Layer- and Gate-tunable Spin-Orbit Coupling in a 2D semiconductor probed by Shubnikov-de Haas Oscillations.*

In semiconductors spin degeneracy can be lifted by breaking time reversal symmetry or by spin-orbit coupling (SOC) when inversion symmetry is broken. We utilize tunability of ultrathin field-effect transistors combined with high mobility of indium selenide (InSe) to demonstrate SOC and to vary it over an unprecendently wide range by breaking the inversion symmetry with out-of-plane electric field. In addition, we demonstrate dependence of parameters of SOC on the number of InSe layers. High accuracy is achieved by the experimental technique: measurement of beating patterns in Shubnikov-de Haas oscillations. We achieve tuning of spin splitting from 0 and 20 meV. However, this is not the limit, as some devices demonstrate an order of magnintude higher SOC, suggesting additional paths of manipulation.