Large photoluminescence enhancement by an out-of-plane magnetic field in exfoliated WS$_2$ flakes

We report an out-of-plane magnetic field induced large photoluminescence enhancement in WS${}_2$ flakes at $4$ K, in contrast to the photoluminescence enhancement provided by in-plane field in general. Two mechanisms for the enhancement are proposed. One is a larger overlap of electron and hole caused by the magnetic field induced confinement. The other is that the energy difference between $\Lambda$ and K valleys is reduced by magnetic field, and thus enhancing the corresponding indirect-transition trions. Meanwhile, the Land\'e g factor of the trion is measured as $-0.8$, whose absolute value is much smaller than normal exciton, which is around $|-4|$. A model for the trion g factor is presented, confirming that the smaller absolute value of Land\'e g factor is a behavior of this $\Lambda$-K trion. By extending the valley space, we believe this work provides a further understanding of the valleytronics in monolayer transition metal dichalcogenides.