No Arabic abstract
Negative refraction usually demands complex structure engineering while it is very natural for massless Dirac fermions (MDFs) across the textit{p-n} junction, this leads to Dirac electron optics. The emergent Dirac materials may exhibit hitherto unidentified phenomenon due to their nontrivial band structures in contrast to the isotropic MDFs in graphene. Here, as a specific example, we explore the negative refraction induced caustics and Veselago focusing of tilted MDFs across 8-textit{Pmmn} borophene textit{p-n} junctions. To this aim, we develop a technique to effectively construct the electronic Greens function in textit{p-n} junctions with arbitrary junction directions. Based on analytical discussions and numerical calculations, we demonstrate the strong dependence of interference pattern on the junction direction. As the junction direction perpendicular to the tilt direction, Veselago focusing or normal caustics (similar to that in graphene) appears resting on the doping configuration of the textit{p-n} junctions, otherwise anomalous caustics (different from that in graphene) occurs which is manipulated by the junction direction and the doping configuration. Finally, the developed Greens function technique is generally promising to uncover the unique transport of emergent MDFs, and the discovered anomalous caustics makes tilted MDFs potential applications in Dirac electron optics.
The tunneling of electrons and holes in quantum structures plays a crucial role in studying the transport properties of materials and the related devices. 8-Pmmn borophene is a new two-dimensional Dirac material, which hosts tilted Dirac cone and chiral, anisotropic massless Dirac fermions. We develop the transfer matrix method to investigate the Klein tunneling of massless fermions across the smooth NP junctions and NPN junctions of 8-Pmmn borophene. Like the sharp NP junctions of 8-Pmmn borophene, the tilted Dirac cones induce the oblique Klein tunneling. The angle of perfect transmission to the normal incidence is 20.4 degrees, a constant determined by the Hamiltonian of 8-Pmmn borophene. For the NPN junction, there are branches of the Klein tunneling in the phase diagram. We find that the asymmetric Klein tunneling is induced by the chirality and anisotropy of the carriers. Furthermore, we show the oscillation of electrical resistance related to the Klein tunneling in the NPN junctions. One may analyze the pattern of electrical resistance and verify the existence of asymmetric Klein tunneling experimentally.
First-principles calculations on monolayer 8-{it Pmmn} borophene are reported to reveal unprecedented electronic properties in a two-dimensional material. Based on a Born effective charge analysis, 8-{it Pmmn} borophene is the first single-element based monolayered material exhibiting two sublattices with substantial ionic features. The observed Dirac cones are actually formed by the p$_z$ orbitals of one of the inequivalent sublattices composed of uniquely four atoms, yielding an underlying hexagonal network topologically equivalent to distorted graphene. A significant physical outcome of this effect includes the possibility of converting metallic 8-{it Pmmn} borophene into an indirect band gap semiconductor by means of external shear stress. The stability of the strained structures are supported by a phonon frequency analysis. The Dirac cones are sensitive to the formation of vacancies only in the inequivalent sublattice electronically active at the Fermi level.
As a new two-dimensional Dirac material, 8-textit{Pmmn} borophene hosts novel anisotropic and tilted massless Dirac fermions (MDFs) and has attracted increasing interest. However, the potential application of 8-textit{Pmmn} borophene in spin fields has not been explored. Here, we study the long-range RKKY interaction mediated by anisotropic and tilted MDFs in magnetically-doped 8-textit{Pmmn} borophene. To this aim, we carefully analyze the unique real-space propagation of anisotropic and tilted MDFs with noncolinear momenta and group velocities. As a result, we analytically demonstrate the anisotropic behaviors of long-range RKKY interaction, which have no dependence on the Fermi level but are velocity-determined, i.e., the anisotropy degrees of oscillation period and envelop amplitude are determined by the anisotropic and tilted velocities. The velocity-determined RKKY interaction favors to fully determine the characteristic velocities of anisotropic and tilted MDFs through its measurement, and has high tunability by engineering velocities shedding light on the application of 8-textit{Pmmn} borophene in spin fields.
Electrical transport in three dimensional topological insulators(TIs) occurs through spin-momentum locked topological surface states that enclose an insulating bulk. In the presence of a magnetic field, surface states get quantized into Landau levels giving rise to chiral edge states that are naturally spin-polarized due to spin momentum locking. It has been proposed that p-n junctions of TIs in the quantum Hall regime can manifest unique spin dependent effects, apart from forming basic building blocks for highly functional spintronic devices. Here, for the first time we study electrostatically defined n-p-n junctions of bulk insulating topological insulator BiSbTe$_{1.25}$Se$_{1.75}$ in the quantum Hall regime. We reveal the remarkable quantization of longitudinal resistance into plateaus at 3/2 and 2/3 h/e$^2$, apart from several partially developed fractional plateaus. Theoretical modeling combining the electrostatics of the dual gated TI n-p-n junction with Landauer Buttiker formalism for transport through a network of chiral edge states explains our experimental data, while revealing remarkable differences from p-n junctions of graphene and two-dimensional electron gas systems. Our work not only opens up a route towards exotic spintronic devices but also provides a test bed for investigating the unique signatures of quantum Hall effects in topological insulators.
Spatial separation of electrons and holes in graphene gives rise to existence of plasmon waves confined to the boundary region. Theory of such guided plasmon modes within hydrodynamics of electron-hole liquid is developed. For plasmon wavelengths smaller than the size of charged domains plasmon dispersion is found to be omega ~ q^(1/4). Frequency, velocity and direction of propagation of guided plasmon modes can be easily controlled by external electric field. In the presence of magnetic field spectrum of additional gapless magnetoplasmon excitations is obtained. Our findings indicate that graphene is a promising material for nanoplasmonics.