Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>expansion

Abstract

Recently the renormalization of the band gap $m$, in both tungsten diselenide (${\mathrm{WSe}}_{2}$) and molybdenumm disulfide (${\mathrm{MoS}}_{2}$), 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 $m(n)/{m}_{0}=(n/{n}_{0}{)}^{{C}_{\ensuremath{\lambda}}/2}$, where ${m}_{0}=m({n}_{0})$ and ${C}_{\ensuremath{\lambda}}$ is a function of the coupling constant $\ensuremath{\lambda}=\ensuremath{\pi}\ensuremath{\alpha}/4$, where $\ensuremath{\alpha}$ is the fine-structure constant. We compare our theoretical results with the experimental findings for ${\mathrm{WSe}}_{2}$ and ${\mathrm{MoS}}_{2}$, and we conclude that our approach is in agreement with these experimental results for reasonable values of $\ensuremath{\lambda}$. 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, ${\ensuremath{\lambda}}_{c}\ensuremath{\approx}0$, 66 in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $\ensuremath{\lambda}&gt;{\ensuremath{\lambda}}_{c}$, the renormalized mass decreases while for $\ensuremath{\lambda}&lt;{\ensuremath{\lambda}}_{c}$ it increases with the carrier concentration.

Topics & Concepts