Black phosphorous (BP) is a layered semiconductor with high carrier mobility, anisotropic optical response and wide bandgap tunability. In view of its application in optoelectronic devices, understanding transient photo-induced effects is crucial. Here, we investigate by time- and angle-resolved photoemission spectroscopy BP in its pristine state and in the presence of Stark splitting, chemically induced by Cs ad-sorption. We show that photo-injected carriers trigger bandgap renormalization and a concurrent valence band attening caused by Pauli blocking. In the biased sample, photoexcitation leads to a long-lived (ns) surface photovoltage of few hundreds mV that counterbalances the Cs-induced surface band bending. This allows us to disentangle bulk from surface electronic states and to clarify the mechanism underlying the band inversion observed in bulk samples.
We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ~0.6 eV. High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their moving along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by spacetime inversion symmetry, even in the presence of spin-orbi…
We examine the nature of topological currents in black phosphorus when its inversion symmetry is deliberately broken. Here, the conduction and valence band edges are located at the $Γ$ point of the rectangular Brillouin zone, and they exhibit strong anisotropy along its two crystal axes. We will show below that these salient features lead to a linear transverse neutral topological currents, accompanied also by a non-linear transverse charge current at the Fermi surface. These topological currents are maximal when the in-plane electric field is applied along the zigzag crystal axes, but zero al…
Based on first-principles calculations and tight-binding model analysis, we propose that black phosphorus (BP) can host a three-dimensional topological node-line semimetal state under pressure when spin-orbit coupling (SOC) is ignored. A closed topological node line exists in the first Brillouin zone (BZ) near the Fermi energy, which is protected by the coexistence of time-reversal and spatial inversion symmetry with band inversion driven by pressure. Drumhead-like surface states have been obtained on the beard (100) surface. Due to the weak intrinsic SOC of phosphorus atom, a band gap less th…
Black phosphorus consists of stacked layers of phosphorene, a two-dimensional semiconductor with promising device characteristics. We report the realization of a widely tunable bandgap in few-layer black phosphorus doped with potassium using an in-situ surface doping technique. Through band-structure measurements and calculations, we demonstrate that a vertical electric field from dopants modulates the bandgap owing to the giant Stark effect and tunes the material from a moderate-gap semiconductor to a band-inverted semimetal. At the critical field of this band inversion, the material becomes …
The electronic structure of few-layer(FL) black phosphorus(BP) sensitively depends on the sample thickness, strain and doping. In this paper, we show that it is also vulnerable to air-exposure. The oxidation of BP caused by air-exposure gives several optical signatures, including the broadening of resonance peaks and increased Stokes shift between infrared (IR) absorption and photoluminescence (PL) peaks. More importantly, air exposure causes blue shifts of all resonance peaks in IR absorption and PL spectra, with more prominent effects for thinner samples and higher order subband transitions.…
Phosphorene is a novel two-dimensional material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, monolayer phosphorene has a large band gap. It was thus unsuspected to exhibit band inversion and the ensuing topological insulator behavior. It has recently attracted interest because of its proposed application as field effect transistors. Using first-principles calculations with applied perpendicular electric field F we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal…
We investigate the effect of charge carrier interaction with surface optical phonons on the band properties of monolayer black phosphorus induced by polar substrates. We develop an analytical method based on the Lee-Low-Pines theory to calculate the spectrum of Fröhlich type continuum Hamiltonian in the long-wavelength limit. We examine the modification of a band gap and renormalization of effective masses due to the substrate-related polaronic effect. Our results show that an energy gap in supported monolayer black phosphorus is enlarged depending on a particular substrate and the interlayer …
We have calculated numerically electron exchange, correlation energies and dynamical polarization function for newly discovered silicene, germanene and black phosphorus (BP), consisting of puckered layers of elemental phosphorus atoms, broadening the range of two-dimensional (2D) materials at various temperatures. As a matter of fact, monolayer BP, produced by mechanical and liquid exfoliation techniques, has been predicted to be an insulator with a large energy splitting 1.6 eV for the quasiparticle band structure. We compare the dependence of these energies on the chemical potential, field-i…
This work presents theoretical demonstration of Aharonov-Bohm (AB) effect in monolayer phosphorene nanorings (PNR). Atomistic quantum transport simulations of PNR are employed to investigate the impact of multiple modulation sources on the sample conductance. In presence of a perpendicular magnetic field, we find that the conductance of both armchair and zigzag PNR oscillate periodically in a low-energy window as a manifestation of the AB effect. Our numerical results have revealed a giant magnetoresistance (MR) in zigzag PNR (with a maximum magnitude approaching two thousand percent). It is a…
Black phosphorus is a material with an intrinsic anisotropy in electronic and optical properties due to its puckered honeycomb lattice. Optical absorption is different for incident light with linear polarization in the armchair and zigzag directions (linear dichroism). These directions are also used in the cuts of materials to create black phosphorus nanoribbons. Edges of nanoribbons usually have small reconstruction effects, with minor electronic effects. Here, we show a reconstruction of the armchair edge that introduces a new valence band, which flattens the puckered lattice and increases t…
Ultrafast nonlinear Hall effect in black phosphorus
Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）；KTH Royal Institute of Technology（皇家理工学院）；CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit)（意大利国家研究委员会材料科学研究所超快过程部门（FLASHit））；CELIA, University of Bordeaux–CNRS–CEA（波尔多大学-法国国家科学研究中心-法国原子能和替代能源委员会联合实验室）；Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences（中国科学院凝聚态物理国家实验室）；Institute for Optics and Atomic Physics, Technical University Berlin（柏林工业大学光学与原子物理研究所）；Department of Physics, Tor Vergata University of Rome（罗马托尔维尔加塔大学物理系）
Black phosphorus (BP) is a two-dimensional layered material composed of phosphorus atoms. Recently, it was demonstrated that external perturbations such as an electric field close the band gap in few-layer BP, and can even induce a band inversion, resulting in an insulator phase with a finite energy gap or a Dirac semimetal phase characterized by two separate Dirac nodes. At the transition between the two phases, a semi-Dirac state appears in which energy disperses linearly along one direction and quadratically along the other. In this work, we study the optical conductivity of few-layer BP us…
We propose and evaluate the heterostructure based on the graphene-layer (GL) with the lateral electron injection from the side contacts and the hole vertical injection via the black phosphorus layer (PL) (p$^+$PL-PL-GL heterostructure). Due to a relatively small energy of the holes injected from the PL into the GL (about 100 meV, smaller than the energy of optical phonons in the GL which is about 200 meV), the hole injection can effectively cool down the two-dimensional electron-hole plasma in the GL. This simplifies the realization of the interband population inversion and the achievement of …
We have performed angle-resolved photoemission spectroscopy (ARPES) of LaSb and CeSb, a candidate of topological insulator. Using soft-x-ray photons, we have accurately determined the three-dimensional bulk band structure and revealed that the band inversion at the Brillouin-zone corner - a prerequisite for realizing topological-insulator phase - is absent in both LaSb and CeSb. Moreover, unlike the ARPES data obtained with soft-x-ray photons, those with vacuum ultraviolet (VUV) photons were found to suffer significant $k_z$ broadening. These results suggest that LaSb and CeSb are topologicall…
We propose and analyze the heterostructure comprising a black-arsenic-phosphorus layer (b-As$_{1-x}$P$_x$L) and a graphene layer (GL) integrated with a light-emitting diode (LED). The integrated b-As$_{1-x}$P$_x$L-GL-LED heterostructure can serve as an active part of the terahertz (THz) laser using the interband radiative transitions in the GL. The feasibility of the proposed concept is enabled by the combination of relatively narrow energy gap in the b-As$_{1-x}$P$_x$L and the proper band alignment with the GL. The operation of the device in question is associated with the generation of the e…
Two-dimensional ($2$D) semi-Dirac systems, such as $2$D black phosphorus and arsenene, can exhibit a rich topological phase transition between insulating, semi-Dirac, and band inversion phases when subjected to an external modulation. How these phase transitions manifest within the quantum transport and shot noise signatures remain an open question thus far. Here, we show that the Fano factor converges to the universal $F\approx0.179$ at the semi-Dirac phase, and transits between the sub-Poissonian ($F\approx1/3$) and the Poissonian shot noise ($F\approx1$) limit at the band inversion and the …
The gap in bilayer graphene (BLG) can directly be controlled by a perpendicular electric field. By tuning the field through zero at a finite rate in neutral BLG, excited states are produced. Due to screening, the resulting dynamics is determined by coupled non-linear Landau-Zener models. The generated defect density agrees with Kibble-Zurek theory in the presence of subleading logarithmic corrections. After the quench, population inversion occurs for wavevectors close to the Dirac point. This could, at least in principle provide a coherent source of infra-red radiation with tunable spectral pr…
In recent years, there have been conflicting reports regarding the ultrafast photoconductive response of films of single walled carbon nanotubes (CNTs), which apparently exhibit photoconductivities that can differ even in sign. Here, we observe explicitly that the THz photoconductivity of CNT films is a highly variable quantity which correlates with the length of the CNTs, while the chirality distribution has little influence. Moreover, by comparing the photo-induced change in THz conductivity with heat-induced changes, we show that both occur primarily due to heat-generated modification of th…
The influence of the inelastic nature of electron scattering by surface excitations of liquid helium (ripplons) on the shape of magnetoconductivity oscillations induced by resonance microwave (MW) excitation is theoretically studied. The MW field provides a substantial filling of the first excited surface subband which sparks off inter-subband electron scattering by ripplons. This scattering is the origin of magneto-oscillations in the momentum relaxation rate. The inelastic effect becomes important when the energy of a ripplon involved compares with the collision broadening of Landau levels. …
