Recently the renormalization of the band gap $m$, in both tungsten diselenide (WSe${}_2$) and Molybdenumm disulfide (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 (TMDs) 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 $m(n)/m_0=(n/n_0{)}^{C_{\lambda }/2}$, where $m_0=m(n_0)$ and $C_{\lambda }$ is a function of the coupling constant $\lambda =\pi \alpha /4$, where $\alpha$ is the fine-structure constant. We compare our theoretical results with the experimental findings for WSe${}_2$ and MoS${}_2$, and we conclude that our approach is in agreement with these experimental results for reasonable values of $\lambda$. Thereafter, we consider the coupling of massless Dirac particles with the Gross-Neveu (GN) 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, ${\lambda }_c\approx 0,66$ 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 $

中文翻译：

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通过大N扩展中的电磁和四费米相互作用之间的竞争使2D材料中的带隙重新归一化

最近带隙重新规范化 $米$，在二硒化钨（WSe${}_2$）和二硫化钼（MoS${}_2$），已通过实验测量为载流子浓度的函数 $ñ$。与裸带隙相比，随着载流子浓度的增加，主要结果表明降低了数百meV。这些材料被称为过渡金属二硫化氢（TMD），其低能激发近似由大规模狄拉克方程描述。使用伪量子电动力学（PQED）来描述这些准粒子之间的电磁相互作用，以及从大型$ñ$ 极限，我们得到重归一化质量描述了带隙重归一化，其函数为 $米（ñ）/{米}_0=（ñ/{ñ}_0{）}^{C_{\lambda }/2}$，在哪里 ${米}_0=米（{ñ}_0）$ 和 $C_{\lambda }$ 是耦合常数的函数 $\lambda =\pi \alpha /4$，在哪里 $\alpha$是精细结构常数。我们将我们的理论结果与WSe的实验结果进行比较${}_2$ 和MoS${}_2$，我们得出结论，对于合理的，我们的方法与这些实验结果相符 $\lambda$。此后，我们考虑无质量Dirac粒子与Gross-Neveu（GN）相互作用的耦合，这通过间隙方程和PQED为Dirac场生成质量。在这种情况下，我们表明存在一个临界耦合常数，即${\lambda }_C\approx 0，66$其中质量的β功能消失，在紫外线范围内提供稳定的固定点。对于$\lambda >{\lambda }_C$，则重新标准化的质量会降低，而对于$