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

Abstract

Recently the renormalization of the band gap m, in both tungsten diselenide (WSe2) and molybdenumm disulfide (MoS2), has been experimentally measured as a function of the carrier concentration 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 their low-energy excitations are, approximately, described by the massive Dirac equation. Using pseudo-quantum electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis at the large-N limit, we obtain that the renormalized mass describes the band gap renormalization with a function given by m(n)/m0=(n/n0)Cλ/2, where m0=m(n0) and Cλ is a function of the coupling constant λ=πα/4, where α is the fine-structure constant. We compare our theoretical results with the experimental findings for WSe2 and MoS2, and we conclude that our approach is in agreement with these experimental results for reasonable values of λ. Thereafter, we consider the coupling of massless Dirac particles with the Gross-Neveu interaction, which generates a mass for the Dirac field through the gap equation, and PQED. In this case, we show that there exists a critical coupling constant, namely, λc≈0, 66 in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For λ>λc, the renormalized mass decreases while for λ