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Optical and electronic properties of black phosphorus strongly depend on the number of layers and type of stacking. Using first-principles calculations within the framework of density functional theory, we investigate the electronic properties of bilayer black phosphorus with an interlayer twist angle of 90$^circ$. These calculations are complemented with a simple $vec{k}cdotvec{p}$ model which is able to capture most of the low energy features and is valid for arbitrary twist angles. The electronic spectrum of 90$^circ$ twisted bilayer black phosphorus is found to be x-y isotropic in contrast to the monolayer. However x-y anisotropy, and a partial return to monolayer-like behavior, particularly in the valence band, can be induced by an external out-of-plane electric field. Moreover, the preferred hole effective mass can be rotated by 90$^circ$ simply by changing the direction of the applied electric field. In particular, a +0.4 (-0.4) V/{AA} out-of-plane electric field results in a $sim$60% increase in the hole effective mass along the y (x) axis and enhances the $m^*_{y}/m^*_{x}$ ($m^*_{x}/m^*_{y}$) ratio as much as by a factor of 40. Our DFT and $vec{k}cdotvec{p}$ simulations clearly indicate that the twist angle in combination with an appropriate gate voltage is a novel way to tune the electronic and optical properties of bilayer phosphorus and it gives us a new degree of freedom to engineer the properties of black phosphorus based devices.
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We investigate the band structure of twisted monolayer-bilayer graphene (tMBG), or twisted graphene on bilayer graphene (tGBG), as a function of twist angles and perpendicular electric fields in search of optimum conditions for achieving isolated nearly flat bands. Narrow bandwidths comparable or smaller than the effective Coulomb energies satisfying $U_{textrm{eff}} /W gtrsim 1$ are expected for twist angles in the range of $0.3^{circ} sim 1.5^{circ}$, more specifically in islands around $theta sim 0.5^{circ}, , 0.85^{circ}, ,1.3^{circ}$ for appropriate perpendicular electric field magnitudes and directions. The valley Chern numbers of the electron-hole asymmetric bands depend intrinsically on the details of the hopping terms in the bilayer graphene, and extrinsically on factors like electric fields or average staggered potentials in the graphene layer aligned with the contacting hexagonal boron nitride substrate. This tunability of the band isolation, bandwidth, and valley Chern numbers makes of tMBG a more versatile system than twisted bilayer graphene for finding nearly flat bands prone to strong correlations.
Anisotropy describes the directional dependence of a materials properties such as transport and optical response. In conventional bulk materials, anisotropy is intrinsically related to the crystal structure, and thus not tunable by the gating techniques used in modern electronics. Here we show that, in bilayer black phosphorus with an interlayer twist angle of 90{deg}, the anisotropy of its electronic structure and optical transitions is tunable by gating. Using first-principles calculations, we predict that a laboratory-accessible gate voltage can induce a hole effective mass that is 30 times larger along one Cartesian axis than along the other axis, and the two axes can be exchanged by flipping the sign of the gate voltage. This gate-controllable band structure also leads to a switchable optical linear dichroism, where the polarization of the lowest-energy optical transitions (absorption or luminescence) is tunable by gating. Thus, anisotropy is a tunable degree of freedom in twisted bilayer black phosphorus.
Twisted bilayer graphene (tBLG) forms a quasicrystal whose structural and electronic properties depend on the angle of rotation between its layers. Here we present a scanning tunneling microscopy study of gate-tunable tBLG devices supported by atomically-smooth and chemically inert hexagonal boron nitride (BN). The high quality of these tBLG devices allows identification of coexisting moire patterns and moire super-superlattices produced by graphene-graphene and graphene-BN interlayer interactions. Furthermore, we examine additional tBLG spectroscopic features in the local density of states beyond the first van Hove singularity. Our experimental data is explained by a theory of moire bands that incorporates ab initio calculations and confirms the strongly non-perturbative character of tBLG interlayer coupling in the small twist-angle regime.
The environmental stability of the layered semiconductor black phosphorus (bP) remains a challenge. Passivation of the bP surface with phosphorus oxide, POx, grown by a reactive ion etch with oxygen plasma is known to improve photoluminescence efficiency of exfoliated bP flakes. We apply phosphorus oxide passivation in the fabrication of bP field effect transistors using a gate stack consisting of a POx layer grown by reactive ion etching followed by atomic layer deposition of Al2O3. We observe room temperature top-gate mobilities of 115 cm2/Vs in ambient conditions, which we attribute to the low defect density of the bP/POx interface.
The layered semiconductor black phosphorus has attracted attention as a 2D atomic crystal that can be prepared in ultra-thin layers for operation as field effect transistors. Despite the susceptibility of black phosphorus to photo-oxidation, improvements to the electronic quality of black phosphorus devices has culminated in the observation of the quantum Hall effect. In this work, we demonstrate the room temperature operation of a dual gated black phosphorus transistor operating as a velocity modulated transistor, whereby modification of hole density distribution within a black phosphorus quantum well leads to a two-fold modulation of hole mobility. Simultaneous modulation of Schottky barrier resistance leads to a four-fold modulation of transcon- ductance at a fixed hole density. Our work explicitly demonstrates the critical role of charge density distribution upon charge carrier transport within 2D atomic crystals.
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