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The discovery of two-dimensional (2D) materials comes at a time when computational methods are mature and can predict novel 2D materials, characterize their properties, and guide the design of 2D materials for applications. This article reviews the recent progress in computational approaches for 2D materials research. We discuss the computational techniques and provide an overview of the ongoing research in the field. We begin with an overview of known 2D materials, common computational methods, and available cyber infrastructures. We then move onto the discovery of novel 2D materials, discussing the stability criteria for 2D materials, computational methods for structure prediction, and interactions of monolayers with electrochemical and gaseous environments. Next, we describe the computational characterization of the 2D materials' electronic, optical, magnetic, and superconducting properties and the response of the properties under applied mechanical strain and electrical fields. From there, we move on to discuss the structure and properties of defects in 2D materials, and describe methods for 2D materials device simulations. We conclude by providing an outlook on the needs and challenges for future developments in the field of computational research for 2D materials.

The dissociation of icosahedral viral capsids was investigated by a homogeneous and a heterogeneous lattice model. In thermal dissociation experiments with cowpea chlorotic mottle virus and probed by small-angle neutron scattering, we observed a slight shrinkage of viral capsids, which can be related to the strengthening of the hydrophobic interaction between subunits at increasing temperature. By considering the temperature dependence of hydrophobic interaction in the homogeneous lattice model, we were able to give a better estimate of the effective charge. In the heterogeneous lattice model, two sets of lattice sites represented different capsid subunits with asymmetric interaction strengths. In that case, the dissociation of capsids was found to shift from a sharp one-step transition to a gradual two-step transition by weakening the hydrophobic interaction between AB and CC subunits. We anticipate that such lattice models will shed further light on the statistical mechanics underlying virus assembly and disassembly.

Two systems of suspended nanoparticles have been studied with near-ambient pressure x-ray photoelectron spectroscopy: silver nanoparticles in water and strontium fluoride—calcium fluoride core-shell nanoparticles in ethylene glycol. The corresponding dry samples were measured under ultra high vacuum for comparison. The results obtained under near-ambient pressure were overall comparable to those obtained under ultra high vacuum, although measuring silver nanoparticles in water requires a high pass energy and a long acquisition time. A shift towards higher binding energies was found for the silver nanoparticles in aqueous suspension compared to the corresponding dry sample, which can be assigned to a change of surface potential at the water-nanoparticle interface. The shell-thickness of the core-shell nanoparticles was estimated based on simulated spectra from the National Institute of Standards and Technology database for simulation of electron spectra for surface analysis. With the instrumental set-up presented in this paper, nanoparticle suspensions in a suitable container can be directly inserted into the analysis chamber and measured without prior sample preparation.

We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions. Previous studies of the capsid self-assembly involved solid objects of a supramolecular scale, e.g. corresponding to capsomeres, with engineered couplings and stochastic movements. In our approach, a single capsid is dissociated by an application of a high temperature for a variable period and then the system is cooled down to allow for self-assembly. The restoration of the capsid proceeds to various extent, depending on the nature of the dissociated state, but is rarely complete because some proteins depart too far unless the process takes place in a confined space.

Large scale tetraoctylammonium-assisted electrochemical transfer of graphene grown on single-crystalline Ir(1 1 1) films by chemical vapour deposition is reported. The transferred samples are characterized in air with optical microscopy, Raman spectroscopy and four point transport measurements, providing the sheet resistance and the Hall carrier concentration. In vacuum we apply low energy electron diffraction and photoelectron spectroscopy that indicate transferred large-scale single orientation graphene. Angular resolved photoemission reveals a Fermi surface and a Dirac point energy which are consistent with charge neutral graphene.

Thermophoretic forces acting on nanoparticles are investigated using molecular dynamics simulation. We assume the Lennard-Jones (LJ) potential for the interaction between fluid molecules. On the other hand, the interaction between the nanoparticle and the surrounding fluid molecules are assumed to be either LJ or Weeks–Chandler–Andersen (WCA) potential, where the latter is purely-repulsive. The effect of the interaction potential on the thermophoretic force is investigated for various situations. It is found that the thermophoretic force basically acts in the direction from the hotter side to the colder side of the nanoparticle. However, when the surrounding fluid is in the liquid phase, the force acts in the reversed direction for the case of the WCA potential. It is clarified that the sign reversal is caused by the different structures observed in the distribution of repulsive forces acting on the nanoparticle.

Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles). Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities.

We propose a method for monitoring the large-scale homogeneity of the reduction process of graphene oxide. For this purpose, a Raman mapping technique is employed to probe the evolution of the phonon properties of two different graphene oxide (GO) thin films upon controllable thermal reduction. The reduction of GO is reflected by the upshift of the statistical distribution of the relative intensity ratio of the G and D peaks (I_D/I_G) of the Raman spectra and is consistent with the ratio obtained for chemically reduced GO. In addition, the shifts of the position distributions of the main Raman modes (${{\omega }_{{\rm D}}}$, ${{\omega }_{{\rm G}}}$) and their cross-correlation with the I_D/I_G ratio provides evidence of a change of the doping level, demonstrating the influence of reduction processes on GO films.

In IV–VI semiconductor heterojunctions with band-inversion, such as those made of ${\rm Pb}_{1-x}$${\rm Sn}_{x}$Te or ${\rm Pb}_{1-x}$${\rm Sn}_{x}$Se, interface states are properly described by a two-band model, predicting the appearance of a Dirac cone in single junctions. However, in quantum wells the interface dispersion is quadratic in momentum and the energy spectrum presents a gap. We show that the interface gap shrinks under an electric field parallel to the growth direction. Therefore, the interface gap can be dynamically tuned in experiments on double-gated quantum wells based on band-inverted compounds.

The orbital effect on the Fulde–Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. Confinement in the radial direction results in quantization of the electron motion with energies determined by the radial j and orbital m quantum numbers. In the external magnetic field, the twofold degeneracy with respect to the orbital magnetic quantum number m is lifted which leads to the Fermi wave vector mismatch between the paired electrons, $(k, j, m, \uparrow) \leftrightarrow (-k, j, -m, \downarrow)$. This mismatch is transferred to the nonzero total momentum of the Cooper pairs, which results in a formation of the FF phase occurring sequentially with increasing magnetic field. By changing the nanowire radius R and the superconducting shell thickness d, we discuss the role of the orbital effect in the FF phase formation in both the nanowire-like ($R/d \ll 1$) and nanofilm-like ($R/d \gg 1$) regime. We have found that the irregular pattern of the FF phase which appears for the case of the nanowire-like regime, for the nanofilm-like geometry evolves towards the regular distribution in which the FF phase stability regions emerge periodically between the BCS states. The transition between these two different phase diagrams is explained as resulting from the orbital effect and the multigap character of superconductivity in the core/shell nanowires.

The stabilities of Ni metal and its derived compounds, including oxides, hydroxides, and oxyhydroxides under electrochemical conditions, can be readily predicted from the Ni Pourbaix diagram, where the formation free energies of the involved species are utilized to construct the phase stability map with respect to electrode potential and pH. We calculate and analyze the crystal structures, electronic structures, and thermodynamic energies of Ni metal and its compounds using different exchange-correlation functionals to density-functional-theory (DFT), including the semilocal LDA and GGA density functionals, the nonlocal metaGGA, and the hybrid density functionals. Next, we simulate the corresponding Ni Pourbaix diagrams to compare systematically the performance of the functional to each other and to experimental observations. We show that the structures and energies obtained from experimental databases may not be sufficiently accurate to describe direct electrochemical observations, and we explain how the electronic exchange within the density functionals plays a key role in determining the accuracy of the DFT calculated electronic, thermodynamic, and electrochemical properties. We find that only the hybrid density functional produces reliable results owing to the fractional contribution of exact Fock exchange included therein. Last, based on our accurate Ni Pourbaix diagram, we construct band-gap and magnetic electrochemical maps which can facilitate more experimental measurements and property assessments under variable potential and pH in the future.

Electronic structures of ferromagnetic heavy fermion Yb compounds of YbPdSi, YbPdGe, and YbPtGe are studied by photoelectron spectroscopy around the Yb 4d–4f resonance, resonant x-ray emission spectroscopy at the Yb L₃ absorption edge, and density functional theory combined with dynamical mean field theory calculations. These compounds all have a temperature-independent intermediate Yb valence with large ${\rm Yb}^{3+}$ and small ${\rm Yb}^{2+}$ components. The magnitude of the Yb valence is evaluated to be YbPtGe $<$ YbPdGe $\lesssim$ YbPdSi, suggesting that YbPtGe is the closest to the quantum critical point among the three Yb compounds. Our results support the scenario of the coexistence of heavy fermion behavior and ferromagnetic ordering which is described by a magnetically-ordered Kondo lattice where the magnitude of the Kondo effect and the RKKY interaction are comparable.

We present the universal features of the topological invariant for p-wave superconducting wires after the inclusion of spatial inhomogeneities. Three classes of distributed potentials are studied, a single-defect, a commensurate and an incommensurate model, using periodic site modulations. An analytic polynomial description is achieved by splitting the topological invariant into two parts; one part depends on the chemical potential and the other does not. For the homogeneous case, an elliptical region is found where the topological invariant oscillates. The zeros of these oscillations occur at points where the fermion parity switches for finite wires. The increase of these oscillations with the inhomogeneity strength leads to new isolated non-topological phases. We characterize these new phases according to each class of spatial distributions. Such phases could also be observed in the XY model, to which our model is dual.

We report on magnetotransport measurements at $T=4.2$ K in a high-quality InAs nanowire ($R_{\rm wire} \sim 20$ kΩ) in the presence of the charged tip of an atomic force microscope serving as a mobile gate. We demonstrate the crucial role of the external magnetic field on the amplitude of the charge density waves with a wavelength of 0.8 μm. The observed suppression rate of their amplitude is similar or slightly higher than the one for weak localization correction in our investigated InAs nanowire.

The electronic properties of the heavy metal superconductor ${\rm LaIr}_{3}$ are reported. The estimated superconducting parameters obtained from physical properties measurements indicate that ${\rm LaIr}_{3}$ is a BCS-type superconductor. Electronic band structure calculations show that Ir d-states dominate the Fermi level. A comparison of electronic band structures of ${\rm LaIr}_{3}$ and ${\rm LaRh}_{3}$ shows that the Ir-compound has a strong spin–orbit-coupling effect, which creates a complex Fermi surface.

We characterized intrinsic deep level defects created in ion collision cascades which were produced by patterned implantation of single accelerated 2.0 MeV He and 600 keV H ions into n-type 4H-SiC epitaxial layers using a fast-scanning reduced-rate ion microbeam. The initial deep level transient spectroscopy measurement performed on as-grown material in the temperature range 150–700 K revealed the presence of only two electron traps, Z_1/2 (0.64 eV) and EH_6/7 (1.84 eV) assigned to the two different charge state transitions of the isolated carbon vacancy, V_C (=/0) and (0/+). C–V measurements of as-implanted samples revealed the increasing free carrier removal with larger ion fluence values, in particular at depth corresponding to a vicinity of the end of an ion range. The first DLTS measurement of as-implanted samples revealed formation of additional deep level defects labelled as ET1 (0.35 eV), ET2 (0.65 eV) and EH3 (1.06 eV) which were clearly distinguished from the presence of isolated carbon vacancies (Z_1/2 and EH_6/7 defects) in increased concentrations after implantations either by He or H ions. Repeated C–V measurements showed that a partial net free-carrier recovery occurred in as-implanted samples upon the low-temperature annealing following the first DLTS measurement. The second DLTS measurement revealed the almost complete removal of ET2 defect and the partial removal of EH3 defect, while the concentrations of Z_1/2 and EH_6/7 defects increased, due to the low temperature annealing up to 700 K accomplished during the first temperature scan. We concluded that the ET2 and EH3 defects: (i) act as majority carrier removal traps, (ii) exhibit a low thermal stability and (iii) can be related to the simple point-like defects introduced by light ion implantation, namely interstitials and/or complex of interstitials and vacancies in both carbon and silicon sub-lattices.

In this work we study analytically and numerically the spectrum and localization properties of three quasi-one-dimensional (ribbons) split-ring resonator arrays which possess magnetic flatbands, namely, the stub, Lieb and kagome lattices, and how their spectra are affected by the presence of perturbations that break the delicate geometrical interference needed for a magnetic flatband to exist. We find that the stub and Lieb ribbons are stable against the three types of perturbations considered here, while the kagome ribbon is, in general, unstable. When losses are incorporated, all flatbands remain dispersionless but become complex, with the kagome ribbon exhibiting the highest loss rate. The stability of flatband modes of certain split-ring resonator arrays suggests that they could be used as components of future stable magnetic storage devices.

In order to understand the origin of the huge quasielastic magnetic scattering observed previously with a back-scattering neutron spectrometer, we have re-investigated the low energy excitations in HoCrO₃ by inelastic neutron scattering in a much wider energy range with time-of-flight neutron spectrometers. The inelastic signals are due to the excitations between the ground state doublet of the Ho ion. The quasielastic signal is due to the fluctuation of the disordered Ho moments. At low temperature the intensity of quasielastic scattering is small. It starts increasing as the temperature increases above 30 K. At the same temperature, the elastic intensity due to Ho moment ordering decreases in a similar way. This observation strengthens the hypothesis that the quasielastic scattering is due the fluctuations of the disordered Ho moments. The time scale of fluctuations has been determine from the quasielastic scattering and was found to vary from about 22 ps at $T = 70$ K to about 2.5 ps at $T = 160$ K. The stretched exponential line shape indicates a distribution of decay rates at low temperatures.

Considerable progress in contemporary spintronics has been made in recent years for developing nanoscale data memory and quantum information processing. It is, however, still a great challenge to achieve the ultimate limit of storage bit. 2D materials, fortunately, provide an alternative solution for designing materials with the expected miniaturizing scale, chemical stability as well as giant magnetic anisotropy energy. By performing first-principles calculations, we have examined two possible doping sites on a WS₂ monolayer using three kinds of transition metal (TM) atoms (Mn, Fe and Co). It is found that the TM atoms prefer to stay on the W atom site. Additionally, differently from the case of Mn, doping Co and Fe atoms on the W vacancy can achieve perpendicular magnetic anisotropy with a much larger magnitude, which provides a bright prospect for generating atomic-scale magnets of storage devices.

We report the experimental observation of spin reorientation in the double perovskite Ho₂FeCoO₆. The magnetic phase transitions in this compound are characterized and studied through magnetization and specific heat, and the magnetic structures are elucidated through neutron powder diffraction. Two magnetic phase transitions are observed in this compound-one at $T_{\rm N1} \approx 250$ K, from paramagnetic to antiferromagnetic, and the other at $T_{\rm N2} \approx 45$ K, from a phase with mixed magnetic structures to a single phase through a spin reorientation process. The magnetic structure in the temperature range 200–45 K is a mixed phase of the irreducible representations $\Gamma_1$ and $\Gamma_3$, both of which are antiferromagnetic. The phase with mixed magnetic structures that exists in Ho₂FeCoO₆ gives rise to a large thermal hysteresis in magnetization that extends from 200 K down to the spin reorientation temperature. At T_N2, the magnetic structure transforms to $\Gamma_1$. Though long-range magnetic order is established in the transition metal lattice, it is seen that only short-range magnetic order prevails in the Ho³⁺ lattice. Our results should motivate further detailed studies on single crystals in order to explore the spin reorientation process, spin switching and the possibility of anisotropic magnetic interactions giving rise to electric polarization in Ho₂FeCoO₆.

The recent development of experimental techniques in ultracold atomic Fermi gases is extremely helpful in the progress of the realization of the unconventional Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superfluid phase in quasi-one dimensional systems (Liao et al 2010 Nature467 567). Due to a Fermi surface nesting, which is enhanced in 1D, the low-dimensional systems are particularly good candidates to find the FFLO phase stable. We investigate the influence of a dimensional crossover (from one dimension (1D) to two dimensions (2D) or three dimensions (3D)) on the stability of the FFLO state in the spin-imbalanced attractive Hubbard model.

In this work, the phase field crystal (PFC) method is used to study the localized solid-state amorphization (SSA) and its dynamic transformation process in polycrystalline materials under the uniaxial tensile deformation with different factors. The impacts of these factors, including strain rates, temperatures and grain sizes, are analyzed. Kinetically, the ultra-high strain rate causes the lattice to be seriously distorted and the grain to gradually collapse, so the dislocation density rises remarkably. Therefore, localized SSA occurs. Thermodynamically, as high temperature increases the activation energy, the atoms are active and prefer to leave the original position, which induce atom rearrangement. Furthermore, small grain size increases the percentage of grain boundary and the interface free energy of the system. As a result, Helmholtz free energy increases. The dislocations and Helmholtz free energy act as the seed and driving force for the process of the localized SSA. Also, the critical diffusion-time step and the percentage of amorphous region areas are calculated. Through this work, the PFC method is proved to be an effective means to study localized SSA under uniaxial tensile deformation.

To overcome the limitation of conventional fixed charge potential methods for the study of Li-ion battery cathode materials, a dynamic charge potential method, charge-transfer modified embedded atom method (CT-MEAM), has been developed and applied to the Li–Co–O ternary system. The accuracy of the potential has been tested and validated by reproducing a variety of structural and electrochemical properties of LiCoO₂. A detailed analysis on the local charge distribution confirmed the capability of this potential for dynamic charge modeling. The transferability of the potential is also demonstrated by its reliability in describing Li-rich Li₂CoO₂ and Li-deficient LiCo₂O₄ compounds, including their phase stability, equilibrium volume, charge states and cathode voltages. These results demonstrate that the CT-MEAM dynamic charge potential could help to overcome the challenge of modeling complex ternary transition metal oxides. This work can promote molecular dynamics studies of Li ion cathode materials and other important transition metal oxides systems that involve complex electrochemical and catalytic reactions.