Fig. 1: Gate-tunable TI nanowire device and the theory of MCA.
a, False-colour scanning electron microscope image of device 1 with schematics of the electrical wiring; the Pt/Au leads are in dark yellow, the TI nanowire etched from an MBE-grown BST thin film are in red and the top-gate electrode are in green. The resistance of the nanowire was measured on different sections: sections 1, 2, 3, 4 and 5 correspond to the voltage contact pairs 2–3, 3–4, 4–5, 5–6 and 2–6 (the numbers shown), respectively. b, Schematic of MCA in TI nanowires. A gate, applied here to the top of the nanowire, breaks the inversion symmetry along the wire. Applying a magnetic field along the gate normal (z direction) results in a giant MCA rectification such that current flows more easily in one direction along the wire than in the opposite one (indicated by red and blue arrows, respectively). c, Energy dispersion ε(k) of the TI nanowire surface states, which form degenerate subbands (dashed line). When a finite Vg is applied, the inversion symmetry is broken and the subbands split (solid lines). A new minimum subband energy occurs at εmin and the states possess a finite spin polarization in the yz plane (red and blue lines indicate subbands with opposite spin polarization). A magnetic field B shifts the subband pair relative to each other in terms of energy due to the Zeeman effect, which is maximal for B along the z axis and leads to an MCA (the size of the shift shown here is used for clarity and is not to scale). d, Size of the MCA rectification γl (equation (1)) as a function of chemical potential μ within a given subband pair. Owing to the peculiar dispersion of a TI nanowire, the curvature, \({\hslash }^{2}{{{V}}}_l^{\eta }(k)\equiv {\partial }_{k}^{2}{\varepsilon }_l^{\eta }(k)\), is large and highly anisotropic at opposite Fermi momenta, which results in a giant MCA. As the chemical potential μ is tuned from the bottom of the subband, γl changes sign. Here, for clarity, we used B = 1 T (see Supplementary Note 5 for further parameters). e–g, The theoretically expected magnetic-field dependence of R2ω at the chemical potentials indicated in d.
