Effects of the two-dimensional Coulomb interaction in both Fermi velocity and energy gap for Dirac-like electrons at finite temperature

Abstract

We describe both the Fermi velocity and the mass renormalization due to the two-dimensional Coulomb interaction in the presence of a thermal bath. To achieve this, we consider an anisotropic version of pseudo quantum electrodynamics (PQED), within a perturbative approach in the fine-structure constant $\alpha$. Thereafter, we use the so-called imaginary-time formalism for including the thermal bath. In the limit $T\to 0$, we calculate the renormalized mass $m^R(p)$ and compare this result with the experimental findings for the energy band gap in monolayers of transition metal dichalcogenides, namely, WSe${}_2$ and MoS${}_2$. In these materials, the quasi-particle excitations behave as a massive Dirac-like particles in the low-energy limit, hence, its mass is related to the energy band gap of the material. In the low-temperature limit $T\ll v_{F}p$, where $v_{F}p$ is taken as the Fermi energy, we show that $m^R(p)$ decreases linearly on the temperature, i.e, $m^R(p,T)-m^R(p,T\to 0)\approx -A_{\alpha }T+O(T^3)$, where $A_{\alpha }$ is a positive constant. On the other hand, for the renormalized Fermi velocity, we find that $v_F^R(p,T)-v_F^R(p,T\to 0)\approx -B_{\alpha }{T}^3+O(T^5)$, where $B_{\alpha }$ is a positive constant. We also perform numerical tests which confirm our analytical results.

11 pages

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• The electronic properties of graphene
• Direct Determination of Band Gap Renormalization in Photo-Excited Monolayer MoS2
• Electromagnetic current correlations in reduced quantum electrodynamics
• Unitarity of theories containing fractional powers of the d'Alembertian operator
• Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$
• Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Gross-Neveu Interaction at finite temperature

Cited by in corpus (1)

• Renormalization of the optical band gap through an effective Thirring interaction for massive Dirac-like electrons