The influence of a Lorentz-violating fixed background on fermions is considered by means of a torsion-free nonminimal coupling. The nonrelativistic regime is assessed and the Lorentz-violating Hamiltonian is determined. The effect of this Hamiltonian on the hydrogen spectrum is determined to first-order evaluation (in the absence and in the presence of an external magnetic field), revealing that there appear some energy shifts that modify the fine structure of the spectrum. In the case the nonminimal coupling is torsionlike, no first order correction shows up in the absence of an external field; in the presence of an external field, a secondary Zeeman effect is implied. Such effects are then used to set up stringent bounds on the parameters of the model.

To unravel the structural, energetic stability, electronic, optical, excitonic, vibrational, and thermodynamic properties of monoclinic 1A’-OsO2 monolayer, we employed the first-principles calculations based on density functional theory (DFT) within the generalized gradient approximation (GGA) and the HSE06 hybrid functional, considering the norm-conserved pseudopotentials, and a combination of a tight binding plus BSE (TB+BSE) approach for the analysis of optical and excitonic properties at IPA and BSE levels. Our simulations demonstrate that the 1A’-OsO2 monolayer is a structurally and energetically stable semiconductor, and gives us a direct bandgap value, E(Γ→Γ), of 0.304, 0.254, and 1.119 eV, which were obtained through GGA-PBE, GGA-PBE+SOC, and HSE06-level of calculation, respectively. From the excitonic and optical properties, we observe that this system shows a large exciton binding energy of around 0.3 eV for the indirect ground state exciton, displaying an optical bandgap of 0.78 eV. We also show the use of light polarization as a mechanism to control the refractive index. The phonon dispersion and the infrared (IR) and Raman spectra were obtained, with its main peaks being assigned. Lastly, through thermodynamic potentials calculations, the Free energy (F) indicates that the synthesis of the 1A’-OsO2 monolayer would be spontaneous even at low temperatures. All theses properties demonstrate that the 1A’-OsO2 monolayer has potential applications in optoelectronic and thermal devices at the nanoscale.

Rolling tachyon field models are among the candidates suggested as explanations for the recent acceleration of the Universe. In these models the field is expected to interact with gauge fields and lead to variations of the fine-structure constant $\alpha$. Here we take advantage of recent observational progress and use a combination of background cosmological observations of type Ia supernovas and astrophysical and local measurements of $\alpha$ to improve constraints on this class of models. We show that the constraints on $\alpha$ imply that the field dynamics must be extremely slow, leading to a constraint of the present-day dark energy equation of state $(1+w_0)<2.4\times {10}^{-7}$ at the 99.7% confidence level. Therefore current and forthcoming standard background cosmology observational probes cannot distinguish this class of models from a cosmological constant, while detections of $\alpha$ variations could possibly do so since they would have a characteristic redshift dependence.