arXiv subjects

Luis Fernández

Publications and source records attributed to Luis Fernández.

6 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, $E - M \propto \sqrt{2b}\,ω$ for harmonic trapping, and $E - M \sim α\ln\sqrt{b}$ 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↗

arXiv2025

Transport of Dirac magnons driven by gauge fields

We present a unified quantum field theory for Dirac magnons coupled to emergent gauge fields. At zero temperature, any space- and time-dependent gauge perturbation drives magnons out of equilibrium, generating spin currents and magnon accumulation without conventional thermal or chemical potential gradients. For a honeycomb ferromagnet, we derive closed-form expressions for the induced density and current. In the DC limit, the transverse spin conductivity quantizes to $σ^{xy}=α^2\text{sgn}(m)\hbar/4π$, a magnonic analog of the quantum Hall effect, where $m$ is the topological magnon mass and $α$ a dimensionless coupling constant. In the AC regime, the conductivity exhibits a sharp resonance when the drive frequency matches the topological gap $Δ$, signaling interband transitions. Our work establishes gauge fields as a versatile tool for controlling magnon transport and reveals topologically protected quantized responses.

cond-mat.mes-hall↗

arXiv2025

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, $Λ\approx 1$ 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↗

arXiv2021

Influence of the four-fermion interactions in (2+1)D massive electrons system

The description of the electromagnetic interaction in two-dimensional Dirac materials, such as graphene and transition-metal dichalcogenides, in which electrons move in the plane and interact via virtual photons in 3d, leads naturally to the emergence of a projected non-local theory, called pseudo-quantum electrodynamics (PQED), as an effective model suitable for describing electromagnetic interaction in these systems. In this work, we investigate the role of a complete set of four-fermion interactions in the renormalization group functions when we coupled it with the anisotropic version of massive PQED, where we take into account the fact that the Fermi velocity is not equal to the light velocity. We calculate the electron self-energy in the dominant order in the $1/N$ expansion in the regime where $m ^ 2 \ll p ^ 2$. We show that the Fermi velocity renormalization is insensitive to the presence of quartic fermionic interactions, whereas the renormalized mass may have two different asymptotic behaviors at the high-density limit, which means a high-energy scale.

hep-th↗

arXiv2020

Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Gross-Neveu Interaction at finite temperature

We study the dynamical mass generation in Pseudo Quantum Electrodynamics (PQED) coupled to the Gross-Neveu (GN) interaction, in (2+1) dimensions, at both zero and finite temperatures. We start with a gapless model and show that, under particular conditions, a dynamically generated mass emerges. In order to do so, we use a truncated Schwinger-Dyson equation, at the large-N approximation, in the imaginary-time formalism. In the instantaneous-exchange approximation (the static regime), we obtain two critical parameters, namely, the critical number of fermions $N_c(T)$ and the critical coupling constant $α_c(T)$ as a function of temperature and of the cutoff $Λ$, which must be provided by experiments. In the dynamical regime, we find an analytical solution for the mass function $Σ(p,T)$ as well as a zero-external momentum solution for $p=0$. We compare our analytical results with numerical tests and a good agreement is found.

hep-th↗

arXiv2020

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

Recently the renormalization of the band gap $m$, in both WSe$_2$ and 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, we obtain that the renormalized mass describes the band gap renormalization with a function given by $m(n)/m_0=(n/n_0)^{C_λ/2}$, where $m_0=m(n_0)$ and $C_λ$ is a function of the coupling constant $λ$. 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 $λ$. In addition we introduced a Gross-Neveu (GN) interaction which could simulate an disorder/impurity-like microscopic interaction. In this case, we show that there exists a critical coupling constant, namely, $λ_c \approx 0,66$ in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $λ>λ_c$, the renormalized mass decreases while for $λ<λ_c$ it increases with the carrier concentration.

hep-th↗