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Optically bright $p$-excitons indicating strong Coulomb coupling in transition-metal dichalcogenides

It is shown that the strong Coulomb coupling in intrinsic suspended semiconducting transition metal dichalcogenides can exceed the critical value needed for an excitonic ground state. The dipole-allowed optical excitations then correspond to intra-excitonic transitions such that the optically bright excitonic transitions near the Dirac points have a $p$-like symmetry whereas the $s$-like states are dipole forbidden. The large intrinsic coupling strength seems to be a generic property of the semiconducting transition metal dichalcogenides and strong Coulomb-coupling signatures in the form of the optical selection rules can be observed even in samples grown on typical substrates like SiO$_2$. For the examples of WS$_2$ and WSe$_2$, excellent agreement of the computed excitonic resonance energies with recent experiments is demonstrated.