Raimundo Nogueira Costa Filho

The δ-kicked rotor, a dynamic system that exhibits chaotic behavior, depending on the intensity of the applied perturbation (kicks), was studied. Previous studies have studied the dynamical properties of the classical kicked rotor model and demonstrated that its chaotic behavior leads to momentum diffusion. According to Bohr’s correspondence principle, the dynamics of a quantum system should reproduce those of its classical counterpart in the classical limit, implying that if a classical system exhibits chaos, its quantum equivalent may also be chaotic. However, it is known that in the quantum kicked rotor, classical chaos leads to a suppression of wave-function diffusion in momentum space, a phenomenon known as dynamical localization, analogous to Anderson localization in time-periodic systems. Using the Floquet operator, the kicked rotor was numerically investigated under random variations in the kick intensity (noise). Since it is unlikely to achieve true randomness in a controlled experiment, it is examined how long-range correlated random sequences affect dynamical localization in the noise-kicked rotor.

The sublattice-symmetry breaking in the α−T3 lattice leads to a bandgap opening. A defect line in the substrate on which the α−T3 lattice is deposited can be viewed as a topological change in the substrate that induces translational in-plane symmetry breaking, resulting in mid-gap states. These topologically protected states are confined along the defect line and exhibit preferential directional motion, with different signs for the different Dirac valleys. Within this context, we investigate how these unidirectional interface chiral states are affected in the presence of a perpendicular magnetic field and how they can be tuned by varying the controlling system parameter α. The latter tunes the α−T3 structure from a honeycomb-like lattice (α = 0) to a dice lattice (α = 1). Our theoretical framework is based on the continuum approximation described by a 3×3 matrix Hamiltonian with a sublattice symmetry-breaking term given by ∆(x)diag(1, −1, 1), assuming ∆(x) as a kink-like mass potential profile. Results for dispersion relations and wavefunction distributions for different α parameters and magnetic field amplitudes are discussed. We demonstrate lifting of Landau levels degeneracy and of valley degeneracy. Our findings pave the way for proposing valley filter devices based on any evolutionary stage between the honeycomb-like and dice lattice structures of the α−T3 phase, controlled by external fields.

We theoretically investigate the electronic transport properties of three-terminal ballistic junctions based on bilayer phosphorene nanoribbons, subjected to a uniform perpendicular electric field. We exploit the intrinsic anisotropy of phosphorene by considering different edge terminations for the nanoribbons that form such junctions, namely normal armchair, normal zigzag, skewed armchair, and skewed zigzag. Unlike bilayer graphene, the Bernal-stacked bilayer phosphorene, when subjected to an inversion symmetry breaking, such as the application of a perpendicular electric field, exhibits a semiconductor to metal transition, whereas in AB-stacked bilayer graphene, one observes a gap opening and a metal to semiconductor transition instead. Thus, by adopting this electric-field-controlled band gap strategy for bilayer phosphorene, we demonstrate the possibility of modulating the current flowing through bilayer-BP-based Y-junctions, redirecting it to one or both output terminals under specific conditions. The role played on the electron conductance and probability density currents by the different Y-junction constituents is also explored, and such results are interpreted in light of nanoribbons’ dispersion relations. In this sense, the proposed system acts as a nanoscale switching device, and its current modulation effect can be used to develop phosphorene-based logic gates with a large on/off current ratio, benefiting from the material’s high carrier mobility.

This work establishes a series of no-go conjectures that impose rigorous constraints on the zero mode localization of bulk fields in braneworld scenarios, specifically affecting gauge and spinor fields within five-dimensional spacetimes. Our approach differs from traditional methods as it does not rely on specific equations of motion, making our results broadly applicable across various braneworld models. These no-go conditions reveal fundamental limitations in field localization, challenging the feasibility of embedding fields on the brane. For instance, our analysis demonstrates that existing models fail to achieve consistent localization for gauge and spinor fields. Additionally, one of our conditions indicates that the effective Lagrangian on the brane cannot exhibit conformal invariance.