  Systems with strong spin orbit coupling support a number of new phases of
matter and novel phenomena. This work focuses on the interplay of spin orbit
coupling and interactions in yielding correlated phenomena in two dimensional
transition metal dichalcogenides. In particular we explore the physics of Kondo
screening resulting from the lack of centro-symmetry, large spin splitting and
spin valley locking in hole doped systems. The key ingredients are i) valley
dependent spin-momentum locking perpendicular to the two dimensional crystal;
ii) single nondegenerate Fermi surface per valley, and iii) nontrivial Berry
curvature associated with the low energy bands. The resulting Kondo resonance
has a finite triplet component and nontrivial momentum space structure which
facilitates new approaches to both probe and manipulate the correlated state.
Using a variational wave function and the numerical renormalization group
approaches we study the nature of the Kondo resonance both in the absence and
presence of circularly polarized light. The latter induces an imbalance in the
population of the two valleys leading to novel magnetic phenomena in the
correlated state.
