# Quantized many-body spin-valley textures in charge tunable monolayer MoS$_2$

Research paper by Julian Klein, Alexander Hötger, Matthias Florian, Alexander Steinhoff, Alex Delhomme, Takashi Taniguchi, Kenji Watanabe, Frank Jahnke, Alexander W. Holleitner, Clément Faugeras, Marek Potemski, Jonathan J. Finley, Andreas V. Stier

Indexed on: 30 Jul '20Published on: 28 Jul '20Published in: arXiv - Physics - Mesoscopic Systems and Quantum Hall Effect

#### Abstract

We explore the many-body interaction of neutral, positively and negatively charged electron-hole pairs in a MoS$_2$ monolayer with the distinct spin and valley textures of resident charges via density dependent high field magneto-optical spectroscopy. For the neutral exciton we unexpectedly observe nonlinear valley Zeeman effects, which we explain by dipolar spin-interactions of the exciton with the spin and valley polarized Fermi sea. At electron densities below $4 \cdot 10^{12}cm^{-2}$ we observe quantum oscillations in the photoluminescence of the intravalley trion as well as a Landau level occupation dependent non-uniform Zeeman shifts from which we determine both effective electron and hole masses. By increasing the local charge density to a situation where the Fermi energy dominates over the other relevant energy scales in the system, the magneto-optical response becomes dependent on the occupation of the fully spin-polarized Landau levels in both $K/K^{\prime}$ valleys producing magneto-optical signatures of a many-body state. Our experiments unequivocally demonstrate that the exciton in monolayer semiconductors is a single particle boson only close to charge neutrality and that it smoothly transitions into a polaronic state with a spin-valley flavour that is defined by the local Landau level quantized spin and valley texture away from charge neutrality.