Fig. 4: Observation of hole spin accumulation at the band edge.

a, Degree of polarization (DOP) for positive and negative magnetic fields (±5 T), defined as \({\delta }_{{\rm{P}}}^{\pm }=({I}_{{\sigma }_{\mp }}-{I}_{{\sigma }_{\pm }})/({I}_{{\sigma }_{+}}+{I}_{{\sigma }_{-}})\), where \({I}_{{\sigma }_{\mp }}{(I}_{{\sigma }_{\pm }})\) represents the current recorded under circularly polarized excitation σ_– (σ₊) for positive magnetic fields and circularly polarized excitation σ₊ (σ_–) for negative fields. Two regimes can be identified, with a low-power regime characterized by a constant DOP and a high-power regime characterized by a linear increase in the DOP as the laser power is increased (on a logarithmic scale). A vertical dashed grey line shows the division between the two regimes. The mechanism responsible for the observation of this phenomenon was predicted almost a decade ago²⁶, and demonstrated here. b, Spin-polarized hole accumulation mechanism for monolayer InSe as discussed in the literature²⁶, and revised for clarity. A spin-up electron is excited from the lower valence band to the CB, and it decays by recombining with a hole in the upper valence band with the same spin. As a result, oppositely polarized holes will accumulate in the upper valence band on recombination. This effect causes an increase in spin accumulation, which follows the trend observed in this work. c, Spin-polarized hole accumulation mechanism in multilayer InSe (ML InSe). In this scenario, a positive out-of-plane magnetic field (B_z > 0) causes the spin-up band of hBN to shift upwards in energy, reducing the energy barrier height for the spin-up carriers tunnelling from InSe. Thus, a spin-polarized current contribution is added to the unpolarized part, leading to the differential tunnelling conductance discussed in Fig. 3b. The upper valence band hosts carriers with spins lying prevalently in plane (orange arrows), causing the out-of-plane spin polarization to be reduced in our experiments. Importantly, since the spin accumulation is along the out-of-plane direction, the points neighbouring the VBM are responsible for such a spin accumulation to occur. Owing to the suppressed S_z and low g-factor at those points, the spin accumulation is rather modest, reaching ~10% at ±5 T. However, the ability to detect such a small spin polarization represents a remarkable result that is allowed by our method. Moreover, the observed spin polarization values follow the trend described by the theory²⁶, confirming the physical origin of the observed phenomenon.