Anisotropic Two-dimensional Materials Research Articles

Edge orientations of mechanically exfoliated anisotropic two-dimensional materials

Mechanical exfoliation is an approach widely applied to prepare high-quality two-dimensional (2D) materials for investigating their intrinsic physical properties. During mechanical exfoliation, in-plane cleavage results in new edges whose orientations play an important role in determining the properties of the as-exfoliated 2D materials especially those with high anisotropy. Here, we systematically investigate the factors affecting the edge orientation of 2D materials obtained by mechanical exfoliation. Our theoretical study manifests that the fractured direction during mechanical exfoliation is determined synergistically by the tearing direction and material anisotropy of fracture energy. For a specific 2D material, our theory enables us to predict the possible edge orientations of the exfoliated flakes as well as their occurring probabilities. The theoretical prediction is experimentally verified by examining the inter-edge angles of the exfoliated flakes of four typical 2D materials including graphene, MoS2, PtS2, and black phosphorus. This work not only sheds light on the mechanics of exfoliation of the 2D materials but also provides a new approach to deriving information of edge orientations of mechanically exfoliated 2D materials by data mining of their macroscopic geometric features.

Resolving the Spatial Structures of Bound Hole States in Black Phosphorus.

Understanding the local electronic properties of individual defects and dopants in black phosphorus (BP) is of great importance for both fundamental research and technological applications. Here, we employ low-temperature scanning tunnelling microscope (LT-STM) to probe the local electronic structures of single acceptors in BP. We demonstrate that the charge state of individual acceptors can be reversibly switched by controlling the tip-induced band bending. In addition, acceptor-related resonance features in the tunnelling spectra can be attributed to the formation of Rydberg-like bound hole states. The spatial mapping of the quantum bound states shows two distinct shapes evolving from an extended ellipse shape for the 1s ground state to a dumbbell shape for the 2px excited state. The wave functions of bound hole states can be well-described using the hydrogen-like model with anisotropic effective mass, corroborated by our theoretical calculations. Our findings not only provide new insight into the many-body interactions around single dopants in this anisotropic two-dimensional material but also pave the way to the design of novel quantum devices.

Magneto-optical conductivity of anisotropic two-dimensional Dirac–Weyl materials

In the presence of an external magnetic field, the optical response of two-dimensional materials, whose charge carriers behave as massless Dirac fermions with arbitrary anisotropic Fermi velocity, is investigated. Using Kubo formalism, we obtain the magneto-optical conductivity tensor for these materials, which allows to address the magneto-optical response of anisotropic Dirac fermions from the well known magneto-optical conductivity of isotropic Dirac fermions. As an application, we analyse the combined effects of strain-induced anisotropy and magnetic field on the transmittance, as well as on the Faraday rotation, of linearly polarized light after passing strained graphene. The reported analytical expressions can be a useful tool to predict the absorption and the Faraday angle of strained graphene under magnetic field. Finally, our study is extended to anisotropic two-dimensional materials with Dirac fermions of arbitrary pseudospin.

Tunable plasmon-enhanced birefringence in ribbon array of anisotropic two-dimensional materials

We explore the far-field scattering properties of anisotropic 2D materials in ribbon array configuration. Our study reveals the plasmon-enhanced linear birefringence in these ultrathin metasurfaces, where linearly polarized incident light can be scattered into its orthogonal polarization or be converted into circular polarized light. We found wide modulation in both amplitude and phase of the scattered light via tuning the operating frequency or material's anisotropy and develop models to explain the observed scattering behavior.

Continuum thin-shell model of the anisotropic two-dimensional materials: Single-layer black phosphorus

Using the geometric parameters and the elastic moduli determined by the density functional theory (DFT) calculations as the benchmarks, the original Stillinger–Weber (SW) potential of the single layer black phosphorus (SLBP) is revised. The revised SW potential can effectively describe the elastic behavior of SLBP, including both the elastic moduli and the stress–strain relationship under large deformation. Using the molecular dynamics (MD) simulations (based on the revised SW potential), it is found that the continuum thin-shell theory can effectively describe the bending and buckling behavior of SLBP: although the elastic behavior of SLBP is highly anisotropic, the thin-shell thicknesses along different directions determined from the continuum theory are very close to each other. In addition, the thin-shell thickness of SLBP is very close to its physical thickness, and the thin-shell thickness determined from the bending theory is also very close to that determined from its buckling behavior, which are highly different from the corresponding behaviors of graphene. Thus, the lower limit for effectively applying the continuum thin-shell theory to investigating the mechanical behavior of two-dimensional (2D) materials is that 2D-materials include at least two atomic layers.

Angle resolved vibrational properties of anisotropic transition metal trichalcogenide nanosheets.

Layered transition metal trichalcogenides (TMTCs) are a new class of anisotropic two-dimensional materials that exhibit quasi-1D behavior. This property stems from their unique highly anisotropic crystal structure where vastly different material properties can be attained from different crystal directions. Here, we employ density functional theory predictions, atomic force microscopy, and angle-resolved Raman spectroscopy to investigate their fundamental vibrational properties which differ significantly from other 2D systems and to establish a method in identifying anisotropy direction of different types of TMTCs. We find that the intensity of certain Raman peaks of TiS3, ZrS3, and HfS3 have strong polarization dependence in such a way that intensity is at its maximum when the polarization direction is parallel to the anisotropic b-axis. This allows us to readily identify the Raman peaks that are representative of the vibrations along the b-axis direction. Interestingly, similar angle resolved studies on the novel TiNbS3 TMTC alloy reveal that determination of anisotropy/crystalline direction is rather difficult possibly due to loss of anisotropy by randomization distribution of quasi-1D MX6 chains by the presence of defects which are commonly found in 2D alloys and also due to the complex Raman tensor of TMTC alloys. Overall, the experimental and theoretical results establish non-destructive methods used to identify the direction of anisotropy in TMTCs and reveal their vibrational characteristics which are necessary to gain insight into potential applications that utilize direction dependent thermal response, optical polarization, and linear dichroism.

Mobility anisotropy of two-dimensional semiconductors

The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, ${\mathrm{BC}}_{2}\mathrm{N}$, MXene, ${\mathrm{TiS}}_{3}$, and ${\mathrm{GeCH}}_{3}$) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.

Unusual lattice vibration characteristics in whiskers of the pseudo-one-dimensional titanium trisulfide TiS3.

Transition metal trichalcogenides form a class of layered materials with strong in-plane anisotropy. For example, titanium trisulfide (TiS3) whiskers are made out of weakly interacting TiS3 layers, where each layer is made of weakly interacting quasi-one-dimensional chains extending along the b axis. Here we establish the unusual vibrational properties of TiS3 both experimentally and theoretically. Unlike other two-dimensional systems, the Raman active peaks of TiS3 have only out-of-plane vibrational modes, and interestingly some of these vibrations involve unique rigid-chain vibrations and S–S molecular oscillations. High-pressure Raman studies further reveal that the AgS–S S-S molecular mode has an unconventional negative pressure dependence, whereas other peaks stiffen as anticipated. Various vibrational modes are doubly degenerate at ambient pressure, but the degeneracy is lifted at high pressures. These results establish the unusual vibrational properties of TiS3 with strong in-plane anisotropy, and may have relevance to understanding of vibrational properties in other anisotropic two-dimensional material systems.

Theoretical investigation of electron-hole complexes in anisotropic two-dimensional materials

Trions and biexcitons in anisotropic two-dimensional materials are investigated within an effective mass theory. Explicit results are obtained for phosphorene and arsenene, materials that share features such as a direct quasi-particle gap and anisotropic conduction and valence bands. Trions are predicted to have remarkably high binding energies and an elongated electron-hole structure with a preference for alignment along the armchair direction, where the effective masses are lower. We find that biexciton binding energies are also notably large, especially for monolayer phosphorene, where they are found to be twice as large as those for typical monolayer transition metal dichalcogenides.

Titanium trisulfide (TiS3): a 2D semiconductor with quasi-1D optical and electronic properties.

We present characterizations of few-layer titanium trisulfide (TiS3) flakes which, due to their reduced in-plane structural symmetry, display strong anisotropy in their electrical and optical properties. Exfoliated few-layer flakes show marked anisotropy of their in-plane mobilities reaching ratios as high as 7.6 at low temperatures. Based on the preferential growth axis of TiS3 nanoribbons, we develop a simple method to identify the in-plane crystalline axes of exfoliated few-layer flakes through angle resolved polarization Raman spectroscopy. Optical transmission measurements show that TiS3 flakes display strong linear dichroism with a magnitude (transmission ratios up to 30) much greater than that observed for other anisotropic two-dimensional (2D) materials. Finally, we calculate the absorption and transmittance spectra of TiS3 in the random-phase-approximation (RPA) and find that the calculations are in qualitative agreement with the observed experimental optical transmittance.

Photoresponse: Highly Sensitive Detection of Polarized Light Using Anisotropic 2D ReS2 (Adv. Funct. Mater. 8/2016)

Light polarization is an important concept in optics for generation, detection and manipulation of light. ReS2, a highly anisotropic two-dimensional material, has excellent capabilities for high detection sensitivity of polarized light, as shown by X. He, Z. Liu, and co-workers on page 1169. Atomically thin ReS2 may pave a promising way to applications in integrated photonic circuits, optical switches and interconnects for detecting the various orientations of linearly polarized light in a highly integrated photonic platform.

Modeling of anisotropic two-dimensional materials monolayer HfS2 and phosphorene metal-oxide semiconductor field effect transistors

Ballistic transport characteristics of metal-oxide semiconductor field effect transistors (MOSFETs) based on anisotropic two-dimensional materials monolayer HfS2 and phosphorene are explored through quantum transport simulations. We focus on the effects of the channel crystal orientation and the channel length scaling on device performances. Especially, the role of degenerate conduction band (CB) valleys in monolayer HfS2 is comprehensively analyzed. Benchmarking monolayer HfS2 with phosphorene MOSFETs, we predict that the effect of channel orientation on device performances is much weaker in monolayer HfS2 than in phosphorene due to the degenerate CB valleys of monolayer HfS2. Our simulations also reveal that at 10 nm channel length scale, phosphorene MOSFETs outperform monolayer HfS2 MOSFETs in terms of the on-state current. However, it is observed that monolayer HfS2 MOSFETs may offer comparable, but a little bit degraded, device performances as compared with phosphorene MOSFETs at 5 nm channel length.

Electronic bandgap and edge reconstruction in phosphorene materials.

Single-layer black phosphorus (BP), or phosphorene, is a highly anisotropic two-dimensional elemental material possessing promising semiconductor properties for flexible electronics. However, the direct bandgap of single-layer black phosphorus predicted theoretically has not been directly measured, and the properties of its edges have not been considered in detail. Here we report atomic scale electronic variation related to strain-induced anisotropic deformation of the puckered honeycomb structure of freshly cleaved black phosphorus using a high-resolution scanning tunneling spectroscopy (STS) survey along the light (x) and heavy (y) effective mass directions. Through a combination of STS measurements and first-principles calculations, a model for edge reconstruction is also determined. The reconstruction is shown to self-passivate most dangling bonds by switching the coordination number of phosphorus from 3 to 5 or 3 to 4.