Fig. 2: Non-reciprocal transport in BST TI nanowire.

a, Four-terminal resistance R measured on device 1, section 1, at 30 mK in 0 T as a function of V_g showing reproducible peaks and dips around the resistance maximum, which are consistent with the response expected from quantum-confined surface states²³. As the R value is very sensitive to the details of the charge distributions in or near the nanowires, the R(V_g) behaviour is slightly different for different sweeps; thin red lines show the results of 15 unidirectional V_g sweeps and the thick black line shows their mean average. Inset: data for a wider range of V_g, which demonstrates the typical behaviour of a bulk-insulating TI. b, Antisymmetric component of the second-harmonic resistance, \({R}_{2\omega }^{{\rm{A}}}\), for V_g = 2 and 4.32 V plotted versus a magnetic field B applied along the z direction (the coordinate system is depicted in the inset); coloured thin lines show ten (six) individual B-field sweeps for 2 V (4.32 V), and the thick black line shows their mean. c, \({R}_{2\omega }^{{\rm{A}}}\) measured for V_g = 2 and 4.32 V in the B field (applied in the z direction) of 0.25 and 0.16 T, respectively, as a function of the a.c. excitation current I₀. The dashed lines are a guide to the eye to show the linear behaviour. Error bars are defined using the standard deviation of ten (six) individual B-field sweeps for 2 V (4.32 V). d, Magnetic-field-orientation dependencies of γ at V_g = 2 and 4.32 V when the B field is rotated in the zx plane. Error bars are defined using the minimum–maximum method with six (eight) individual B-field sweeps for 2 V (4.32 V). Solid black lines are the fits to γ ≈ γ₀cosα expected for MCA. Inset: the definition of α and the coordinate system.