Anisotropic ultraviolet-plasmon dispersion in black phosphorus

Near-field detection of gate-tunable anisotropic plasmon polaritons in black phosphorus at terahertz frequencies

Polaritons in two-dimensional layered crystals offer an effective solution to confine, enhance and manipulate terahertz (THz) frequency electromagnetic waves at the nanoscale. Recently, strong THz field confinement has been achieved in a graphene-insulator-metal structure, exploiting THz plasmon polaritons (PPs) with strongly reduced wavelength (λp ≈ λ0/66) compared to the photon wavelength λ0. However, graphene PPs propagate isotropically, complicating the directional control of the THz field, which, on the contrary, can be achieved exploiting anisotropic layered crystals, such as orthorhombic black-phosphorus. Here, we detect PPs, at THz frequencies, in hBN-encapsulated black phosphorus field effect transistors through THz near-field photocurrent nanoscopy. The real-space mapping of the thermoelectrical near-field photocurrents reveals deeply sub-wavelength THz PPs (λp ≈ λ0/76), with dispersion tunable by electrostatic control of the carrier density. The in-plane anisotropy of the dielectric response results into anisotropic polariton propagation along the armchair and zigzag crystallographic axes of black-phosphorus. The achieved directional subwavelength light confinement makes this material system a versatile platform for sensing and quantum technology based on nonlinear optics.

Energy loss of charged particles in anisotropic 2D materials using the oscillator model

We apply the oscillator model to study the energy loss processes of external charged particles interacting with a 2D material characterized by an anisotropic conductivity tensor. We model the material as a monolayer of harmonic oscillators, with anisotropic electronic vibration modes. We focus on the cases of parallel and perpendicular trajectories of the external particle, and we obtain analytical expressions for the stopping power and total energy loss in terms of reduced variables. This allows us to analyze in detail the interaction and to adapt the model to the considered material using adequate values for the physical parameters involved.

Semiconductor-to-metal transition from monolayer to bilayer blue phosphorous induced by extremely strong interlayer coupling: a first-principles study

Monolayer blue phosphorous has a large band gap of 2.76 eV but counterintuitively the most stable bilayer blue phosphorous has a negative band gap of -0.51 eV. Such a large band gap reduction from just monolayer to bilayer has not been revealed before, the underlying mechanism behind which is important for understanding interlayer interactions. In this work, we reveal the origin of the semiconductor-to-metal transition using first-principles calculations and tight-binding models. We find that the interlayer interactions are extremely strong, which can be attributed to the short layer distance and strong π-like atomic orbital couplings. Therefore, the upshift of the valence band maximum (VBM) from monolayer to bilayer blue-P is so large that the VBM in the bilayer gets higher than the conduction band minimum, leading to a negative band gap and an energy gain. Besides, the interlayer atomic misplacements weaken the couplings of out-of-plane orbitals. Therefore, the energy gain due to the semiconductor-to-metal transition is larger than the energy cost due to interlayer repulsions, thus stabilizing the metallic phase. The large band gap reduction with layer number increasing is expected to exist in other similar layered systems.

Momentum-Resolved Dielectric Response of Free-Standing Mono-, Bi-, and Trilayer Black Phosphorus

Black phosphorus (BP), a 2D semiconducting material of interest in electronics and photonics, exhibits physical properties characterized by strong anisotropy and band gap energy that scales with reducing layer number. However, the investigation of its intrinsic properties is challenging because thin-layer BP is photo-oxidized under ambient conditions and the energy of its electronic states shifts in different dielectric environments. We prepared free-standing samples of few-layer BP under glovebox conditions and probed the dielectric response in a vacuum using scanning transmission electron microscopy and electron energy loss spectroscopy (STEM-EELS). Thresholds of the excitation energy are measured at 1.9, 1.4, and 1.1 eV for the mono-, bi-, and trilayer BP, respectively, and these values are used to estimate the corresponding optical band gaps. A comparison of our results with electronic structure calculations indicates that the variation of the quasi-particle gap is larger than that of the exciton binding energy. The dispersion of the plasmons versus momentum for one- to three-layer BP and bulk BP highlights a deviation from parabolic to linear dispersion and strong anisotropic fingerprints.