as shown in the image. c (Upper panel) MR of the InAs/(Ga,Fe)Sb heterostructure of sample A, measured with a DC current of 1 μA and an external magnetic field B applied parallel to z at 2.5 K. The blue and red arrows indicate the sweep direction of B. (Bottom panel) Extracted odd components of the upper panel data (R₂₃^odd = [R₂₃(B) − R₂₃(−B)]/2). d Temperature dependences of R₂₃ and R₂₃^odd of sample A at 2.5–300 K with I = 1 μA. Although the even-function MR and the Shubnikov–de Haas oscillation disappear at high temperatures, the OMR component remains up to 300 K. The inset of the lower panel shows the temperature dependence of ΔR/R₀, where ΔR = R₂₃^odd(10 T) and R₀ = R₂₃(0 T) (blue circles). The green curve is the fitting result obtained using the logarithmic function ln(1/T) + c (T temperature, c temperature-independent parameter).