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Moire superlattices formed in van der Waals heterostructures due to twisting, lattice mismatch and strain present an opportunity for creating novel metamaterials with unique properties not present in the individual layers themselves. Ferroelectricity for example, arises due to broken inversion symmetry in twisted and strained bilayers of 2D semiconductors with stacking domains of alternating out-of-plane polarization. However, understanding the individual contributions of twist and strain to the formation of topological polar nanostructures remains to be established and has proven to be experimentally challenging. Inversion symmetry breaking has been predicted to give rise to an in-plane component of polarization along the domain walls, leading to the formation of a network of topologically non-trivial merons (half-skyrmions) that are Bloch-type for twisted and Neel-type for strained systems. Here we utilise angle-resolved, high-resolution vector piezoresponse force microscopy (PFM) to spatially resolve polarization components and topological polar nanostructures in marginally twisted bilayer WSe2, and provide experimental proof for the existence of topologically non-trivial meron/antimeron structures. We observe both Bloch-type and Neel-type merons, allowing us to differentiate between moire superlattices formed due to twist or heterogeneous strain. This first demonstration of non-trivial real-space topology in a twisted van der Waals heterostructure opens pathways for exploring the connection between twist and topology in engineered nano-devices.

Coherent optical manipulation of electronic bandstructures via Floquet Engineering is a promising means to control quantum systems on an ultrafast timescale. However, the ultrafast switching on/off of the driving field comes with questions regarding the limits of validity of the Floquet formalism, which is defined for an infinite periodic drive, and to what extent the transient changes can be driven adibatically. Experimentally addressing these questions has been difficult, in large part due to the absence of an established technique to measure coherent dynamics through the duration of the pulse. Here, using multidimensional coherent spectroscopy we explicitly excite, control, and probe a coherent superposition of excitons in the $K$ and $K^\prime$ valleys in monolayer WS$_2$. With a circularly polarized, red-detuned, pump pulse, the degeneracy of the $K$ and $K^\prime$ excitons can be lifted and the phase of the coherence rotated. We demonstrate phase rotations during the 100 fs driving pulse that exceed $\pi$, and show that this can be described by a combination of the AC-Stark shift of excitons in one valley and Bloch-Siegert shift of excitons in the opposite valley. Despite showing a smooth evolution of the phase that directly follows the intensity envelope of the pump pulse, the process is not perfectly adiabatic. By measuring the magnitude of the macroscopic coherence as it evolves before, during, and after the pump pulse we show that there is additional decoherence caused by power broadening in the presence of the pump. This non-adiabaticity may be a problem for many applications, such as manipulating q-bits in quantum information processing, however these measurements also suggest ways such effects can be minimised or eliminated.

Interactions between quasiparticles are of fundamental importance and ultimately determine the macroscopic properties of quantum matter. A famous example is the phenomenon of superconductivity, which arises from attractive electron-electron interactions that are mediated by phonons or even other more exotic fluctuations in the material. Here we introduce mobile exciton impurities into a two-dimensional electron gas and investigate the interactions between the resulting Fermi polaron quasiparticles. We employ multi-dimensional coherent spectroscopy on monolayer WS$_2$, which provides an ideal platform for determining the nature of polaron-polaron interactions due to the underlying trion fine structure and the valley specific optical selection rules. At low electron doping densities, we find that the dominant interactions are between polaron states that are dressed by the same Fermi sea. In the absence of bound polaron pairs (bipolarons), we show using a minimal microscopic model that these interactions originate from a phase-space filling effect, where excitons compete for the same electrons. We furthermore reveal the existence of a bipolaron bound state with remarkably large binding energy, involving excitons in different valleys cooperatively bound to the same electron. Our work lays the foundation for probing and understanding strong electron correlation effects in two-dimensional layered structures such as moir\'e superlattices.