Stacked bilayer phosphorene: strain-induced quantum spin Hall state and optical measurement

Phase Engineering of 2D Materials

Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.

Effects of spin-orbit coupling on transmission and absorption of electromagnetic waves in strained armchair phosphorene nanoribbons

We compute the optical conductivity, both the imaginary and real parts of the dielectric constant, and the optical coefficients of armchair phosphorene nanoribbons under application of biaxial and uniaxial strains. The Kane-Mele model Hamiltonian has been applied to obtain the electronic band structure of phosphorene nanoribbons in the presence of a magnetic field. The effects of uniaxial and biaxial in-plane strain on the frequency behavior of the optical dielectric constant, and the frequency behavior of the optical absorption and refractive index of phosphorene nanoribbons have been studied, in terms of magnetic field, spin-orbit coupling and strain effects. Linear response theory and the Green's function approach have been exploited to obtain the frequency behavior of the optical properties of the structure. Moreover, the transmissivity and reflectivity of electromagnetic waves between two media separated by a phosphorene-nanoribbon layer are determined. Our numerical results indicate that the frequency dependence of the optical absorption includes a peak due to applying a magnetic field. Moreover, the effects of both in-plane uniaxial and biaxial strains on the refractive index of single-layer phosphorene have been addressed. Also, the frequency dependence of the transmissivity and reflectivity of electromagnetic waves between two media separated by armchair phosphorene nanoribbons for normal incidence has been investigated in terms of the effects of magnetic field and strain parameters. Both compressive and tensile strain have been considered for the armchair phosphorene nanoribbons in order to study the optical properties of the structure. In particular, the control of the optical properties of phosphorene nanoribbons could lead to extensive applications of phosphorene in the optoelectronics industry. Also, such a study of the optical properties of phosphorene nanoribbons has further applications in light sensors. Meanwhile, the effects of spin-orbit coupling on the optical absorption and transmissivity of electromagnetic waves in phosphorene nanoribbons could be a novel topic in condensed-matter physics.

Superior mechanical flexibility, lattice thermal conductivity and electron mobility of the hexagonal honeycomb carbon nitride monolayer

Nitrogen is the nearest neighbor element of carbon and, thus, the hexagonal honeycomb carbon nitride monolayer (C_xN_y), which consists of a covalent network of carbon and nitrogen atoms, usually has attractive physical and chemical properties similar to those in graphene. Here, we systematically investigate the geometric structure, mechanical properties, thermal transport properties, and plasmon excitation of a new phase, labeled C₃N₂, and make a detailed comparison with other possible C_xN_y allotropes. All C_xN_y have a super-high layer modulus and Young's modulus. But compared with the others, C₃N₂ exhibits excellent mechanical flexibility, and can withstand a relatively high critical strain up to 20% (18%) along the X(Y) direction. Additionally, C₃N₂ also has excellent thermal and electronic transport properties, with a super-high lattice thermal conductivity of ∼110.9 W m^-1 K^-1 and electron mobility of ∼1617.52 cm² V^-1 s^-1 at 300 K. By performing time-dependent density functional theory (TDDFT), we obtain the optical absorptions of C₃N₂ and C₃N, and meanwhile analyze their Fourier transforms of induced charge densities at some resonant frequencies. The main optical absorption peaks of the C₃N₂ nanostructure are located in the ultraviolet region, and its plasmon peaks are far higher than those in C₃N. Its excellent mechanical and optical properties, the larger electronic band gap, and the higher electron mobility suggest that C₃N₂ has great potential for application in nanoelectronics and optoelectronics.

Designing Direct Z-Scheme Heterojunctions Enabled by Edge-Modified Phosphorene Nanoribbons for Photocatalytic Overall Water Splitting

Direct Z-scheme photocatalyst possess promising potential to utilize solar radiation for photocatalytic overall water splitting; however, the design and characterization remain challenging. Here, we construct and verify a direct Z-scheme heterojunction using edge-modified phosphorene-nanoribbons (X-PNRs, where X = OH and OCN) with first-principles ground-state and excited-state density functional theory (DFT) calculations. The ground-state calculations provide fundamental properties such as geometric structure and band alignment. The linear-response time-dependent DFT (LR-TDDFT) calculations exhibit the photogenerated charge distribution and demonstrate the generation of interlayer excitons in heterojunctions, which are advantageous to the electron-hole recombination in Z-scheme heterojunctions. The ultrafast charge transfer at the interface studied by time-dependent ab initio nonadiabatic molecular dynamics (NAMD) simulations indicates that interlayer electron-hole recombination is prior to intralayer recombination for the OH/OCN-PNRs heterojunction, showing the characteristics of a Z-scheme heterojunction. Therefore, our computational work provides a universal strategy to design direct Z-scheme heterojunction photocatalysts for overall water splitting.

Strain-controlled thermoelectric properties of phosphorene-carbon monosulfide hetero-bilayers

The application of strain to 2D materials allows manipulating the electronic, magnetic, and thermoelectric properties. These physical properties are sensitive to slight variations induced by tensile and compressive strain and the uniaxial strain direction. Herein, we take advantage of the reversible semiconductor-metal transition observed in certain monolayers to propose a hetero-bilayer device. We propose to pill up phosphorene (layered black phosphorus) and carbon monosulfide monolayers. In the first, such transition appears for positive strain, while the second appears for negative strain. Our first-principle calculations show that depending on the direction of the applied uniaxial strain; it is possible to achieve reversible control in the layer that behaves as an electronic conductor while the other layer remains as a thermal conductor. The described strain-controlled selectivity could be used in the design of novel devices.

First-Principles Study of Linear and Nonlinear Optical Properties of Multi-Layered Borophene

Anisotropic materials are of great interest due to their unique direction-dependent optical properties. Borophene, the two-dimensional analog of graphene consisting of boron atoms, has attracted immense research interest due to its exciting anisotropic electronic and mechanical properties. Its synthesis in several structural polymorphic configurations has recently been reported. The present work reports the layer-dependent optical absorption and hyperpolarizabilities of the buckled borophene (δ6-borophene). The results, based on density functional theory, show that multilayer borophene is nearly transparent with only a weak absorbance in the visible region, reflecting its anisotropic structural characteristics. The static first-order hyperpolarizability significantly increases with the number of layers, due mainly to interactions among the frontier orbitals in multilayer borophene. Transparency in the visible region combined with enhanced nonlinear optical properties makes the multilayer borophene important for future photonics technologies.

Atomically Thin Quantum Spin Hall Insulators

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Among them is the quantum spin Hall (QSH) insulator-a 2D state of matter that arises from interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk bandgaps up to 800 meV and gapless, 1D edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, the QSH materials library is surveyed with focus on the prospects for QSH-based device applications. In particular, theoretical predictions of nontrivial superconducting pairing in the QSH state toward Majorana-based topological quantum computing are discussed, which are the next frontier in QSH materials research.

Prediction of nodal-line semimetals in two-dimensional black phosphorous films

Semimetals are a new kind of quantum materials, in which the conduction and valence bands cross each other near the Fermi level. Based on density-functional theory calculations and symmetry analysis, we propose nodal-line semimetals in layered stacked black phosphorus (BP) films which are designed to have a mirror symmetry lying in the BP layer plane and thus rendering them different from the BP film systems previously studied. A closed nodal-line degenerate band can appear around the Fermi level in the BP films after a biaxial compressive strain is applied. The calculated Z2 number of Z2 =  - 1 indicates the robustness of the nodal-line semimetals obtained in the BP films, protected by the in-plane mirror symmetry. Intriguingly, with the increase of the film thickness, a smaller biaxial compressive strain is required to produce the nodal-line semimetals, more accessible in experiments. Our results provide a promising route to carrying out the nodal-line semimetals based on various two-dimensional materials.

Anomalous magneto-transport properties of bilayer phosphorene

The magneto-transport properties of phosphorene are investigated by employing the generalized tight-binding model to calculate the energy bands. For bilayer phosphorene, a composite magnetic and electric field is shown to induce a feature-rich Landau level (LL) spectrum which includes two subgroups of low-lying LLs. The two subgroups possess distinct features in level spacings, quantum numbers, as well as field dependencies. These together lead to anomalous quantum Hall (QH) conductivities which include a well-shape, staircase and composite quantum structures with steps having varying heights and widths. The Fermi energy-magnetic field-Hall conductivity (EF-Bz-σxy) and Fermi energy-electric field-Hall conductivity (EF-Ez-σxy) phase diagrams clearly exhibit oscillatory behaviors and cross-over from integer to half-integer QH effect. The predicted results should be verifiable by magneto-transport measurements in a dual-gated system.

Raman Activity of Multilayer Phosphorene under Strain

Using computational tools, we study the behavior of activities of lattice vibrational Raman modes in few-layered phosphorene of up to four layers subjected to a uniaxial strain of -2 to +6% applied in the armchair and zigzag directions. We study both high- and low-frequency modes and find very appreciable frequency shifts in response to the applied strain of up to ≈20 cm^-1. The Raman activities are characterized by A_g ²/A_g ¹ activity ratios, which provide very meaningful characteristics of functionalization via layer- and strain-engineering. The ratios exhibit a pronounced vibrational anisotropy, namely a linear increase with the applied armchair strain and a highly nonlinear behavior with a strong drop of the ratio with the strain applied along the zigzag direction. For the low-frequency modes, which are Raman active exclusively in few-layered systems, we find the breathing interlayer modes of primary importance due to their strong activities. For few-layered structures with a thickness ≥4, a splitting of the breathing modes into a pair of modes with complementary activities is found, with the lower frequency mode being strain activated. Our calculated database of results contains full angular information on activities of both low- and high-frequency Raman modes. These results, free of experimental complexities, such as dielectric embedding, defects, and size and orientation of the flakes, provide a convenient benchmark for experiments. Combined with high-spatial-resolution Raman scattering experiments, our calculated results will aid in the understanding of the complicated inhomogeneous strain distributions in few-layered phosphorene or the manufacture of materials with desired electronic properties via strain- or layer-engineering.

Two-dimensional layered materials: from mechanical and coupling properties towards applications in electronics

With the increasing interest in nanodevices based on two-dimensional layered materials (2DLMs) after the birth of graphene, the mechanical and coupling properties of these materials, which play an important role in determining the performance and life of nanodevices, have drawn increasingly more attention. In this review, both experimental and simulation methods investigating the mechanical properties and behaviour of 2DLMs have been summarized, which is followed by the discussion of their elastic properties and failure mechanisms. For further understanding and tuning of their mechanical properties and behaviour, the influence factors on the mechanical properties and behaviour have been taken into consideration. In addition, the coupling properties between mechanical properties and other physical properties are summarized to help set up the theoretical blocks for their novel applications. Thus, the understanding of the mechanical and coupling properties paves the way to their applications in flexible electronics and novel electronics, which is demonstrated in the last part. This review is expected to provide in-depth and comprehensive understanding of mechanical and coupling properties of 2DLMs as well as direct guidance for obtaining satisfactory nanodevices from the aspects of material selection, fabrication processes and device design.

Superior Photo-thermionic electron Emission from Illuminated Phosphorene Surface

This work demonstrates that black phosphorene, a two dimensional allotrope of phosphorus, has the potential to be an efficient photo-thermionic emitter. To investigate and understand the novel aspects we use a combined approach in which ab initio quantum simulation tools are utilized along with semiclassical description for the emission process. First by using density functional theory based formalism, we study the band structure of phosphorene. From the locations of electronic bands, and band edges, we estimate the Fermi level and work function. This leads us to define a valid material specific parameter space and establish a formalism for estimating thermionic electron emission current from phosphorene. Finally we demonstrate how the emission current can be enhanced substantially under the effect of photon irradiation. We observe that photoemission flux to strongly dominate over its coexisting counterpart thermionic emission flux. Anisotropy in phosphorene structure plays important role in enhancing the flux. The approach which is valid over a much wider range of parameters is successfully tested against recently performed experiments in a different context. The results open up a new possibility for application of phosphorene based thermionic and photo-thermionic energy converters.

Optical interband transitions in strained phosphorene

In this paper, we have concentrated on the orbital and hybridization effects induced by applied triaxial strain on the interband optical conductivity (IOC) of phosphorene using a two-band Hamiltonian model, linear response theory and the Kubo formula. In particular, we study the dependence of the electronic band structure and of the IOC of a phosphorene single layer on the modulus and direction of the applied triaxial strain. The triaxial strain is included in a model through the introduction of strain-dependent hopping parameters using the Harrison rule. Among the various configurations for applying the triaxial strain, considerable findings are presented here in three classes: (i) uniform, (ii) in-plane uniform and (iii) non-uniform triaxial strain. The main consequence of applying triaxial strain is that of increasing and decreasing the band gap depending on the considered class of study, resulting in a blue shift and red shift of the interband optical transitions, respectively. Our results show that a pure blue shift independent of the strain modulus as well as strain sign (tensile or compressive) emerges when applying non-uniform triaxial strain. The overall feature of our outcomes is tailoring the edge-dependent optical responses of phosphorene in the presence of triaxial strain, which provides the required conditions of tuning the optical properties of phosphorene for future experimental research.

Physical Fingerprints of the 2O-tαP Phase in Phosphorene Stacking

The 2O-tαP phase is a bilayer phosphorene stacking twisted by ∼70.5° standing out from all the potential candidates predicted by our previous work. Here, by linear response theory, we directly verified that the 2O-tαP phase preserves the intrinsic features of phonon spectrum of the existing AB phase, reflecting a stable thermodynamic behavior. Then we provided three distinct fingerprints to help finding this new phase: upon comparison to the existing shifting bilayer phosphorene, the in-plane elastic constants showed a much weaker anisotropic response, providing a characteristic mechanical criterion; the calculated Raman spectrum revealed for the low frequency rang the layer-breathing mode and the out-of-plane twisted mode, L-A¹ and L-A², both of which together stabilize the twisted structure; in particular, the simulated scanning tunneling microscope image presented recognizable cross stripes, which should withstand an examination of exfoliated bilayer and few-layer black phosphorus.

Strain engineering of optical activity in phosphorene

Optical activity is one of the most fascinating fields in current physics. The strong anisotropic feature in monolayer phosphorene leads to the emergence of non-trivial optoelectronic physics. This paper is devoted to a detailed analysis of strain effects on the optical activity of phosphorene ranging from low-optical-field to high-optical-field. To do so, a numerical study of the two-band tight-binding model is accomplished using the Harrison rule and the linear response theory. Although the transparency of phosphorene confirms at all frequencies independent of the strain modulus and direction, on average, from low- to high-optical-field limit, the polarization of the reflected wave at critical strains becomes circular and the ellipse axis tends to a rotation of 180°. It is found that the maximum absorption takes place at high-energy transitions, which quantitatively depends strongly on the strain modulus and direction. Furthermore, a detailed investigation of compressive and tensile strains results in the dominant contribution of the in-plane compressive and out-of-plane tensile strains to the reflected/transmitted light for low- and intermediate-optical-field ranges, whilst both contribute for the high-optical-field limit. However, overall, in-plane compressive and out-of-plane tensile strains come in to play a role in the absorption spectra. Thereby, the quality of the determined reflection, transmission and absorption waves depends on the regarded regime of the optical field, strain modulus, and strain orientation. These findings if sufficient can be performed and/or tuned experimentally, and a vast number of phosphorene-based optoelectronic devices can be achieved.

This paper is devoted to a detailed analysis of strain effects on the optical activity of phosphorene ranging from low-optical-field to high-optical-field.

Quantum anomalous/valley Hall effect and tunable quantum state in hydrogenated arsenene decorated with a transition metal

The quantum anomalous Hall (QAH) effect is superior to the quantum spin Hall (QSH) effect, which can avoid the inelastic scattering of two edge electrons located on one side of a topological nontrivial material, and thus it has attracted both theoretical and experimental interest. Here, we systematically investigate the lattice structures, and electronic and magnetic properties of hydrogenated arsenene decorated with certain transition metals (Cr, Mo and Cu) based on density-functional theory. A unique QAH effect in Mo@AsH is predicted, whose Chern number (C = 1) indicates only one chiral edge channel located on its one side. Then, we prove that this QAH effect realization is closely related with band inversion, which is the competitive result between its spin-orbit coupling (SOC) strength and exchange field. The quantum state of Mo@AsH can also be tuned by an external strain, similar to SOC, and it is noted that its increased topological gap of about 35 meV under 5.0% tensile strain, is large enough to realize the QAH effect at room-temperature. Additionally, the quantum valley Hall effect in Cu@AsH contributed by the inequality of AB sublattices is also found. Our results reveal the physical mechanism to realize the QAH effect in TM@AsH and provide a platform for electrically controllable topological states, which are highly desirable for nanoelectronics and spintronics.

Stacking sequences of black phosphorous allotropes and the corresponding few-layer phosphorenes

Possible bulk black phosphorus (BP) allotropes are constructed based on single-layer BP with various stacking sequences. Our stacking algorithm shows that there are eight possible allotropes with two stacking layers in their unit cells possessing relatively high symmetries, and six of them are retained after structural relaxation using a van der Waals correction of optB88-vdW. The AF, AG, and AH bulk structures are presented for the first time. The structural relationship of these configurations has been explained via an interlayer slipping process. The total energy of the AF allotrope is closest to the most stable bulk BP structure (AB stacking) among all explored 2-layer stacked bulk structures. The calculated band structure of the AF allotrope using HSE06 shows a direct band gap of 0.48 eV with anisotropic electronic structures. We also presented six possible BP allotropes with three stacking layers in their unit cells. The newly reported AAF and ABC stacked structures show semiconducting and metallic features, respectively. After the bulk structures were explored, we further built the corresponding few-layer phosphorene structures and investigated their electronic properties. The results show that all the few-layer phosphorenes show semiconducting features. The AE, AAE, and AEA phosphorenes have indirect band gaps while the other explored phosphorenes possess direct band gaps located at the Γ point.

Topological behaviour of ternary non-symmorphic crystals KZnX (X = P, As, Sb) under pressure and strain: a first principles study

An ab initio study on the impact of hydrostatic pressure and strain on the electronic properties of an unexplored class of ternary Zintl phases KZnX (X = P, As, Sb) is reported. Density functional theory (DFT) based studies revealed that all the three materials are direct band gap semiconductors under ambient conditions. We have theoretically demonstrated that KZnX can be driven into different metallic phases under pressure. In contrast, by applying strain the compounds can be realized as topological insulators. This is confirmed by the observed non-trivial topological character in the electronic band structure of the present ternary systems. For the precise determination of low energy band topology, the Tran Blaha modified Becke-Johnson (TBmBJ) exchange potential was used by incorporating spin-orbit coupling. The concomitant change of electronic band shapes as a function of pressure indicates a semi-metallic nature in KZnX (X = P, As, Sb) at 30 GPa, 21 GPa and 11 GPa respectively. Based on an analysis of the parity eigenvalues, we anticipate that a band inversion occurs between the Zn-s and X-p states, thus demonstrating a weak topological behaviour in semi-metallic states. Also, a weak non-trivial topologically insulating phase is realized in strained KZnAs (18%) and KZnSb (10%) which appears to be due to overlapping of the Zn-s and X-p orbitals. The calculated surface spectral functions further validate the non-triviality of strained KZnX (X = As, Sb), whereas strained KZnP is found to be a trivial insulator. We confirm the topological behaviour of these materials by calculating topological surface states and defining a Z₂ topological invariant. Our work based on sophisticated first-principles calculations highlights that both pressure and strain can trigger topological phases in non-symmorphic trivial band insulators even with a weak spin orbit interaction. This study paves the way for realizing semi-metallic and topological insulating states in non-symmorphic ternary semiconductors, which have not been experimentally demonstrated so far.

Effect of stacking order and in-plane strain on the electronic properties of bilayer GeSe

Bilayer germanium selenide as a new layered material is promising for nanoelectronic applications due to its unique optoelectronic properties and tunable band gap.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z_{2} topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Magnetic properties of transition metal Mn, Fe and Co dimers on monolayer phosphorene

We studied the geometries, electronic structure and magnetic properties of substitutional doping and adsorption of transition metal (Mn, Fe and Co) dimers on phosphorene monolayer in the framework of the generalized gradient approximation (GGA) and GGA + U. Electronic band structures and magnetic properties were dependent on the doping type and dopant materials. For Mn and Fe substitutional and adsorption dimers, we obtained semiconducting band structures with spin polarization. However, we found a half-metallic feature in Co substitutional dimer while the Co adsorption dimer showed a semiconducting behavior without any spin polarization. With GGA + U, all the systems showed spin polarized semiconducting band structures except Co adsorption dimer which remained unaffected. The hybridization between transition metal (TM) and phosphorene sheet contributed to suppressing the magnetic moment of TM dimers. For instance, the total magnetic moments of -2.0, 4.24 and 1.28 μ B/cell for Mn, Fe and Co substitutional dimers were obtained while the Mn and Fe adsorption dimers showed magnetic moments of -1.69 and 0.46 μ B/cell. These magnetic moments were enhanced with GGA + U. The same magnetic ground states were obtained both from GGA and GGA + U approaches except for the Mn dimers. We observed that the Mn and Fe substitutional dimers showed an out-of-plane magnetization while an in-plane magnetization was observed in Co substitutional dimer. The Mn adsorption dimer still displayed a perpendicular magnetization whereas the Fe adsorption dimer had an in-plane magnetization. We found that the both GGA and GGA + U showed the same magnetization direction in all the systems.