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Recently the renormalization of the band gap $m$, in both WSe$_2$ andMoS$_2$, has been experimentally measured as a function of the carrierconcentration $n$. The main result establishes a decreasing of hundreds of meV,in comparison with the bare band gap, as the carrier concentration increases.These materials are known as transition metal dichalcogenides and theirlow-energy excitations are, approximately, described by the massive Diracequation. Using Pseudo Quantum Electrodynamics (PQED) to describe theelectromagnetic interaction between these quasiparticles and fromrenormalization group analysis, we obtain that the renormalized mass describesthe band gap renormalization with a function given by$m(n)/m_0=(n/n_0)^{C_\lambda/2}$, where $m_0=m(n_0)$ and $C_\lambda$ is afunction of the coupling constant $\lambda$. We compare our theoretical resultswith the experimental findings for WSe$_2$ and MoS$_2$, and we conclude thatour approach is in agreement with these experimental results for reasonablevalues of $\lambda$. In addition we introduced a Gross-Neveu (GN) interactionwhich could simulate an disorder/impurity-like microscopic interaction. In thiscase, we show that there exists a critical coupling constant, namely,$\lambda_c \approx 0,66$ in which the beta function of the mass vanishes,providing a stable fixed point in the ultraviolet limit. For$\lambda>\lambda_c$, the renormalized mass decreases while for$\lambda<\lambda_c$ it increases with the carrier concentration.

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions