Abstract
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- borophene is a new two-dimensional Dirac material that hosts tilted Dirac cone and chiral, anisotropic massless Dirac fermions. We adopt the transfer matrix method to investigate the Klein tunneling of massless fermions across the smooth NP junctions and NPN junctions of 8- borophene. Like the sharp NP junctions of 8- borophene, the tilted Dirac cones induce the oblique Klein tunneling. The angle of perfect transmission to the normal incidence is , a constant determined by the Hamiltonian of 8- 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.
Highlights
Two-dimensional (2D) materials have been the superstars for their novel properties in condensed matter physics since its first isolation of graphene in 2004 [1]
We show the angle of oblique Klein tunneling is 20.4◦, a constant determined by the Hamiltonian parameters of 8-Pmmn borophene
We present the numerical results for the transmission probability and electrical conduction of the massless Dirac fermions across the borophene NP junction and NPN junction
Summary
Two-dimensional (2D) materials have been the superstars for their novel properties in condensed matter physics since its first isolation of graphene in 2004 [1]. Due to the suppression of backscattering, massless Dirac fermions could tunnel a single square barrier with 100% transmission probability. This kind of structure is the most stable symmetric phase of borophene and may be kinetically stable at ambient conditions It revealed the tilted Dirac cone and anisotropic massless Dirac fermions by first-principles calculations [27,28].These unique Dirac fermions attracts people to explore the various physical properties such as Nanomaterials 2021, 11, 1462. The oblique Klein tunneling, the deviation of the perfect transmission direction to the normal direction of the interface, is induced by the anisotropic massless Dirac fermions or the tilted Dirac cone [39,53]. Similar to the sharp NP junction, the oblique Klein tunneling retains due to the tilted Dirac cone.
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