arXiv subjects

Nilberto Bezerra

Publications and source records attributed to Nilberto Bezerra.

3 recordsLinked to original sources

arXiv2026

Bound-State Spectra of a Lifshitz-Type Dirac Equation in (2+1) Dimensions

We investigate a Dirac-type equation in $(2+1)$ dimensions modified by Lifshitz spatial derivatives with dynamical exponent $z=2$, focusing on the spectral properties of bound-states under radial confinement. Analytical solutions are obtained for constant backgrounds, hard-wall confinement, and harmonic potentials, while logarithmic confinement is treated numerically via the Numerov method and complemented by a semiclassical WKB analysis. The resulting spectra exhibit characteristic scaling laws governed by the Lifshitz parameter $b$, including $E - M \propto b/R_0^2$ for hard-wall confinement, $E - M \propto \sqrt{2b}\,\omega$ for harmonic trapping, and $E - M \sim \alpha \ln\sqrt{b}$ in the semiclassical regime of logarithmic confinement, where $M$ is a mass scale. These results provide a consistent characterization of how higher-order spatial derivatives modify the energy spectra in two-dimensional Dirac systems and may be relevant for effective descriptions of materials with quadratic low-energy dispersion, such as bilayer graphene and related anisotropic 2D systems.

cond-mat.str-el↗

arXiv2024

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

We analyze mass renormalization in massive Dirac-like systems in (2+1) dimensions arising from electron-phonon interactions at finite temperatures, employing the large-$N$ expansion. Our model combines the low-energy description of charge carriers in a buckled honeycomb lattice with the low-energy approximation for phonons and electron-phonon interactions in two-dimensional materials. Consequently, the system is modeled as a massive Dirac-like field coupled to a two-component vector field $\mathcal{A}_i$, representing the phonon modes. This framework allows us to compute the one-loop electron self-energy at finite temperature, from which we derive the renormalized band gap, $m^R$. The effective model is subsequently applied to describe the renormalized optical band gap in monolayers of transition metal dichalcogenides (TMDs), including MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$. A good agreement is observed with experimental data for reasonable values of the ultraviolet cutoff, $\Lambda \approx 1$ eV. Our main findings indicate that $m^R$ remains nearly constant at low temperatures, whereas at higher temperatures it decreases linearly with the temperature $T$. Specifically, we find that $m^R$ reduces by approximately $\approx [0.1,0.2]$ eV as the temperature increases from $\approx 4$ K to $500$ K, consistent with recent experimental observations. Furthermore, we estimate the temperature range at which the transition to the linear regime occurs, obtaining typical values within $\approx [110,150]$ K for the four materials under consideration.

cond-mat.str-el↗

arXiv2023

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

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 $T\rightarrow 0$, 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, $m^R(p,T)-m^R(p,T\rightarrow 0)\approx -A_\alpha T +O(T^3)$, where $A_\alpha$ is a positive constant. On the other hand, for the renormalized Fermi velocity, we find that $v^R_F(p,T)-v^R_F(p,T\rightarrow 0)\approx -B_\alpha T^3 +O(T^5)$, where $B_\alpha$ is a positive constant. We also perform numerical tests which confirm our analytical results.

cond-mat.mes-hall↗