Anisotropic thermal transport in phosphorene: effects of crystal orientation

Improved Thermal Anisotropy of Multi-Layer Tungsten Telluride on Silicon Substrate

WTe₂, a low-symmetry transition metal dichalcogenide, has broad prospects in functional device applications due to its excellent physical properties. When WTe₂ flake is integrated into practical device structures, its anisotropic thermal transport could be affected greatly by the substrate, which matters a lot to the energy efficiency and functional performance of the device. To investigate the effect of SiO₂/Si substrate, we carried out a comparative Raman thermometry study on a 50 nm-thick supported WTe₂ flake (with κ_zigzag = 62.17 W·m^-1·K^-1 and κ_armchair = 32.93 W·m^-1·K^-1), and a suspended WTe₂ flake of similar thickness (with κ_zigzag = 4.45 W·m^-1·K^-1, κ_armchair = 4.10 W·m^-1·K^-1). The results show that the thermal anisotropy ratio of supported WTe₂ flake (κ_zigzag/κ_armchair ≈ 1.89) is about 1.7 times that of suspended WTe₂ flake (κ_zigzag/κ_armchair ≈ 1.09). Based on the low symmetry nature of the WTe₂ structure, it is speculated that the factors contributing to thermal conductivity (mechanical properties and anisotropic low-frequency phonons) may have affected the thermal conductivity of WTe₂ flake in an uneven manner when supported on a substrate. Our findings could contribute to the 2D anisotropy physics and thermal transport study of functional devices based on WTe₂ and other low-symmetry materials, which helps solve the heat dissipation problem and optimize thermal/thermoelectric performance for practical electronic devices.

Enhanced Thermoelectric Performance in Black Phosphorene via Tunable Interlayer Twist

Twist-angle two-dimensional (2D) systems are attractive in their exotic and tunable properties by the formation of the moiré superlattices, allowing easy access to manipulating intrinsic electrical and thermal properties. Here, the angle-dependent thermoelectric properties of twisted bilayer black phosphorene (tbBP) by first-principles calculations are reported. The simulations show that significantly enhanced Seebeck coefficient and power factor can be achieved in p-type tbBP due to merging of the multi-valley electronic states and flat moiré bands. Moreover, the twisted layers bring in a strong anharmonic phonon scattering and thus very low lattice thermal conductivity of 4.51 W m^-1  K^-1 at 300 K. Consequently, a maximal ZT value can be achieved in p-type 10.11° tbBP along the armchair direction up to 0.57 and 1.06 at 300 and 500 K, respectively. The room-temperature ZT value along the zigzag direction is also significantly increased by almost 40 times compared to pristine BP when the twist angle is close to 70.68°. This work demonstrates a platform to manipulate thermoelectric performance in 2D materials by creating moiré patterns, leading tbBP as a promising eco-friendly candidate for thermoelectric applications.

Role of initial conditions in one-dimensional diffusive systems: Compressibility, hyperuniformity, and long-term memory

We analyze the long-lasting effects of initial conditions on dynamical fluctuations in one-dimensional diffusive systems. We consider the mean-squared displacement of tracers in homogeneous systems with single-file diffusion, and current fluctuations for noninteracting diffusive particles. In each case we show analytically that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the quenched cases studied previously, alongside a continuous family of other classes among which equilibrated (or annealed) initial conditions are but one member. We verify our predictions through extensive Monte Carlo simulations.

Ultra-low thermal conductivity and high thermoelectric performance of monolayer BiP3: a first principles study

The thermoelectric properties of monolayer triphosphide BiP₃ are studied via first principles calculations and Boltzmann transport equation. First, the Seebeck coefficient, electrical conductivity and electron thermal conductivity at different temperatures are calculated using the Boltzmann transport equation with relaxation time approximation. It has been observed that BiP₃ has a large power factor (265 × 10^-4 W K^-2 m^-1, 700 K). Then, by analyzing the second-order interatomic force constant (IFCS), the atomic structure and phonon dispersion were studied, and the thermal conductivity of monolayer BiP₃ was predicted in the temperature range of 300-800 K, and it was found that it had a very low thermal conductivity (2.13 W m^-1 K^-1) at room temperature. The thermal conductivity is mainly contributed by the branches of acoustics along in-plane transverse (TA). Finally, the maximum ZT value of monolayer BiP₃ is 3.06 at 700 K, when the electron doping concentration is 2.35 × 10¹¹ cm^-2, which indicates that it is a promising thermoelectric material.

Thermal transport in monolayer zinc-sulfide: effects of length, temperature and vacancy defects

Of late, atomically thin two-dimensional zinc-sulfide (2D-ZnS) shows great potential for advanced nanodevices and as a substitute to graphene and transition metal di-chalcogenides owing to its exceptional optical and electronic properties. However, the functional performance of nanodevices significantly depends on the effective heat management of the system. In this paper, we explored the thermal transport properties of 2D-ZnS through molecular dynamics simulations. The impact of length, temperature, and vacancy defects on the thermal properties of 2D-ZnS are systematically investigated. We found that the thermal conductivity (TC) rises monotonically with increasing sheet length, and the bulk TC of ∼30.67 W mK^-1is explored for an infinite length ZnS. Beyond room temperature (300 K), the TC differs from the usual 1/Trule and displays an abnormal, slowly declining behavior. The point vacancy (PV) shows the largest decrease in TC compared to the bi vacancy (BV) defects. We calculated phonon modes for various lengths, temperatures, and vacancies to elucidate the TC variation. Conversely, quantum corrections are used to avoid phonon modes' icing effects on the TC at low temperatures. The obtained phonon density of states (PDOS) shows a softening and shrinking nature with increasing temperature, which is responsible for the anomaly in the TC at high temperatures. Owing to the increase of vacancy concentration, the PDOS peaks exhibit a decrease for both types of defects. Moreover, the variation of the specific heat capacity and entropy with BV and PV signify our findings of 2D-ZnS TC at diverse concentrations along with the different forms of vacancies. The results elucidated in this study will be a guide for efficient heat management of ZnS-based optoelectronic and nano-electronic devices.

Exploring edge functionalised blue phosphorene nanoribbons as novel photocatalysts for water splitting

1D phosphorene nanoribbon edges activating water molecules under sunlight.

Remarkable Role of Grain Boundaries in the Thermal Transport Properties of Phosphorene

In this work, we study the effect of grain boundary (GB) on the thermal transport of phosphorene by using molecular dynamics simulations. By exploring a total of 19 GBs with different GB defect types and densities, we find that there is a relatively high Kapitza thermal boundary resistance at these boundaries. By analyzing the spatial distributions of the heat flux, we find that this high thermal boundary resistance can be attributed to the strong phonon-boundary scattering at the GBs. With the same type of defect, the thermal boundary resistance is found to increase with the increase of the defect density along the GBs, which can be attributed to the nonuniform distribution of stress and lattice distortion. Finally, we investigate the anisotropy in the thermal conductivity of phosphorene with GBs and reveal a strikingly high anisotropy ratio of thermal conductivities, which is found to arise from the different influences of boundaries on the thermal transport along the zigzag and armchair directions. Our results highlight the importance of GBs in the transport behavior of phosphorene and the need to include their effects in the thermal management of phosphorene-based electronic devices.

First-principles study on the anisotropic transport of electrons and phonons in monolayer and bulk GaTe: a comparative study

Recently, monoclinic-phase GaTe has attracted much attention due to its potential applications in nanoelectronics. Despite the experimental research, theoretical studies on the thermal and transport properties, which are necessary to provide information for future applications, are still absent. We have systematically investigated the electronic, phonon and electron transporting, and thermoelectric properties of monolayer and bulk GaTe using first-principles calculations plus the Boltzmann transport equation. At the valence band maximum and conduction band minimum, the effective mass shows large anisotropy as the band dispersions are along different k-paths. The group velocity of acoustic modes also shows large anisotropy owing to the in-plane low-symmetry. Our calculations reveal that the in-plane thermal conductivities, κ_a and κ_b, take 3.5 and 8.9 W m^-1 K^-1, respectively, for the bulk at 300 K, compared to κ_a = 5.5 and κ_b = 10.4 W m^-1 K^-1 of the monolayer. Due to the van der Waals interactions between interlayers, the out-of-plane thermal conductivity is very small, κ_c = 1.8 W m^-1 K^-1. The difference between the in-plane thermal conductivities of the bulk and the monolayer can be attributed to the strengthened Umklapp scattering, which is caused by the stiffening of the lowest-frequency optical mode in the bulk. The hole mobilities of the bulk is found to be about 12-35 cm² V^-1 s^-1 at 300 K, in good agreement with the experimental results. The monolayer is found to have smaller mobility but larger anisotropy than those of the bulk. Interestingly, the out-of-plane conductivity is anomalously larger than the in-plane one for the bulk, which is attributed to the orbital overlaps between the interlayer Te atoms. Moreover, n-type GaTe is found to have much larger mobility and anisotropy than the p-type one, which is useful for future applications. Compared with the case of monolayer GaTe, thermoelectric performance can be enhanced by one order of magnitude for the bulk GaTe by exploiting the out-of-plane thermal and electrical conductivities.

Thermodynamic stability and vibrational anharmonicity of black phosphorene-beyond quasi-harmonic analysis

Thermodynamic stability and vibrational anharmonicity of single layer black phosphorene (SLBP) are studied using a spectral energy density (SED) method. At finite temperatures, SLBP sheet undergoes structural deformation due to the formation of thermally excited ripples. Thermal stability of deformed SLBP sheet is analyzed by computing finite temperature phonon dispersion, which shows that SLBP sheet is thermodynamically stable and survives the crumpling transition. To analyze the vibrational anharmonicity, temperature evolution of all zone center optic phonon modes are extracted, including experimentally forbidden IR and Raman active modes. Mode resolved phonon spectra exhibits red-shift in mode frequencies with temperature. The strong anharmonic phonon-phonon coupling is the predominant reason for the observed red-shift of phonon modes, the contribution of thermal expansion is marginal. Further, temperature sensitivity of all optic modes are analyzed by computing their first order temperature co-efficient (χ), and it can be expressed asB_2g>Ag2>B3g1>B3g2>B_1g>Ag1&B_2u>B_1ufor Raman and IR active modes, respectively. The quasi-harmonicχvalues are much smaller than the SED and experimental values; which substantiate that quasi-harmonic methods are inadequate, and a full anharmonic analysis is essential to explain structure and dynamics of SLBP at finite temperatures.

Atomic-scale analysis of the physical strength and phonon transport mechanisms of monolayer β-bismuthene

Bismuthene has opened up a new avenue in the field of nanotechnology because of its spectacular electronic and thermoelectric features. The strong spin-orbit-coupling enables its operation as the largest nontrivial bandgap topological insulator and quantum spin hall material at room temperature, which is unlikely for any other 2D material. It is also known to be the most promising thermoelectric material due to its remarkable thermoelectric properties, including a substantially high power factor. However, an in-depth understanding of the mechanical and thermal transport properties of bismuthene is crucial for its practical implementation and efficient operation. Employing the Stillinger-Weber potential, we utilized molecular dynamics simulations to inspect the mechanical strength and thermal conductivity of the monolayer β-bismuthene for the first time. We analyzed the effect of temperature on the tensile mechanical properties along the armchair and zigzag directions of bismuthene nanosheets and found that increasing temperature causes a significant deterioration in these properties. The material shows superior fracture resistance with zigzag loading, whereas the armchair direction exhibits an improved elasticity. Next, we showed that increasing vacancy concentration and crack length notably reduce the fracture stress and strain of β-bismuthene. Under all these conditions, β-bismuthene showed a strong chirality effect under tensile loading. We also explored the fracture phenomena of a pre-cracked β-bismuthene, which reveal that the armchair-directed crack possesses a higher fracture resistance than the zigzag-directed crack. Interestingly, branching phenomena occurred during crack propagation for the armchair crack; meanwhile, the crack propagates perpendicular to loading for the zigzag crack. Afterward, we investigated the effect of loading rate on the fracture properties of bismuthene along the armchair and zigzag directions. Finally, we calculated the thermal conductivity of bismuthene under the influence of temperature and vacancy and recorded a substantial decrement in thermal conductivity with increasing temperature and vacancy. The obtained results are comprehensively discussed in the light of phonon density of states, phonon dispersion spectrum, and phonon group velocities. It is also disclosed that the thermal conductivity of β-bismuthene is considerably lower than that of other analogous honeycomb structures. This study can add a new dimension to the successful realization of bismuthene in future (opto)electronic, spintronic, and thermoelectric devices.

Quantum Phonon Transport in Nanomaterials: Combining Atomistic with Non-Equilibrium Green's Function Techniques

A crucial goal for increasing thermal energy harvesting will be to progress towards atomistic design strategies for smart nanodevices and nanomaterials. This requires the combination of computationally efficient atomistic methodologies with quantum transport based approaches. Here, we review our recent work on this problem, by presenting selected applications of the PHONON tool to the description of phonon transport in nanostructured materials. The PHONON tool is a module developed as part of the Density-Functional Tight-Binding (DFTB) software platform. We discuss the anisotropic phonon band structure of selected puckered two-dimensional materials, helical and horizontal doping effects in the phonon thermal conductivity of boron nitride-carbon heteronanotubes, phonon filtering in molecular junctions, and a novel computational methodology to investigate time-dependent phonon transport at the atomistic level. These examples illustrate the versatility of our implementation of phonon transport in combination with density functional-based methods to address specific nanoscale functionalities, thus potentially allowing for designing novel thermal devices.

Green function, quasi-classical Langevin and Kubo-Greenwood methods in quantum thermal transport

With the advances in fabrication of materials with feature sizes at the order of nanometers, it has been possible to alter their thermal transport properties dramatically. Miniaturization of device size increases the power density in general, hence faster electronics require better thermal transport, whereas better thermoelectric applications require the opposite. Such diverse needs bring new challenges for material design. Shrinkage of length scales has also changed the experimental and theoretical methods to study thermal transport. Unsurprisingly, novel approaches have emerged to control phonon flow. Besides, ever increasing computational power is another driving force for developing new computational methods. In this review, we discuss three methods developed for computing vibrational thermal transport properties of nano-structured systems, namely Green function, quasi-classical Langevin, and Kubo-Green methods. The Green function methods are explained using both nonequilibrium expressions and the Landauer-type formula. The partitioning scheme, decimation techniques and surface Green functions are reviewed, and a simple model for reservoir Green functions is shown. The expressions for the Kubo-Greenwood method are derived, and Lanczos tridiagonalization, continued fraction and Chebyshev polynomial expansion methods are discussed. Additionally, the quasi-classical Langevin approach, which is useful for incorporating phonon-phonon and other scatterings is summarized.

Transport characteristics and dwell time in a bilayer phosphorene barrier

In this paper, transport properties, dwell time and electron conductance were theoretically investigated through a rectangular electrostatic potential barrier in bilayer phosphorene and compared the results with monolayer phosphorene and graphene. It has been shown that in bilayer phosphorene, in the presence of an interlayer induced bias, a four-band approximation describes transport process in the system. The results show that interlayer bias parameter drastically affect transport properties. These effects include: (1) appearance of eight transmission and reflection coefficients from a band within the same band and between the two bands; (2) appearance of the anti-Klein tunnelling phenomenon and tuning the bias of system in such a way which is observed in specified biases and removed in other biases; (3) tuning conductance of the system. Results of dwell time in bilayer phosphorene show that this parameter in terms of barrier thickness does not have a strictly ascending behaviour and in limited range of incident energies (incident angles), the dwell time in the barrier reduces significantly which can be exploited in designing switching devices in nano-electronics. We found that increasing the interlayer bias decreases the intrinsic gap of the bilayer phosphorene which enables us to control the electron transmission rate in the system. In addition, our findings also demonstrate that by tuning the interlayer bias, a large electrical conductance can be achieved which can be used in semiconductor technology. Our study could serve as a basis for investigations of the basic physics of tunnelling mechanisms and using bilayer phosphorene as a proper candidate in low dimensional semiconductor industry.

Phonon transport and thermoelectric properties of semiconducting Bi2Te2X (X = S, Se, Te) monolayers

Confinement or dimensionality reduction is a novel strategy to reduce the lattice thermal conductivity and, consequently, to improve the thermoelectric conversion performance.

A distinct correlation between the vibrational and thermal transport properties of group VA monolayer crystals

The investigation of thermal transport properties of novel two-dimensional materials is crucially important in order to assess their potential to be used in future technological applications, such as thermoelectric power generation. In this respect, the lattice thermal transport properties of the monolayer structures of group VA elements (P, As, Sb, Bi, PAs, PSb, PBi, AsSb, AsBi, SbBi, P3As1, P3Sb1, P1As3, and As3Sb1) with a black phosphorus like puckered structure were systematically investigated by first-principles calculations and an iterative solution of the phonon Boltzmann transport equation. Phosphorene was found to have the highest lattice thermal conductivity, κ, due to its low average atomic mass and strong interatomic bonding character. As a matter of course, anisotropic κ was obtained for all the considered materials, owing to anisotropy in frequency values and phonon group velocities calculated for these structures. However, the determined linear correlation between the anisotropy in the κ values of P, As, and Sb is significant. The results corresponding to the studied compound structures clearly point out that thermal (electronic) conductivity of pristine monolayers might be suppressed (improved) by alloying them with the same group elements. For instance, the room temperature κ of PBi along the armchair direction was predicted to be as low as 1.5 W m-1 K-1, whereas that of P was predicted to be 21 W m-1 K-1. In spite of the apparent differences in structural and vibrational properties, we peculiarly revealed an intriguing correlation between the κ values of all the considered materials as κ = c1 + c2/m2, in particular along the zigzag direction. Furthermore, our calculations on compound structures clearly showed that the thermoelectric potential of these materials can be improved by suppressing their thermal properties. The presence of ultra-low κ values and high electrical conductivity (especially along the armchair direction) makes this class of monolayers promising candidates for thermoelectric applications.

Thermal Transport in Phosphorene

Phosphorene, a novel elemental 2D semiconductor, possesses fascinating chemical and physical properties which are distinctively different from other 2D materials. The rapidly growing applications of phosphorene in nano/optoelectronics and thermoelectrics call for comprehensive studies of thermal transport properties. In this Review, based on the theoretical and experimental progresses, the thermal transport properties of single-layer phosphorene, multilayer phosphorene (nanofilms), and bulk black phosphorus are summarized to give a general view of the overall thermal conductivity trend from single-layer to bulk form. The mechanism underlying the discrepancy in the reported thermal conductivity of phosphorene is discussed by reviewing the effect of different functionals and cutoff distances on the thermal transport evaluations. This Review then provides fundamental insight into the thermal transport in phosphorene by reviewing the role of resonant bonding in driving giant phonon anharmonicity and long-range interactions. In addition, the extrinsic thermal conductivity of phosphorene is reviewed by discussing the effects of strain and substrate, together with phosphorene based heterostructures and nanoribbons. This Review summarizes the progress of thermal transport in phosphorene from both theoretical calculations and experimental measurements, which would be of significance to the design and development of efficient phosphorene based nanoelectronics.

Efficient selection methods for black phosphorene nanoribbons

Black phosphorene (BP) has shown anisotropic, electronic, mechanical, and thermal properties for various promising applications in recent years. To take full advantage of this unique anisotropy in its further functional design and application, it is of paramount importance to separate BP with well-defined chirality quickly and precisely. In this paper, we propose three efficient methods to separate BP ribbons with different chiralities by utilizing their strong chirality-dependent bending stiffness. Our results show that the bending stiffness in the zigzag direction is 4 times larger than that in the armchair direction. The mechanical anisotropy and bending-binding competition are used to realize chirality-dependent design. To fold, wrap or scroll the BP nanoribbons, it is necessary to overcome the bending stiffness by applying the binding energy between the BP nanoribbons and the contact surfaces. Due to the mechanical anisotropy, the BP nanoribbons could easily be folded, wrapped and scrolled along the armchair direction rather than the zigzag direction. Therefore, we introduce this characteristic in our chirality separation designs as, the self-folding model to fold up the armchair BP nanoribbons by nanoparticles, the suspension-bridge sieve model to pull down the armchair BP nanoribbons, and the nanorod-roller model to scroll up the armchair nanoribbons. Our separation methods in this research can be extended to other 2D materials with anisotropic mechanical properties. We hope our findings would offer a novel route for the manufacturing of BP-based electronic devices and self-assembly of nano-devices.

Dwell time, Hartman effect and transport properties in a ferromagnetic phosphorene monolayer

In this paper, spin-dependent dwell time, spin Hartman effect and spin-dependent conductance were theoretically investigated through a rectangular barrier in the presence of an exchange field by depositing a ferromagnetic insulator on the phosphorene layer in the barrier region. The existence of the spin Hartman effect was shown for all energies (energies lower than barrier height) and all incident angles in phosphorene. We also compared our results of the dwell time in the phosphorene structure with similar research performed on graphene. We reported a significant difference between the tunneling time values of incident quasiparticles with spin-up and spin-down. We found that the barrier was almost transparent for incident quasiparticles with a wide range of incident angles and energies higher than the barrier height in phosphorene. We also found that the maximum spin-dependent transmission probability for energies higher than barrier height does not necessarily occur in the zero incident angle. In addition, we showed that the spin conductance for energies higher (lower) than barrier height fluctuates (decays) in terms of barrier thickness. We discovered that, in contrast to graphene, the Klein paradox does not occur in the normal incident in the phosphorene structure. Furthermore, the results demonstrated the achievement of good total conductance at certain thicknesses of the barrier for energies higher than the barrier height. This study could serve as a basis for investigations of the basic physics of tunneling mechanisms and also for using phosphorene as a spin polarizer in designing nanoelectronic devices.

Two-dimensional exciton properties in monolayer semiconducting phosphorus allotropes

Excitons play a key role in technological applications since they have a strong influence on determining the efficiency of photovoltaic devices. Recently, it has been shown that the allotropes of phosphorus possess an optical band gap that can be tuned over a wide range of values including the near-infrared and visible spectra, which would make them promising candidates for optoelectronic applications. In this work we carry out ab initio many-body perturbation theory calculations to study the excitonic effects on the optical properties of two-dimensional phosphorus allotropes: the case of blue and black monolayers. We elucidate the most relevant optical transitions, exciton binding energy spectrum as well as real-space exciton distribution, particularly focusing on the absorption spectrum dependence on the incident light polarization. In addition, based on our results, we use a set of effective hydrogenic models, in which the electron-hole Coulomb interaction is included to estimate exciton binding energies and radii. Our results show an excellent agreement between the many-body methodology and the effective models.

Thermal transport properties of antimonene: an ab initio study

Searching for low thermal conductivity materials is crucial for thermoelectric devices. Here we report on the phonon transport properties of recently fabricated single layer antimony, antimonene [Ares, et al., Adv. Mater., 2016, 28, 6332]. Ab initio calculations in combination with the Boltzmann transport equation (BTE) for phonons show that antimonene has a low lattice thermal conductivity (15.1 W m^-1 K^-1 at 300 K), indicating its potential thermoelectric applications. The low lattice thermal conductivity is due to its small group velocity, low Debye temperature and large buckling height. We also investigate in detail the mode contributions to total thermal conductivity and find at low frequency that the longitudinal acoustic (LA) branch dominates the thermal conductivity. Moreover, we show that the lattice thermal conductivity of antimonene can further be reduced by minimizing the sample size. Our findings open the field for thermoelectric applications based on antimonene.

Layered SnSe nano-plates with excellent in-plane anisotropic properties of Raman spectrum and photo-response

In-plane anisotropy in optical, electronic and thermal properties of two-dimensional (2D) materials has attracted significant interest because of the huge potential applications for developing novel devices. In this work, outstanding angle-dependent Raman property of layered SnSe nano-plates is obtained via polarized Raman system and it is confirmed that the Raman polarization directions of two A_g modes (130 cm^-1 and 150 cm^-1) are consistent with specific crystalline directions (zigzag direction or armchair direction) of SnSe flakes under parallel polarization configuration at home temperature and low temperature. Furthermore, the SnSe nano-plate devices show excellent angle-resolved photo-response at home temperature and low temperature (150 K) with a 90° cycle period and the polarized directions are also along zigzag direction and armchair direction, which is ascribed to the unique in-plane asymmetric crystal structure. These prominent in-plane anisotropic properties provide a precise and rapid method to determine the crystal orientation of SnSe nano-flakes and open up the new applications of 2D asymmetric structure materials.

Anisotropic transport of normal metal-barrier-normal metal junctions in monolayer phosphorene

We study transport properties of a phosphorene monolayer in the presence of single and multiple potential barriers of height U ₀ and width d, using both continuum and microscopic lattice models, and show that the nature of electron transport along its armchair edge (x direction) is qualitatively different from its counterpart in both conventional two-dimensional electron gas with Schrödinger-like quasiparticles and graphene or surfaces of topological insulators hosting massless Dirac quasiparticles. We show that the transport, mediated by massive Dirac electrons, allows one to achieve collimated quasiparticle motion along x and thus makes monolayer phosphorene an ideal experimental platform for studying Klein paradox in the context of gapped Dirac materials. We study the dependence of the tunneling conductance [Formula: see text] as a function of d and U ₀, and demonstrate that for a given applied voltage V its behavior changes from oscillatory to decaying function of d for a range of U ₀ with finite non-zero upper and lower bounds, and provide analytical expression for these bounds within which G decays with d. We contrast such behavior of G with that of massless Dirac electrons in graphene and also with that along the zigzag edge (y direction) in phosphorene where the quasiparticles obey an effective Schrödinger equation at low energy. We also study transport through multiple barriers along x and demonstrate that these properties hold for transport through multiple barriers as well. Finally, we suggest concrete experiments which may verify our theoretical predictions.

Imidazolium Ionic Liquid Mediates Black Phosphorus Exfoliation while Preventing Phosphorene Decomposition

Forthcoming applications in electronics and optoelectronics make phosphorene a subject of vigorous research efforts. Solvent-assisted exfoliation of phosphorene promises affordable delivery in industrial quantities for future applications. We demonstrate, using equilibrium, steered and umbrella sampling molecular dynamics, that the 1-ethyl-3-methylimidazolium tetrafluoroborate [EMIM][BF₄] ionic liquid is an excellent solvent for phosphorene exfoliation. The presence of both hydrophobic and hydrophilic moieties, as well as substantial shear viscosity, allows [EMIM][BF₄] simultaneously to facilitate separation of phosphorene sheets and to protect them from getting in direct contact with moisture and oxygen. The exfoliation thermodynamics is moderately unfavorable, which indicates that an external stimulus is necessary. Unexpectedly, [EMIM][BF₄] does not coordinates phosphorene by π-electron stacking with the imidazole ring. Instead, the solvation proceeds via hydrophobic side chains, while polar imidazole rings form an electrostatically stabilized protective layer. The simulations suggest that further efforts in solvent engineering for phosphorene exfoliation should concentrate on use of weakly coordinating ions and grafting groups that promote stronger dispersion interactions and on elongation of nonpolar chains.

Ionic Intercalation in Two-Dimensional van der Waals Materials: In Situ Characterization and Electrochemical Control of the Anisotropic Thermal Conductivity of Black Phosphorus

Two-dimensional van der Waals materials have shown novel fundamental properties and promise for wide applications. Here, we report for the first time an experimental demonstration of the in situ characterization and highly reversible control of the anisotropic thermal conductivity of black phosphorus. We develop a novel platform based on lithium ion batteries that integrates ultrafast optical spectroscopy and electrochemical control to investigate the interactions between lithium ions and the lattices of the black phosphorus electrode. We discover a strong dependence of the thermal conductivity on battery charge states (lithium concentrations) during the discharge/charge process. The thermal conductivity of black phosphorus is reversibly tunable over a wide range of 2.45-3.86, 62.67-85.80, and 21.66-27.58 W·m^-1·K^-1 in the cross-plan, zigzag, and armchair directions, respectively. The modulation in thermal conductivity is attributed to phonon scattering introduced by the ionic intercalation in between the interspacing layers and shows anisotropic phonon scattering mechanism based on semiclassical model. At the fully discharged state (x ∼ 3 in Li_xP), a dramatic reduction of thermal conductivity by up to 6 times from that of the pristine crystal has been observed. This study provides a unique approach to explore the fundamental energy transport involving lattices and ions in the layered structures and may open up new opportunities in controlling energy transport based on novel operation mechanisms and the rational design of nanostructures.

Ultra low lattice thermal conductivity and high carrier mobility of monolayer SnS2and SnSe2: a first principles study

Using density functional theory, we systematically investigate the lattice thermal conductivity and carrier mobility of monolayer SnX₂(X = S, Se).

Thermal stability and thermal conductivity of phosphorene in phosphorene/graphene van der Waals heterostructures

We investigated the thermal stability and thermal conductivity of phosphorene in phosphorene/graphene heterostructures using molecular dynamics simulations.

Promising thermoelectric properties of phosphorenes

Electronic, phononic, and thermoelectric transport properties of single layer black- and blue-phosphorene structures are investigated with first-principles based ballistic electron and phonon transport calculations employing hybrid functionals. The maximum values of room temperature thermoelectric figure of merit, ZT corresponding to armchair and zigzag directions of black-phosphorene, ∼0.5 and ∼0.25, are calculated as rather smaller than those obtained with first-principles based semiclassical Boltzmann transport theory calculations. On the other hand, the maximum value of room temperature ZT of blue-phosphorene is predicted to be substantially high and remarkable values as high as 2.5 are obtained for elevated temperatures. Besides the fact that these figures are obtained at the ballistic limit, our findings mark the strong possibility of high thermoelectric performance of blue-phosphorene in new generation thermoelectric applications.

Intense, stable and excitation wavelength-independent photoluminescence emission in the blue-violet region from phosphorene quantum dots

Nanoscale phosphorene quantum dots (PQDs) with few-layer structures were fabricated by pulsed laser ablation of a bulk black phosphorus target in diethyl ether. An intense and stable photoluminescence (PL) emission of the PQDs in the blue-violet wavelength region is clearly observed for the first time, which is attributed to electronic transitions from the lowest unoccupied molecular orbital (LUMO) to the highest occupied molecular orbital (HOMO) and occupied molecular orbitals below the HOMO (H-1, H-2), respectively. Surprisingly, the PL emission peak positions of the PQDs are not red-shifted with progressively longer excitation wavelengths, which is in contrast to the cases of graphene and molybdenum disulphide quantum dots. This excitation wavelength-independence is derived from the saturated passivation on the periphery and surfaces of the PQDs by large numbers of electron-donating functional groups which cause the electron density on the PQDs to be dramatically increased and the band gap to be insensitive to the quantum size effect in the PQDs. This work suggests that PQDs with intense, stable and excitation wavelength-independent PL emission in the blue-violet region have a potential application as semiconductor-based blue-violet light irradiation sources.

Low lattice thermal conductivity of stanene

A fundamental understanding of phonon transport in stanene is crucial to predict the thermal performance in potential stanene-based devices. By combining first-principle calculation and phonon Boltzmann transport equation, we obtain the lattice thermal conductivity of stanene. A much lower thermal conductivity (11.6 W/mK) is observed in stanene, which indicates higher thermoelectric efficiency over other 2D materials. The contributions of acoustic and optical phonons to the lattice thermal conductivity are evaluated. Detailed analysis of phase space for three-phonon processes shows that phonon scattering channels LA + LA/TA/ZA ↔ TA/ZA are restricted, leading to the dominant contributions of high-group-velocity LA phonons to the thermal conductivity. The size dependence of thermal conductivity is investigated as well for the purpose of the design of thermoelectric nanostructures.

Physical vapor deposition synthesis of two-dimensional orthorhombic SnS flakes with strong angle/temperature-dependent Raman responses

Anisotropic layered semiconductors have attracted significant interest due to the huge possibility of bringing new functionalities to thermoelectric, electronic and optoelectronic devices. Currently, most reports on anisotropy have concentrated on black phosphorus and ReS2, less effort has been contributed to other layered materials. In this work, two-dimensional (2D) orthorhombic SnS flakes on a large scale have been successfully synthesized via a simple physical vapor deposition method. Angle-dependent Raman spectroscopy indicated that the orthorhombic SnS flakes possess a strong anisotropic Raman response. Under a parallel-polarization configuration, the peak intensity of Ag (190.7 cm(-1)) Raman mode reaches the maximum when incident light polarization is parallel to the armchair direction of the 2D SnS flakes, which strongly suggests that the Ag (190.7 cm(-1)) mode can be used to determine the crystallographic orientation of the 2D SnS. In addition, temperature-dependent Raman characterization confirmed that the 2D SnS flakes have a higher sensitivity to temperature than graphene, MoS2 and black phosphorus. These results are useful for the future studies of the optical and thermal properties of 2D orthorhombic SnS.

Charge carrier transport and lifetimes in n-type and p-type phosphorene as 2D device active materials: an ab initio study

Electron and hole non-radiative lifetimes in phosphorene are investigated by first principles calculations.

Diffusive nature of thermal transport in stanene

Using the phonon Boltzmann transport formalism and density functional theory based calculations, we show that stanene has a low thermal conductivity.

Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

The anisotropic thermal conductivity of passivated black phosphorus (BP), a reactive two-dimensional material with strong in-plane anisotropy, is ascertained. The room-temperature thermal conductivity for three crystalline axes of exfoliated BP is measured by time-domain thermo-reflectance. The thermal conductivity along the zigzag direction is ≈2.5 times higher than that of the armchair direction.

Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus

Black phosphorus has been revisited recently as a new two-dimensional material showing potential applications in electronics and optoelectronics. Here we report the anisotropic in-plane thermal conductivity of suspended few-layer black phosphorus measured by micro-Raman spectroscopy. The armchair and zigzag thermal conductivities are ∼20 and ∼40 W m⁻¹ K⁻¹ for black phosphorus films thicker than 15 nm, respectively, and decrease to ∼10 and ∼20 W m⁻¹ K⁻¹ as the film thickness is reduced, exhibiting significant anisotropy. The thermal conductivity anisotropic ratio is found to be ∼2 for thick black phosphorus films and drops to ∼1.5 for the thinnest 9.5-nm-thick film. Theoretical modelling reveals that the observed anisotropy is primarily related to the anisotropic phonon dispersion, whereas the intrinsic phonon scattering rates are found to be similar along the armchair and zigzag directions. Surface scattering in the black phosphorus films is shown to strongly suppress the contribution of long mean-free-path acoustic phonons.

The two-dimensional material black phosphorus could find uses in energy applications. Here, the authors study the difference in in-plane thermal conductivity along the armchair and zigzag directions in suspended few-layer black phosphorus, and show the dependence of this anisotropy on sample thickness.

The electronic structures of group-V–group-IV hetero-bilayer structures: a first-principles study

Van der Waals hetero-bilayer structures can be constructed from group-V and group-IV nanosheets, which exhibit tunable electronic and interfacial properties.

Variable electronic properties of lateral phosphorene–graphene heterostructures

Phosphorene and graphene have a tiny lattice mismatch along the armchair direction, which can result in an atomically sharp in-plane interface.