Energy renormalizations of resident carriers and excitons in transition metal dichalcogenide monolayers

Energy renormalizations of resident carriers and excitons are studied theoretically, and compared with recent experiments of electrostatically-doped WSe₂ monolayers. The calculated energy renormalization of resident carriers, subjected to strong out-of-plane magnetic field, reveals the importance of dynamical screening in transition metal dichalcogenides. The energy renormalization of tightly bound excitons is analyzed through the exchange interaction between the electron (or hole) component of the exciton and resident carriers that share the same spin and valley quantum numbers. Our theory explains the weak energy shift of excitonic resonances despite the strong energy renormalization of resident carriers. We identify the dependence of the energy renormalization on the envelope function of a tightly-bound exciton, showing that unlike free electron-hole pairs, this energy renormalization is not the added renormalizations of a resident electron and resident hole.