Momentum-Resolved Exciton Coupling and Valley Polarization Dynamics in Monolayer WS$_2$

Coupling between exciton states across the Brillouin zone in monolayer transition metal dichalcogenides can lead to ultrafast valley depolarization. Using time- and angle-resolved photoemission, we present momentum- and energy-resolved measurements of exciton coupling in monolayer WS$_2$. By comparing full 4D ($k_x, k_y, E, t$) data sets after both linearly and circularly polarized excitation, we are able to disentangle intervalley and intravalley exciton coupling dynamics. Recording in the exciton binding energy basis instead of excitation energy, we observe strong mixing between the B$_{1s}$ exciton and A$_{n>1}$ states. The photoelectron energy and momentum distributions observed from excitons populated via intervalley coupling (e.g. K$^-$ $\rightarrow$ K$^+$) indicate that the dominant valley depolarization mechanism conserves the exciton binding energy and center-of-mass momentum, consistent with intervalley Coulomb exchange. On longer timescales, exciton relaxation is accompanied by contraction of the momentum space distribution.