Fig. 2: Magnetic field dependence of tunnelling currents in few-layer InSe.

a, Magnetic-field-dependent tunnelling current is shown at different gate voltages corresponding to different charge configurations: within the CB (V_g = 1 V), bandgap region (V_g = –3 V) and valence band (V_g = –6 V). The signal recorded at the valence band energy shows a symmetric increase for both magnetic field polarities, whereas no modulation is observed in the other cases. The signal is recorded under linearly polarized light excitation, at a laser power of 150 μW. b, Valence band structure calculated for 3L γ-InSe. 3L is used for our computations since it shows qualitatively analogous results with respect to 5L, and it requires a simpler computation. The linecuts are shown for two different directions in the Brillouin zone. The solid and dashed lines represent two different spin configurations. The linecuts exhibit the same spin sub-band at higher energies. However, when we consider the Brillouin zone, we observe that three valleys have a higher energy for one spin configuration, whereas the other three valleys favour the other spin configuration. c, Band structure of multilayer hBN. d, Calculated change in the energy barrier as a function of the magnetic field. The increase in tunnelling current (as shown in a) can be translated into an energy barrier change that is proportional to the Zeeman splitting of the energy bands involved. From this measurement, we can extract a total g-factor of around 2 for both magnetic field polarities, which is consistent with our calculations for InSe and hBN. The insets show the energy barrier height at B = 0 \({({\phi }_{{\it{B}}_0})}\), and at higher fields, with the Zeeman splitting contribution E_z. e, First-principles calculations of angular momenta for 3L InSe. The spin (S_z) and orbital (L_z) components are calculated for the band structure shown in b, and the total out-of-plane g-factor is shown. In particular, at the VBM position, both spin and orbital components are suppressed, indicating that the spins are oriented in plane. This result holds for all InSe multilayers. The VBM neighbouring points possess a non-vanishing g-factor, which will be relevant, as displayed in the power dependence measurements. f, Angular momenta computed for the hBN valence band. Here the orbital contribution is vanishingly small across the area of interest in the Brillouin zone, and the total contribution to the out-of-plane g-factor comes from the spin component. Overall, along the out-of-plane direction, only hBN is dominant for a change in energy barrier height, since the holes in InSe relax to the VBM before tunnelling, which possesses a quenched g-factor.