Structural Phase Transition and Material Properties of Few-Layer Monochalcogenides

Defect-Free Nanowelding of Bilayer SnSe Nanoplates

Nanowelding is a bottom-up technique to create custom-designed nanostructures and devices beyond the precision of lithographic methods. Here, a new technique is reported based on anisotropic lubricity at the van der Waals interface between monolayer and bilayer SnSe nanoplates and a graphene substrate to achieve precise control of the crystal orientation and the interface during the welding process. As-grown SnSe monolayer and bilayer nanoplates are commensurate with graphene's armchair direction but lack commensuration along graphene's zigzag direction, resulting in a reduced friction along that direction and a rail-like, 1D movement that permits joining nanoplates with high precision. This way, molecular beam epitaxially grown SnSe nanoplates of lateral sizes 30-100 nm are manipulated by the tip of a scanning tunneling microscope at room temperature. In situ annealing is applied afterward to weld contacting nanoplates without atomic defects at the interface. This technique can be generalized to any van der Waals interfaces with anisotropic lubricity and is highly promising for the construction of complex quantum devices, such as field effect transistors, quantum interference devices, lateral tunneling junctions, and solid-state qubits.

Transition from fractal-dendritic to compact islands for the 2D-ferroelectric SnSe on graphene/Ir(111)

Epitaxial growth is a versatile method to prepare two-dimensional van der Waals ferroelectrics like group IV monochalcogenides which have potential for novel electronic devices and sensors. We systematically study SnSe monolayer islands grown by molecular beam epitaxy, especially the effect of annealing temperature on shape and morphology of the edges. Characterization of the samples by scanning tunneling microscopy reveals that the shape of the islands changes from fractal-dendritic after deposition at room temperature to a compact rhombic shape through annealing, but ripening processes are absent up to the desorption temperature. A two-step growth process leads to large, epitaxially aligned rhombic islands bounded by well-defined110-edges (armchair-like), which we claim to be the equilibrium shape of the stoichiometric SnSe monolayer islands. The relaxation of the energetically favorable edges is detected in atomically resolved STM images. The experimental findings are supported by the results of our first-principles calculations, which provide insights into the energetics of the edges, their reconstructions, and yields the equilibrium shapes of the islands which are in good agreement with the experiment.

Fully Electrically Controlled van der Waals Multiferroic Tunnel Junctions

The fully electrical control of the magnetic states in magnetic tunnel junctions is highly pursued for the development of the next generation of low-power and high-density information technology. However, achieving this functionality remains a formidable challenge at present. Here we propose an effective strategy by constructing a trilayer van der Waals multiferroic structure, consisting of CrI3-AgBiPSe6 and Cr2Ge2Te6-In2Se3, to achieve full-electrical control of multiferroic tunnel junctions. Within this structure, two different magnetic states of the magnetic bilayers (CrI3/Cr2Ge2Te6) can be modulated and switched in response to the polarization direction of the adjacent ferroelectric materials (AgBiPSe6/In2Se3). The intriguing magnetization reversal is mainly attributed to the polarization-field-induced band structure shift and interfacial charge transfer. On this basis, we further design two multiferroic tunnel junction devices, namely, graphene/CrI3-AgBiPSe6/graphene and graphene/Cr2Ge2Te6-In2Se3/graphene. In these devices, good interfacial Ohmic contacts are successfully obtained between the graphene electrode and the heterojunction, leading to an ultimate tunneling magnetoresistance of 9.3 × 106%. This study not only proposes a feasible strategy and identifies a promising candidate for achieving fully electrically controlled multiferroic tunnel junctions but also provides insights for designing other advanced spintronic devices.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Proton-mediated reversible switching of metastable ferroelectric phases with low operation voltages

The exploration of ferroelectric phase transitions enables an in-depth understanding of ferroelectric switching and promising applications in information storage. However, controllably tuning the dynamics of ferroelectric phase transitions remains challenging owing to inaccessible hidden phases. Here, using protonic gating technology, we create a series of metastable ferroelectric phases and demonstrate their reversible transitions in layered ferroelectric α-In₂Se₃ transistors. By varying the gate bias, protons can be incrementally injected or extracted, achieving controllable tuning of the ferroelectric α-In₂Se₃ protonic dynamics across the channel and obtaining numerous intermediate phases. We unexpectedly discover that the gate tuning of α-In₂Se₃ protonation is volatile and the created phases remain polar. Their origin, revealed by first-principles calculations, is related to the formation of metastable hydrogen-stabilized α-In₂Se₃ phases. Furthermore, our approach enables ultralow gate voltage switching of different phases (below 0.4 volts). This work provides a possible avenue for accessing hidden phases in ferroelectric switching.

Two-Dimensional Ferroelasticity and Domain-Wall Flexoelectricity in HgX2 (X = Br or I) Monolayers

Electromechanical phenomena in two-dimensional (2D) materials can be related to sizable electric polarizations and switchable spontaneous ferroelasticity, allowing them to be used as miniaturized electronic and memory devices. Even in a parent centrosymmetric (nonpolar) ferroelastic (FE) material, non-zero polarization can be produced around the FE domain wall, owing to the strain-gradient-induced flexoelectricity. Compared with the negligibly weak flexoelectric effect in bulk compounds, significant electric polarizations can be expected in 2D FE materials that sustain a large elastic strain and a strain gradient. Using first-principles calculations, we predict that spontaneous 2D ferroelasticity and domain-wall flexoelectricity can be simultaneously realized in synthetic HgX₂ (X = Br or I) monolayers. The FE phase renders three oriented variants, which form FE domain walls with a large strain gradient and the associated domain-wall flexoelectric polarizations. Our thermodynamic stability analysis and kinetic barrier simulations allow us to manipulate the domain-wall flexoelectricity via applied mechanical stress, thereby enabling future electromechanical applications in nanoelectronics.

Slippery Paraelectric Transition-Metal Dichalcogenide Bilayers

Traditional ferroelectrics undergo thermally induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed paraelectric. Ferroelectric transition-metal dichalcogenide bilayers have been recently shown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires macroscopically large areas to slip in unison.

Anomalous Thermal Expansion in Ising-like Puckered Sheets

Motivated by efforts to create thin nanoscale metamaterials and understand atomically thin binary monolayers, we study the finite temperature statistical mechanics of arrays of bistable buckled dilations embedded in free-standing two-dimensional crystalline membranes that are allowed to fluctuate in three dimensions. The buckled nodes behave like discrete, but highly compressible, Ising spins, leading to a phase transition at T_{c} with singularities in the staggered "magnetization," susceptibility, and specific heat, studied via molecular dynamics simulations. Unlike conventional Ising models, we observe a striking divergence and sign change of the coefficient of thermal expansion near T_{c} caused by the coupling of flexural phonons to the buckled spin texture. We argue that a phenomenological model coupling Ising degrees of freedom to the flexural phonons in a thin elastic sheet can explain this unusual response.

Identifying the Transition Order in an Artificial Ferroelectric van der Waals Heterostructure

Two-dimensional semiconducting ferroelectrics can enable new technology for low-energy electronic switching. However, conventional ferroelectric materials are usually electrically insulating and suffer from severe depolarization effects when downscaled to atomic thickness. Following recent work, we show that robust ferroelectricity can be obtained from nonferroelectric semiconducting 2H-WSe₂ by creating R-stacked bilayers with broken inversion symmetry. Here, we identify that the phase transition order of this artificial ferroelectric heterostructure is first-order, with a discontinuous jump in the order parameter across the phase transition temperature. The Curie temperature has been experimentally determined as 353 K. Using the Landau-Devonshire theory, we further determine the Curie-Weiss temperatures to be 351.2 K. We additionally demonstrate the robustness of this artificial ferroelectric material using consecutive polarization measurements, where no appreciable deterioration was detected.

Electric-Field-Induced Room-Temperature Antiferroelectric-Ferroelectric Phase Transition in van der Waals Layered GeSe

Searching van der Waals ferroic materials that can work under ambient conditions is of critical importance for developing ferroic devices at the two-dimensional limit. Here we report the experimental discovery of electric-field-induced reversible antiferroelectric (AFE) to ferroelectric (FE) transition at room temperature in van der Waals layered α-GeSe, employing Raman spectroscopy, transmission electron microscopy, second-harmonic generation, and piezoelectric force microscopy consolidated by first-principles calculations. An orientation-dependent AFE-FE transition provides strong evidence that the in-plane (IP) polarization vector aligns along the armchair rather than zigzag direction in α-GeSe. In addition, temperature-dependent Raman spectra showed that the IP polarization could sustain up to higher than 700 K. Our findings suggest that α-GeSe, which is also a potential ferrovalley material, could be a robust building block for creating artificial 2D multiferroics at room temperature.

Rippling Ferroic Phase Transition and Domain Switching In 2D Materials

Ripples are a class of native structural defects widely existing in 2D materials. They originate from the out-of-plane flexibility of 2D materials introducing spatially evolving electronic structure and friction behavior. However, the effect of ripples on 2D ferroics has not been reported. Here a molecular dynamics study of the effect of ripples on the temperature-induced ferroic phase transition and stress-induced ferroic domain switching in ferroelastic-ferroelectric monolayer GeSe is presented. Ripples stabilize the short-range ferroic orders in the high-temperature phase with stronger ferroicity and longer lifetime, thereby increasing the transition temperature upon cooling. In addition, ripples significantly affect the domain switching upon loading, changing it from a highly correlated process into a ripple-driven localized one where ripples act as source of dynamical random stress. These results reveal the fundamental role of ripples on 2D ferroicity and provide theoretical guidance for ripple engineering of controlled phase transition and domain switching with potential applications in flexible 2D electronics.

Solution-processed two-dimensional materials for next-generation photovoltaics

In the ever-increasing energy demand scenario, the development of novel photovoltaic (PV) technologies is considered to be one of the key solutions to fulfil the energy request. In this context, graphene and related two-dimensional (2D) materials (GRMs), including nonlayered 2D materials and 2D perovskites, as well as their hybrid systems, are emerging as promising candidates to drive innovation in PV technologies. The mechanical, thermal, and optoelectronic properties of GRMs can be exploited in different active components of solar cells to design next-generation devices. These components include front (transparent) and back conductive electrodes, charge transporting layers, and interconnecting/recombination layers, as well as photoactive layers. The production and processing of GRMs in the liquid phase, coupled with the ability to "on-demand" tune their optoelectronic properties exploiting wet-chemical functionalization, enable their effective integration in advanced PV devices through scalable, reliable, and inexpensive printing/coating processes. Herein, we review the progresses in the use of solution-processed 2D materials in organic solar cells, dye-sensitized solar cells, perovskite solar cells, quantum dot solar cells, and organic-inorganic hybrid solar cells, as well as in tandem systems. We first provide a brief introduction on the properties of 2D materials and their production methods by solution-processing routes. Then, we discuss the functionality of 2D materials for electrodes, photoactive layer components/additives, charge transporting layers, and interconnecting layers through figures of merit, which allow the performance of solar cells to be determined and compared with the state-of-the-art values. We finally outline the roadmap for the further exploitation of solution-processed 2D materials to boost the performance of PV devices.

Vortex-Oriented Ferroelectric Domains in SnTe/PbTe Monolayer Lateral Heterostructures

Heterostructures formed from interfaces between materials with complementary properties often display unconventional physics. Of especial interest are heterostructures formed with ferroelectric materials. These are mostly formed by combining thin layers in vertical stacks. Here the first in situ molecular beam epitaxial growth and scanning tunneling microscopy characterization of atomically sharp lateral heterostructures between a ferroelectric SnTe monolayer and a paraelectric PbTe monolayer are reported. The bias voltage dependence of the apparent heights of SnTe and PbTe monolayers, which are closely related to the type-II band alignment of the heterostructure, is investigated. Remarkably, it is discovered that the ferroelectric domains in the SnTe surrounding a PbTe core form either clockwise or counterclockwise vortex-oriented quadrant configurations. In addition, when there is a finite angle between the polarization and the interface, the perpendicular component of the polarization always points from SnTe to PbTe. Supported by first-principles calculation, the mechanism of vortex formation and preferred polarization direction is identified in the interaction between the polarization, the space charge, and the strain effect at the horizontal heterointerface. The studies bring the application of 2D group-IV monochalcogenides on in-plane ferroelectric heterostructures a step closer.

Coexistence of Ferroelectricity and Ferromagnetism in One-Dimensional SbN and BiN Nanowires

Ferroelectricity exists in a variety of three- and two-dimensional materials and is of great significance for the development of electronic devices. However, the presence of ferroelectricity in one-dimensional materials is extremely rare. Here, we predict ferroelectricity in one-dimensional SbN and BiN nanowires. Their polarization strengths are 1 order of magnitude higher than ever reported values in one-dimensional structures. Moreover, we find that spontaneous spin polarization can be generated in SbN and BiN nanowires by moderate hole doping. This is the first time the coexistence of both ferroelectricity and ferromagnetism in a one-dimensional system has been reported. Our finding not only broadens the family of one-dimensional ferroelectric materials but also offers a promising platform for novel electronic and spintronic applications.

Intrinsic Valley Polarization and High-Temperature Ferroelectricity in Two-Dimensional Orthorhombic Lead Oxide

Recent years have witnessed a surge of research in two-dimensional (2D) ferroelectric structures that may circumvent the depolarization effect in conventional perovskite oxide films. Herein, by first-principles calculations, we predict that an orthorhombic phase of lead(II) oxide, PbO, serves as a promising candidate for 2D ferroelectrics with good stability. With a semiconducting nature, 2D ferroelectric PbO exhibits intrinsic valley polarization, which leads to robust ferroelectricity with an in-plane spontaneous polarization of 2.4 × 10^-10 C/m and a Curie temperature of 455 K. Remarkably, we reveal that the ferroelectricity is strain-tunable, and ferroelasticity coexists in the PbO film, implying the realization of 2D multiferroics. The underlying physical mechanism is generally applicable and can be extended to other oxide films such as ferroelectric SnO and GeO, thus paving an avenue for future design and fabrication of functional ultrathin devices that are compatible with Si-based technology.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Microscopic Manipulation of Ferroelectric Domains in SnSe Monolayers at Room Temperature

Two-dimensional (2D) van der Waals ferroelectrics provide an unprecedented architectural freedom for the creation of artificial multiferroics and nonvolatile electronic devices based on vertical and coplanar heterojunctions of 2D ferroic materials. Nevertheless, controlled microscopic manipulation of ferroelectric domains is still rare in monolayer-thick 2D ferroelectrics with in-plane polarization. Here we report the discovery of robust ferroelectricity with a critical temperature close to 400 K in SnSe monolayer plates grown on graphene and the demonstration of controlled room-temperature ferroelectric domain manipulation by applying appropriate bias voltage pulses to the tip of a scanning tunneling microscope (STM). This study shows that STM is a powerful tool for detecting and manipulating the microscopic domain structures in 2D ferroelectric monolayers, which are difficult for conventional approaches such as piezoresponse force microscopy, thus facilitating the hunt for other 2D ferroelectric monolayers with in-plane polarization with important technological applications.

Changes of Structure and Bonding with Thickness in Chalcogenide Thin Films

Extreme miniaturization is known to be detrimental for certain properties, such as ferroelectricity in perovskite oxide films below a critical thickness. Remarkably, few-layer crystalline films of monochalcogenides display robust in-plane ferroelectricity with potential applications in nanoelectronics. These applications critically depend on the electronic properties and the nature of bonding in the 2D limit. A fundamental open question is thus to what extent bulk properties persist in thin films. Here, this question is addressed by a first-principles study of the structural, electronic, and ferroelectric properties of selected monochalcogenides (GeSe, GeTe, SnSe, and SnTe) as a function of film thickness up to 18 bilayers. While in selenides a few bilayers are sufficient to recover the bulk behavior, the Te-based compounds deviate strongly from the bulk, irrespective of the slab thickness. These results are explained in terms of depolarizing fields in Te-based slabs and the different nature of the chemical bond in selenides and tellurides. It is shown that GeTe and SnTe slabs inherit metavalent bonding of the bulk phase, despite structural and electronic properties being strongly modified in thin films. This understanding of the nature of bonding in few-layers structures offers a powerful tool to tune materials properties for applications in information technology.

Screening nature of the van der Waals density functional method: a review and analysis of the many-body physics foundation

We review the screening nature and many-body physics foundation of the van der Waals density functional (vdW-DF) method [Berland Ket al2015Rep. Prog. Phys.78066501], a systematic approach to construct truly nonlocal exchange-correlation energy density functionals. To that end we define and focus on a class of consistent vdW-DF versions that adhere to the Lindhard screening logic of the full method formulation. The consistent-exchange vdW-DF-cx version [Berland K and Hyldgaard P 2014Phys. Rev. B89035412] and its spin extension [Thonhauser Tet al2015Phys. Rev. Lett.115136402] represent the first examples of this class; in general, consistent vdW-DFs reflect a concerted expansion of a formal recast of the adiabatic-connection formula [Hyldgaard Pet al2014Phys. Rev. B90075148], an exponential summation of contributions to the local-field response, and the Dyson equation. We argue that the screening emphasis is essential because the exchange-correlation energy reflects an effective electrodynamics set by a long-range interaction. Two consequences are that (1) there are, in principle, no wiggle room in how one balances exchange and correlation, for example, in vdW-DF-cx, and that (2) consistent vdW-DFs have a formal structure that allows them to incorporate vertex-correction effects, at least in the case of levels that experience recoil-less interactions (for example, near the Fermi surface). We explore the extent to which the strictly nonempirical vdW-DF-cx formulation can serve as a systematic extension of the constraint-based semilocal functionals. For validation, we provide a complete survey of vdW-DF-cx performance for broad molecular processes, for the full set of 55 benchmarks in GMTKN55 [Goerigk Let al2017Phys. Chem. Chem. Phys.1932184] and comparing to the quantum-chemistry calculations that are summarized in that paper. We also provide new vdW-DF-cx results for metal surface energies and work functions that we compare to experiment. Finally, we use the screening insight to separate the vdW-DF nonlocal-correlation term into pure-vdW-interaction and local-field-susceptibility effects and present tools to compute and map the binding signatures.

One-dimensional flat bands in twisted bilayer germanium selenide

Experimental advances in the fabrication and characterization of few-layer materials stacked at a relative twist of small angle have recently shown the emergence of flat energy bands. As a consequence electron interactions become relevant, providing inroads into the physics of strongly correlated two-dimensional systems. Here, we demonstrate by combining large scale ab initio simulations with numerically exact strong correlation approaches that an effective one-dimensional system emerges upon stacking two twisted sheets of GeSe, in marked contrast to all moiré systems studied so far. This not only allows to study the necessarily collective nature of excitations in one dimension, but can also serve as a promising platform to scrutinize the crossover from two to one dimension in a controlled setup by varying the twist angle, which provides an intriguing benchmark with respect to theory. We thus establish twisted bilayer GeSe as an intriguing inroad into the strongly correlated physics of lowdimensional systems.

Peculiar piezoelectricity of atomically thin planar structures

The emergence of piezoelectricity in two-dimensional (2D) materials has represented a milestone towards employing low-dimensional structures for future technologies. 2D piezoelectric materials possess unique and unprecedented characteristics that cannot be found in other morphologies; therefore, the applications of piezoelectricity can be substantially extended. By reducing the thickness into the 2D realm, piezoelectricity might be induced in otherwise non-piezoelectric materials. The origin of the enhanced piezoelectricity in such thin planes is attributed to the loss of centrosymmetry, altered carrier concentration, and change in local polarization and can be efficiently tailored via surface modifications. Access to such materials is important from a fundamental research point of view, to observe the extraordinary interactions between free charge carriers, phonons and photons, and also with respect to device development, for which planar structures provide the required compatibility with the large-scale fabrication technologies of integrated circuits. The existence of piezoelectricity in 2D materials presents great opportunities for applications in various fields of electronics, optoelectronics, energy harvesting, sensors, actuators and biotechnology. Additionally, 2D flexible nanostructures with superior piezoelectric properties are distinctive candidates for integration into nano-scale electromechanical systems. Here we fundamentally review the state of the art of 2D piezoelectric materials from both experimental and theoretical aspects and report the recent achievements in the synthesis, characterization and applications of these materials.

Artificial Multiferroics and Enhanced Magnetoelectric Effect in van der Waals Heterostructures

Multiferroic materials with coupled ferroelectric (FE) and ferromagnetic (FM) properties are important for multifunctional devices because of their potential ability of controlling magnetism via electric field and vice versa. The recent discoveries of two-dimensional (2D) FM and FE materials have ignited tremendous research interest and aroused hope to search for 2D multiferroics. However, intrinsic 2D multiferroic materials and, particularly, those with strong magnetoelectric couplings are still rare to date. In this paper, using first-principles simulations, we propose artificial 2D multiferroics via a van der Waals (vdW) heterostructure formed by FM bilayer chromium triiodide (CrI₃) and FE monolayer Sc₂CO₂. In addition to the coexistence of ferromagnetism and ferroelectricity, our calculations show that, by switching the electric polarization of Sc₂CO₂, we can tune the interlayer magnetic couplings of bilayer CrI₃ between the FM and antiferromagnetic states. We further reveal that such a strong magnetoelectric effect is from a dramatic change of the band alignment induced by the strong built-in electric polarization in Sc₂CO₂ and the subsequent change of the interlayer magnetic coupling of bilayer CrI₃. These artificial multiferroics and enhanced magnetoelectric effect give rise to realizing multifunctional nanoelectronics by vdW heterostructures.

Raman Spectra Shift of Few-Layer IV-VI 2D Materials

Raman spectroscopy is the most commonly used method to investigate structures of materials. Recently, few-layered IV-VI 2D materials (SnS, SnSe, GeS, and GeSe) have been found and ignited significant interest in electronic and optical applications. However, unlike few-layer graphene, in which its interlayer structures such as the number of its layers are confirmed through measurement of the Raman scattering, few-layer IV-VI 2D materials have not yet been developed to the point of understanding their interlayer structure. Here we performed first-principles calculations on Raman spectroscopy for few-layer IV-VI 2D materials. In addition to achieving consistent results with measurements of bulk structures, we revealed significant red and blue shifts of characteristic Raman modes up to 100 cm-1 associated with the layer number. These shifts of lattice vibrational modes originate from the change of the bond lengths between the metal atoms and chalcogen atoms through the change of the interlayer interactions. Particularly, our study shows weak covalent bonding between interlayers, making the evolution of Raman signals according to the thickness different from other vdW materials. Our results suggest a new way for obtaining information of layer structure of few-layer IV-VI 2D materials through Raman spectroscopy.

Room-Temperature Ferroelectricity in Group-IV Metal Chalcogenide Nanowires

The realization of low-dimensional ferroelectrics is both fundamentally intriguing and practically appealing, to be used in nanoscale devices. Here, GeS and SnS nanowires are predicted to be one-dimensional (1D) ferroelectrics with inversion symmetry spontaneously broken by soft optical modes. Despite the low dimensionality, the estimated Curie point for GeS nanowires is above room temperature, benefiting experimental detection and suggesting realistic applications. To this end, further aspects of these 1D ferroelectrics are also examined, revealing the domain wall localization, switchable carrier mobility, and practically effective shieling by confining the nanowires inside the carbon nanotubes, all together potentially useful for nanoscale ferroelectric devices of broad interest.

Standing Waves Induced by Valley-Mismatched Domains in Ferroelectric SnTe Monolayers

Two-dimensional (2D) quasiparticle standing waves originate from the interference of coherent quantum states and are usually created by the scattering off edges, atomic steps, or adatoms that induce large potential barriers. We report standing waves close to the valence band maximum (E_{V}), confined by electrically neutral domain walls of newly discovered ferroelectric SnTe monolayers, as revealed by spatially resolved scanning tunneling spectroscopy. Ab initio calculations show that this novel confinement arises from the polarization lifted hole valley degeneracy and a ∼90° rotation of the Brillouin zones that render holes' momentum mismatched across neighboring domains. These results show a potential for polarization-tuned valleytronics in 2D ferroelectrics.

Ultrafast Zero-Bias Surface Photocurrent in Germanium Selenide: Promise for Terahertz Devices and Photovoltaics

Theory predicts that a large spontaneous electric polarization and concomitant inversion symmetry breaking in GeSe monolayers result in a strong shift current in response to their excitation in the visible range. Shift current is a coherent displacement of electron density on the order of a lattice constant upon above-bandgap photoexcitation. A second-order nonlinear effect, it is forbidden by the inversion symmetry in the bulk GeSe crystals. Here, we use terahertz (THz) emission spectroscopy to demonstrate that ultrafast photoexcitation with wavelengths straddling both edges of the visible spectrum, 400 and 800 nm, launches a shift current in the surface layer of a bulk GeSe crystal, where the inversion symmetry is broken. The direction of the surface shift current determined from the observed polarity of the emitted THz pulses depends only on the orientation of the sample and not on the linear polarization direction of the excitation. Strong absorption by the low-frequency infrared-active phonons in the bulk of GeSe limits the bandwidth and the amplitude of the emitted THz pulses. We predict that reducing GeSe thickness to a monolayer or a few layers will result in a highly efficient broadband THz emission. Experimental demonstration of THz emission by the surface shift current in bulk GeSe crystals puts this 2D material forward as a candidate for next-generation shift current photovoltaics, nonlinear photonic devices, and THz sources.

Quantum Paraelastic Two-Dimensional Materials

We study the elastic energy landscape of two-dimensional tin oxide (SnO) monolayers and demonstrate a transition temperature of T_{c}=8.5±1.8  K using ab initio molecular dynamics (MD) that is close to the value of the elastic energy barrier J derived from T=0  K density functional theory calculations. The power spectra of the velocity autocorrelation throughout the MD evolution permit identifying soft phonon modes likely responsible for the structural transformation. The mean atomic displacements obtained from a Bose-Einstein occupation of the phonon modes suggest the existence of a quantum paraelastic phase that could be tuned with charge doping: SnO monolayers could be 2D quantum paraelastic materials with a charge-tunable quantum phase transition.

Enhanced Spontaneous Polarization in Ultrathin SnTe Films with Layered Antipolar Structure

2D SnTe films with a thickness of as little as 2 atomic layers (ALs) have recently been shown to be ferroelectric with in-plane polarization. Remarkably, they exhibit transition temperatures (T_c ) much higher than that of bulk SnTe. Here, combining molecular beam epitaxy, variable temperature scanning tunneling microscopy, and ab initio calculations, the underlying mechanism of the T_c enhancement is unveiled, which relies on the formation of γ-SnTe, a van der Waals orthorhombic phase with antipolar inter-layer coupling in few-AL thick SnTe films. In this phase, 4n - 2 AL (n = 1, 2, 3…) thick films are found to possess finite in-plane polarization (space group Pmn2₁ ), while 4n AL thick films have zero total polarization (space group Pnma). Above 8 AL, the γ-SnTe phase becomes metastable, and can convert irreversibly to the bulk rock salt phase as the temperature is increased. This finding unambiguously bridges experiments on ultrathin SnTe films with predictions of robust ferroelectricity in GeS-type monochalcogenide monolayers. The observed high transition temperature, together with the strong spin-orbit coupling and van der Waals structure, underlines the potential of atomically thin γ-SnTe films for the development of novel spontaneous polarization-based devices.

Enhancement of photoluminescence efficiency in GeSe ultrathin slab by thermal treatment and annealing: experiment and first-principles molecular dynamics simulations

The effect of thermal treatment and annealing under different temperatures from 100 °C to 250 °C on the photoluminescence spectroscopy of the GeSe ultrathin slab is reported. After the thermal treatment and annealing under 200 °C, we found that the photoluminescence intensity of A exciton and B exciton in GeSe ultrathin slab is increased to twice as much as that in untreated case, while is increased by ~84% in the photoluminescence intensity of C exciton. Combined by our experimental work and theoretical simulations, our study confirms the significant role of thermal treatments and annealing in reducing surface roughness and removing the Se vacancy to form more compact and smoother regions in GeSe ultrathin slab. Our findings imply that the improved quality of GeSe surface after thermal treatments is an important factor for the photoluminescence enhancement.

Water Splits To Degrade Two-Dimensional Group-IV Monochalcogenides in Nanoseconds

The experimental exfoliation of layered group-IV monochalcogenides-semiconductors isostructural to black phosphorus-using processes similar to those followed in the production of graphene or phosphorene has turned out unsuccessful thus far, as if the chemical degradation observed in black phosphorus was aggravated in these monochalcogenides. Here, we document a facile dissociation of water by these materials within 10 ns from room-temperature Car-Parrinello molecular dynamics calculations under standard temperature and pressure conditions. These results suggest that humidity must be fully eradicated to exfoliate monolayers successfully, for instance, by placing samples in a hydrophobic solution during mechanical exfoliation. From another materials perspective, these two-dimensional materials that create individual hydrogen ions out of water without illumination may become relevant for applications in hydrogen production and storage.

Ferroelectric Problem beyond the Conventional Scaling Law

Ferroelectric (FE) size effects against the scaling law were reported recently in ultrathin group-IV monochalcogenides, and extrinsic effects (e.g., defects and lattice strains) were often resorted to. Via first-principles based finite-temperature (T) simulations, we reveal that these abnormalities are intrinsic to their unusual symmetry breaking from bulk to thin film. Changes of the electronic structures result in different order parameters characterizing the FE phase transition in bulk and in thin films, and invalidation of the scaling law. Beyond the scaling law T_{c} limit, this mechanism can help predict materials that are promising for room-T ultrathin FE devices of broad interest.

Microscopic Mechanism of the Helix-to-Layer Transformation in Elemental Group VI Solids

We study the conversion of bulk Se and Te, consisting of intertwined a helices, to structurally very dissimilar, atomically thin two-dimensional (2D) layers of these elements. Our ab initio calculations reveal that previously unknown and unusually stable δ and η 2D allotropes may form in an intriguing multistep process that involves a concerted motion of many atoms at dislocation defects. We identify such a complex reaction path involving zipper-like motion of such dislocations that initiate structural changes. With low activation barriers ≲0.3 eV along the optimum path, the conversion process may occur at moderate temperatures. We find all one-dimensional (1D) and 2D chalcogen structures to be semiconducting.

Intrinsic Origin of Enhancement of Ferroelectricity in SnTe Ultrathin Films

Previous studies showed that, as ferroelectric films become thinner, their Curie temperature (T_{c}) and polarization below T_{c} both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)SCIEAS0036-807510.1126/science.aad8609] observed that atomic-thick SnTe films have a higher T_{c} than their bulk counterpart, which was attributed to extrinsic effects. We find, using first-principles calculations, that the 0-K energy barrier for the polarization switching (which is a quantity directly related to T_{c}) is higher in most investigated defect-free SnTe ultrathin films than that in bulk SnTe, and that the 5-unit-cell (UC) SnTe thin film has the largest energy barrier as a result of an interplay between hybridization interactions and Pauli repulsions. Further simulations, employing a presently developed effective Hamiltonian, confirm that freestanding, defect-free SnTe thin films have a higher T_{c} than bulk SnTe, except for the 1-UC case. Our work, therefore, demonstrates the possibility to intrinsically enhance ferroelectricity of ultrathin films by reducing their thickness.

Room temperature in-plane ferroelectricity in van der Waals In2Se3

Van der Waals (vdW) assembly of layered materials is a promising paradigm for creating electronic and optoelectronic devices with novel properties. Ferroelectricity in vdW layered materials could enable nonvolatile memory and low-power electronic and optoelectronic switches, but to date, few vdW ferroelectrics have been reported, and few in-plane vdW ferroelectrics are known. We report the discovery of in-plane ferroelectricity in a widely investigated vdW layered material, β'-In₂Se₃. The in-plane ferroelectricity is strongly tied to the formation of one-dimensional superstructures aligning along one of the threefold rotational symmetric directions of the hexagonal lattice in the c plane. Surprisingly, the superstructures and ferroelectricity are stable to 200°C in both bulk and thin exfoliated layers of In₂Se₃. Because of the in-plane nature of ferroelectricity, the domains exhibit a strong linear dichroism, enabling novel polarization-dependent optical properties.

Mechanisms of Pyroelectricity in Three- and Two-Dimensional Materials

Pyroelectricity is a very promising phenomenon in three- and two-dimensional materials, but first-principles calculations have not so far been used to elucidate the underlying mechanisms. Here we report density-functional theory (DFT) calculations based on the Born-Szigeti theory of pyroelectricity, by combining fundamental thermodynamics and the modern theory of polarization. We find satisfactory agreement with experimental data in the case of bulk benchmark materials, showing that the so-called electron-phonon renormalization, whose contribution has been traditionally viewed as negligible, is important. We predict out-of-plane pyroelectricity in the recently synthesized Janus MoSSe monolayer and in-plane pyroelectricity in the group-IV monochalcogenide GeS monolayer. It is notable that the so-called secondary pyroelectricity is found to be dominant in GeS monolayer. The present work opens a theoretical route to study the pyroelectric effect using DFT and provides a valuable tool in the search for new candidates for pyroelectric applications.

Unusual Ferroelectricity in Two-Dimensional Perovskite Oxide Thin Films

Two-dimensional (2D) ferroelectricity have attracted much attention due to their applications in novel miniaturized devices such as nonvolatile memories, field effect transistors, and sensors. Since most of the commercial ferroelectric (FE) devices are based on ABO₃ perovskite oxides, it is important to investigate the properties of 2D ferroelectricity in perovskite oxide thin films. Here, based on density functional theory (DFT) calculations, we find that there exist three kinds of in-plane FE states that originate from different microscopic mechanisms: (i) a proper FE state with the polarization along [110] due to the second-order Jahn-Teller effect related to the B ion with empty d-orbitals; (ii) a robust FE state with the polarization along [100] induced by the surface effect; (iii) a hybrid improper FE state with the polarization along [110] that is induced by the trilinear coupling between two rotational modes and the A-site displacement. Interestingly, the ferroelectricity in the latter two cases becomes stronger along with decreasing the thin film thickness, in contrast to the usual behavior. Moreover, the latter two FE states are compatible with magnetism since their stability does not depend on the occupation of the d-orbitals of the B-ion. These two novel 2D FE mechanisms provide new avenues to design 2D multiferroics, as we demonstrated in SrVO and CaFeO thin film cases. Our work not only reveals new physical mechanisms of 2D ferroelectricity in perovskite oxide thin films but also provides a new route to design the high-performance 2D FE and multiferroics.

Effects of stacking method and strain on the electronic properties of the few-layer group-IVA monochalcogenide heterojunctions

Group-IV monochalcogenides (GeSe, SnSe, GeS, SnS) are a class of promising monolayer materials for nanoelectronic applications. However, the GeSe monolayer is the only direct semiconductor in the group-IV monochalcogenides, which limits their application in nanoelectronic fields. Stacking is usually a good strategy to design two-dimensional (2D) materials with novel properties. Taking these monolayer monochalcogenides as basic building blocks, various van der Waals (vdW) heterojunctions can be constructed by different stacking methods. In this study, we systematically investigated the structures, stabilities and electronic properties of thirty-six few-layer group-IV monochalcogenide heterojunctions. All the vdW heterojunctions are proved to be stable. The degree of stability of the few-layer heterojunctions is found to increase with the number of layers. The band gap values of heterojunctions are dependent not only on the components, but also on the stacking order. Five novel 2D direct semiconductors (SnSe/GeSe, GeS/SnS, SnSe/GeSe/SnSe, SnS/GeSe/SnSe and SnS/GeSe/SnSe) are obtained. It's found that biaxial strain can not only tune the values of band gap, but also change the type of the 2D materials. The band gaps of the heterojunctions monotonically increase with the increasing strain and most few-layer heterojunctions transform between direct and indirect semiconductors under biaxial strain. Five heterojunctions (SnSe/GeSe, GeS/SnS, GeSe/SnSe/SnS, SnS/GeSe/SnSe and GeSe/SnS/GeS/SnSe) are found to remain as direct semiconductors under tensile strain (0–0.1). Since the band gaps of these heterojunctions are easy to control in a suitable range, they may have potential applications in nanoelectronic fields.

We studied the effect of stacking method and biaxial strain on the electronic properties of the few-layer group-IV monochalcogenides heterojunction.

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.

Electronic and optical properties of strained graphene and other strained 2D materials: a review

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Large Bulk Photovoltaic Effect and Spontaneous Polarization of Single-Layer Monochalcogenides

We use a first-principles density functional theory approach to calculate the shift current and linear absorption of uniformly illuminated single-layer Ge and Sn monochalcogenides. We predict strong absorption in the visible spectrum and a large effective three-dimensional shift current (∼100  μA/V^{2}), larger than has been previously observed in other polar systems. Moreover, we show that the integral of the shift-current tensor is correlated to the large spontaneous effective three-dimensional electric polarization (∼1.9  C/m^{2}). Our calculations indicate that the shift current will be largest in the visible spectrum, suggesting that these monochalcogenides may be promising for polar optoelectronic devices. A Rice-Mele tight-binding model is used to rationalize the shift-current response for these systems, and its dependence on polarization, in general terms with implications for other polar materials.

Giant Optical Second Harmonic Generation in Two-Dimensional Multiferroics

Nonlinear optical properties of materials such as second and higher order harmonic generation and electro-optic effect play pivotal roles in lasers, frequency conversion, electro-optic modulators, switches, and so forth. The strength of nonlinear optical responses highly depends on intrinsic crystal symmetry, transition dipole moments, specific optical excitation, and local environment. Using first-principles electronic structure theory, here we predict giant second harmonic generation (SHG) in recently discovered two-dimensional (2D) ferroelectric-ferroelastic multiferroics-group IV monochalcogenides (i.e., GeSe, GeS, SnSe, and SnS). Remarkably, the strength of SHG susceptibility in GeSe and SnSe monolayers is more than 1 order of magnitude higher than that in monolayer MoS₂, and 2 orders of magnitude higher than that in monolayer hexagonal BN. Their extraordinary SHG is dominated by the large residual of two opposite intraband contributions in the SHG susceptibility. More importantly, the SHG polarization anisotropy is strongly correlated with the intrinsic ferroelastic and ferroelectric orders in group IV monochalcogenide monolayers. Our present findings provide a microscopic understanding of the large SHG susceptibility in 2D group IV monochalcogenide multiferroics from first-principles theory and open up a variety of new avenues for 2D ferroelectrics, multiferroics, and nonlinear optoelectronics, for example, realizing active electrical/optical/mechanical switching of ferroic orders in 2D multiferroics and in situ ultrafast optical characterization of local atomistic and electronic structures using noncontact noninvasive optical SHG techniques.

Photostrictive Two-Dimensional Materials in the Monochalcogenide Family

Photostriction is predicted for group-IV monochalcogenide monolayers, two-dimensional ferroelectrics with rectangular unit cells (the lattice vector a_{1} is larger than a_{2}) and an intrinsic dipole moment parallel to a_{1}. Photostriction is found to be related to the structural change induced by a screened electric polarization (i.e., a converse piezoelectric effect) in photoexcited electronic states with either p_{x} or p_{y} (in-plane) orbital symmetry that leads to a compression of a_{1} and a comparatively smaller increase of a_{2} for a reduced unit cell area. The structural change documented here is 10 times larger than that observed in BiFeO_{3}, making monochalcogenide monolayers an ultimate platform for this effect. This structural modification should be observable under experimentally feasible densities of photexcited carriers on samples that have been grown already, having a potential usefulness for light-induced, remote mechano-optoelectronic applications.