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Register a new userOblique and asymmetric Klein tunneling across smooth NP junctions or NPN junctions in 8-Pmmn borophene
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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.
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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.
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.
We study the zero temperature conductance and magnetoconductance of ballistic textit{p-n} junctions in Weyl semimetals. Electron transport is mediated by Klein tunneling between textit{n}- and textit{p}- regions. The chiral anomaly that is realized in Weyl semimetals plays a crucial role in the magnetoconductance of the junction. With the exception of field orientations where the angle between $mathbf{B}$ and the junction plane is small, magnetoconductance is positive and linear in $B$ at both weak and strong magnetic fields. In contrast, magnetoconductance in conventional textit{p-n} junctions is always negative.
We have realized a Dirac fermion reflector in graphene by controlling the ballistic carrier trajectory in a sawtooth-shaped npn junction. When the carrier density in the inner p-region is much larger than that in the outer n-regions, the first straight np interface works as a collimator and the collimated ballistic carriers can be totally reflected at the second zigzag pn interface. We observed clear resistance enhancement around the np+n regime, which is in good agreement with the numerical simulation. The tunable reflectance of ballistic carriers could be an elementary and important step for realizing ultrahigh-mobility graphene field effect transistors utilizing Dirac fermion optics in the near future.
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