We present a theoretical study of electron tunneling through a magnetic barrier in 8-Pmmn borophene, created by depositing two ferromagnetic strips on the borophene sheet. Using a low-energy effective Hamiltonian that captures the anisotropic Dirac spectrum, we solve the Dirac equation in three regions and impose wave-function continuity at the interfaces. From the resulting spinor solutions, we compute current densities and determine transmission and reflection probabilities as functions of incident energy, angle, and barrier parameters. The transmission exhibits strong anisotropy due to the tilted Dirac cones, with pronounced suppression for specific incident directions, suggesting directional filtering of carriers. We further calculate the conductance using the Landauer-Büttiker formalism, revealing that both magnetic strength and barrier width can tune the charge transport properties. The results demonstrate that engineered magnetic barriers in 8-Pmmn borophene enable precise control over electron flow, offering a platform for anisotropic transport control and tunable quantum devices. The interplay between the intrinsic anisotropy of borophene and external magnetic barriers provides rich opportunities to manipulate Dirac fermions in two-dimensional systems.
We theoretically investigate spin- and valley-resolved quantum transport in monolayer tungsten diselenide (WSe
2) described by an effective massive Dirac Hamiltonian. Particular attention is devoted to a finite barrier region characterized by simultaneously modulated Fermi velocity and scalar potential. The barrier velocity
v2 is related to the external velocity
v1 through a velocity ratio
ξ=v2/v1, motivated by an optical analogy with the Snell-Descartes law. The exact refraction condition depends on the full spin- and valley-resolved dispersion, and the simple ratio
ξ=v2/v1 is recovered only in the massless, symmetric limit. The interplay of intrinsic spin-orbit coupling in the conduction and valence bands, quantified by
λc and
λv, with spin- and valley-dependent Zeeman fields,
Ms and
Mv, gives rise to substantial changes in the quasiparticle dispersion, leading to pronounced modifications of the transport characteristics. By solving the Dirac equation and enforcing current-conserving matching conditions at the interfaces, we compute the spin- and valley-dependent transmission probability and conductance. Our results demonstrate that the barrier velocity, scalar potential, incidence angle, incident energy, and barrier width serve as effective control parameters for transport, giving rise to strong anisotropy and resonant tunneling features. Furthermore, we show that both the magnitude and orientation of spin- and valley-polarized currents can be continuously tuned via velocity and potential modulation. These findings establish combined velocity and potential engineering as a powerful theoretical framework for controlling spin-valley physics in two-dimensional transition-metal dichalcogenides.
We study electron transport in a strained graphene sheet subjected to a sequence of
N electrostatic and magnetic barriers. Employing a modified and improved transfer-matrix framework, we examine how the transmission and reflection coefficients evolve with variations in uniaxial strain and in the number of barriers. The interplay of mechanical deformation and external magnetic fields is found to generate an anomalous Klein tunnelling, allowing the conductance to be effectively modulated through strain and barrier configurations. These findings highlight the role of strain engineering and magnetic field modulation as powerful tools for tailoring charge transport in two-dimensional materials. More broadly, they underscore how mechanical and electromagnetic control can be used to design next-generation solid-state devices with tunable electronic properties.
We investigate the influence of a magnetic field on the electronic properties of WS
e2 with a focus on spin-orbit coupling, spin and valley polarization, and conductance. We solve the eigenvalue equation analytically and use the continuity equation to determine the transmission probability based on current densities. We calculate the conductance using Büttiker formula. Our numerical results indicate that transmission through the
K valley is more likely than through the
K′ valley. For both valleys, the Klein tunneling effect is clearly observed. The conductance is affected by an increase in the magnetic field because it alters the energy levels of fermions via the Zeeman effect. These modifications enable the confinement of fermions within the barrier. Spin and valley polarization are also influenced by the magnetic field. As the field intensity increases, it steers the fermions and determines which channel can cross the barrier. This adds another tool of controlling fermions, paving the way for relevant applications in valleytronics and valley filtering for information storage.
We study the influence of an external magnetic field on the Goos-Hänchen (GH) shift and the group delay time (GDT) in monolayer WSe
2 in the presence of a magnetic barrier. The transport properties of Dirac-like carriers are obtained by solving the effective low-energy Hamiltonian and evaluating the corresponding transmission amplitudes. The GH shift and the GDT are subsequently extracted from the phase of the transmission coefficient. We systematically analyze their dependence on the magnetic field strength, incident energy, angle of incidence, and barrier width, with particular emphasis on the spin and valley degrees of freedom associated with the
K and
K′ valleys. Our results show that the magnetic barrier strongly modulates both the GH shift and the GDT, leading to oscillatory behavior and pronounced spin-valley-dependent transport characteristics. Remarkably, the magnetic field enables selective control of the lateral shift and traversal time of carriers for each spin and valley channel, allowing for tunable spatial and temporal separation of electronic wave packets. This provides a mechanism for manipulating fermionic trajectories after transmission through the barrier in a highly controllable manner. Such tunability opens promising avenues for designing nanoscale devices based on spin and valley filtering, as well as for potential applications in information storage and processing within spintronic and valleytronic platforms.
The Lorentz covariance of relativistic Dirac equations serves as a fundamental principle underlying the laws of electromagnetism across different inertial frames. Exploiting the covariance, we obtain the general solutions for Dirac fermions under both the in-plane electric
E and perpendicular magnetic
B fields, which reduce to either a magnetic or electric field in the inertial frame with drift velocity along the
E×B direction. This dichotomy defines the magnetic and electric regimes, separated by the critical field ratio
E/B=vF with
vF denoting the Fermi velocity of Dirac fermions. Using these solutions, we revisit Klein tunneling through a heterojunction with generalized electromagnetic potentials. In the magnetic regime, the transmission exhibits oscillations governed by the Fabry-Pérot interference. In the electric regime, perfect transmission occurs at normal incidence in the drifted frame. The interference phase is further analyzed in terms of the solid angles on the Bloch sphere, providing a geometric interpretation of Klein tunneling. Finally, we briefly discuss the relation between the tilting of Dirac cones and the in-plane electric field, establishing the correspondence of the undertilted and overtilted cases to the magnetic and electric regimes, respectively. Our findings reveal the manipulation of Klein tunneling by electromagnetic fields, offering a theoretical basis for designing novel electronic devices.
We study how electrons move across a graphene sheet when it encounters two magnetic barriers with a region in between that is continuously driven by laser light. Rather than acting as a static obstacle, this illuminated middle section becomes a Floquet cavity that opens new transport channels through controlled photon absorption and emission. By combining Floquet theory with the transfer matrix method, we track electron transmission through both the main energy band and the emerging photon-assisted sidebands. We find that the laser does more than modify the potential--it reshapes how electrons interact between the magnetic barriers, enabling a switch from ordinary transmission to transport dominated by photon exchange. Because the magnetic field and the optical drive are applied to separate sections of the device, the system supports interference between cyclotron-filtered motion and discrete photon-pumping channels, producing Fano resonances and angle-dependent transmission zeros that cannot appear in double magnetic or double laser barrier systems alone. Under well-defined conditions, the distance between the magnetic barriers controls the coupling between Floquet channels, allowing highly tunable resonances and even perfect transmission, despite strong magnetic confinement. We also observe that low-energy carriers are efficiently blocked by the magnetic regions, while conductance steadily rises with energy until it reaches a clear saturation plateau. This hybrid design provides a versatile way to steer graphene electrons by balancing optical pumping and magnetic momentum filtering.