Spontaneous valley polarization of interacting carriers in a monolayer semiconductor

We report magneto-absorption spectroscopy of gated WSe${}_2$ monolayers in high magnetic fields up to 60~T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both ${\sigma }^{\pm }$ circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both $K$ and $K^{\mathrm{\prime }}$ valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density $p$. We exploit this tunability to align the LLs in $K$ and $K^{\mathrm{\prime }}$, and find that the 2D hole gas becomes unstable against small changes in LL filling and can spontaneously valley-polarize. These results cannot be understood within a single-particle picture, highlighting the importance of exchange interactions in determining the ground state of 2D carriers in monolayer semiconductors.