Abstract: In the Comment, the authors state that the separation of the relative and center of mass variables in our work is not correct. Here we point out that there is a typographical error, i.e., qi instead of -e, in two of our equations which, when corrected, makes the Comment redundant. Within the ansatzes mentioned in our paper all our results are correct, in contrast to the claims of the Comment.

Abstract: In this work we compute the torque field present in a ferromagnet in contact with a metallic nanowire when a skyrmion is present. If the nanowire is narrow enough, then the current is carried by a single conduction band. In this regime the classical torque model breaks down and we show that a skyrmion driven by spin transfer torque moves in a different direction than predicted by the classical model. However, the amount of charge current required to move a skyrmion with a certain velocity in the single-band regime is similar to a classical model of torque where it is implicitly assumed current transport by many conduction bands. The single-band regime is more efficient creating spin current from charge current because of the perfect polarization of the single band but is less efficient creating torque from spin current. Nevertheless, it is possible to take profit of the single-band regime to move skyrmions even with no net charge or spin current flowing between the device contacts. We have also been able to recover the classical limit considering an ensemble of only a few electronic states. In this limit we have discovered that electron diffusion needs to be considered even in ballistic nanowires due the effect of the skyrmion structure on the electron current.

Abstract: High tunability of two-dimensional magnetic materials (by strain, gating, heterostructuring, or otherwise) provides unique conditions for studying versatile magnetic properties and controlling emergent magnetic phases. Expanding the scope of achievable magnetic phenomena in such materials is important for both fundamental and technological advances. Here we perform atomistic spin-dynamics simulations to explore the (chiral) magnetic phases of atomic monolayers in the limit of suppressed first-neighbors exchange interaction. We report the rich phase diagram of exotic magnetic configurations, obtained for both square and honeycomb lattice symmetries, comprising coexistence of ferromagnetic and antiferromagnetic spin cycloids, as well as multiple types of magnetic skyrmions. We perform a minimum-energy path analysis for the skyrmion collapse to evaluate the stability of such topological objects and reveal that magnetic monolayers could be good candidates to host the antiferromagnetic skyrmions that are experimentally evasive to date.

Abstract: The effect of proximity-induced interactions such as Rashba spin-orbit coupling (SOC) and exchange interaction on the electronic and optical properties of n-type monolayer (ML) MoS2 is investigated. We predict and demonstrate that the Rashba SOC can induce an in-plane spin splitting with terahertz (THz) energy, while the exchange interaction lifts the energy degeneracy in different valleys. Thus, spin polarization can be achieved in an n-type ML MoS2 and valley Hall or optical Hall effect can be observed using linearly polarized THz radiation. In such a case, the transverse optical conductivity sigma(xy) (omega) results from spin-flip transition within spin-split conduction bands and from the fact that contributions from electrons with different spin orientations in different valleys can no longer be canceled out. Interestingly, we find that for fixed effective Zeeman field (or exchange interaction) the lowest spin-split conduction band in ML MoS2 can be tuned from one in the K valley to another one in the K' valley by varying the Rashba parameter lambda(R). Therefore, by changing lambda(R) we can turn the sign of the spin polarization and Im sigma(xy) (omega) from positive to negative. Moreover, we find that the dominant contribution of the selection rules to sigma(xx)(omega) is from electrons in the K valley and to sigma(xy) (omega) is from electrons in the K' valley. These important and interesting theoretical findings can be helpful to experimental observation of the optical Hall effect in valleytronic systems using linearly polarized THz radiation fields.

Abstract: We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data were analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in small domains, each of which consisting of hundreds of skyrmions, and with an activation barrier of several eV.

Abstract: Using first-principle calculations, we systematically study strain tuning of the electronic properties of two- dimensional graphitic carbon nitride nanosheets with empirical formula CnNm. We found the following: (i) the ferromagnetic ordered state in the metal-free systems (n, m) = (4,3), (10,9), and (14,12) remains stable in the presence of strain of about 6%. However, the system (9,7) loses its ferromagnetic ordering when increasing strain. This is due to the presence of topological defects in the (9,7) system, which eliminates the asymmetry between spin up and spin down of the p(z) orbitals when strain is applied. (ii) By applying uniaxial strain, a band gap opens in systems which are initially gapless. (iii) In semiconducting systems which have an initial gap of about 1 eV, the band gap is closed with applying uniaxial strain.

Abstract: The optoelectronic properties of confined water form one of the most active research areas in the past few years. Here we present the multiscale methodology to discern the out-of-plane electronic and dipolar dielectric constants (epsilon(el)(perpendicular to) and epsilon(diP)(perpendicular to)) of strongly confined water. We reveal that epsilon(perpendicular to el) and epsilon(diP)(perpendicular to) become comparable for water confined in angstrom-scale channels (with a height of less than 15 angstrom) within graphene (GE) and hexagonal boron nitride (hBN) bilayers. Channel height (h) associated with a minimum in both epsilon(e)(l)(perpendicular to) and epsilon(dip)(perpendicular to) is linked to the formation of the ordered structure of ice for h approximate to (7 -7.5) angstrom. The recently measured total dielectric constant epsilon(T)(perpendicular to) of nanoconfined water [L. Fumagalli et al., Science 360, 1339 (2018)] is corroborated by our results. Furthermore, we evaluate the contribution from the encapsulating membranes to the dielectric properties, as a function of the interlayer spacing, i.e., the height of the confining channel for water. Finally, we conduct analysis of the optical properties of both confined water and GE membranes, and show that the electron energy loss function of confined water strongly differs from that of bulk water.

Abstract: The surface termination of MXenes greatly determines the electrochemical properties and ion kinetics on their surfaces. So far, hydroxyl-, oxygen-, and fluorine-terminated MXenes have been widely studied for energy storage applications. Recently, sulfur-functionalized MXene structures, which possess low diffusion barriers, have been proposed as candidate materials to enhance battery performance. We performed first-principles calculations on the structural, stability, electrochemical, and ion dynamic properties of Li-adsorbed sulfur-functionalized groups 3B, 4B, 5B, and 6B transition-metal (M)-based MXenes (i.e., M2CS2 with M = Sc, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, and W). We performed phonon calculations, which indicated that all of the above M2CS2 MXenes, except for Sc, are dynamically stable at T = 0 K. The ground-state structure of each M2CS2 monolayer depends on the type of M atom. For instance, while sulfur prefers to sit at the FCC site on Ti2CS2, it occupies the HCP site of Cr-based MXene. We determined the Li adsorption configurations at different concentrations using the cluster expansion method. The highest maximum open-circuit voltages were computed for the group 4B element (i.e., Ti, Zr, and Hf)-based M2CS2, which are larger than 2.1 V, while their average voltages are approximately 1 V. The maximum voltage for the group 6B element (i.e., Cr, Mo, W)-based M2CS2 is less than 1 V, and the average voltage is less than 0.71 V. We found that S functionalization is helpful for capacity improvements over the O-terminated MXenes. In this respect, the computed storage gravimetric capacity may reach up to 417.4 mAh/g for Ti2CS2 and 404.5 mAh/g for V2CS2. Ta-, Cr-, Mo-, and W-based M2CS2 MXenes show very low capacities, which are less than 100 mAh/g. The Li surface diffusion energy barriers for all of the considered MXenes are less than 0.22 eV, which is favorable for high charging and discharging rates. Finally, ab initio molecular dynamic simulations performed at 400 K and bond-length analysis with respect to Li concentration verify that selected promising systems are robust against thermally induced perturbations that may induce structural transformations or distortions and undesirable Li release.

Abstract: By using the full 3D generalized time-dependent Ginzbug-Landau equation, we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a closed vortex experimentally.

Abstract: Flat bands in the energy spectrum have attracted a lot of attention in recent years because of their unique properties and promising applications. Special arrangement of impurities on monolayer graphene are proposed to generate multiflat bands in the electronic band structure. In addition to the single midgap states in the spectrum of graphene with low hydrogen density, we found closely spaced bands around the Fermi level with increasing impurity density, which are similar to discrete lines in the spectrum of quantum dots, as well as the unusual Landau-level energy spectrum of graphene in the presence of a strong magnetic field. The presence of flat bands crucially depends on whether or not there are odd or even electrons of H(F) atoms bound to graphene. Interestingly, we found that a fully hydrogenated (fluoridated) of a hexagon of graphene sheet with six hydrogen (fluorine) atoms sitting on top and bottom in consecutive order exhibits Dirac cones in the electronic band structure with a 20% smaller Fermi velocity as compared to the pristine graphene. Functionalizing graphene introduces various C-C bond lengths resulting in nonuniform strains. Such a nonuniform strain may induce a giant pseudomagnetic field in the system, resulting in quantum Hall effect.

Abstract: A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasiparticles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we consider a system where low-energy electrons can be described as Dirac particles, which is the case for most two-dimensional materials, such as graphene and transition-metal dichalcogenides. However, the method is easily adapted for other cases such as electrons in few-layer black phosphorus or any Schrodinger quasiparticles within the effective mass approximation in semiconductors. We employ the method to revisit Andreev reflection in mono-, bi-, and trilayer graphene, where specular-and retro-reflection cases are observed for electrons scattered by a steplike superconducting region. The effect of opening a zero-gap channel across the superconducting region on the electron and hole scattering is also addressed, as an example of the versatility of the technique proposed here.

Abstract: The self-assembly of nanoparticles into clusters and the effect of the different parameters of the competing interaction potential on it are investigated. For a small number of particles, the structural organization of the clusters is almost unaffected by the attractive part of the potential, and for an intermediate number of particles the configuration strongly depends on the strength of it. The cluster size is controlled by the range of the interaction potential, and the structural arrangement is guided by the strength of the potential: i.e., the self-assembled cluster transforms from a faceted configuration at low strength to a spherical shell-like structure at high strength. Nonmonotonic behavior of the cluster size is found by increasing the interaction range. An approximate analytical expression is obtained that predicts the smallest cluster for a specific set of potential parameters. A Mendeleev-like table is constructed for different values of the strength and range of the attractive part of the potential in order to understand the structural ordering of the ground-state configuration of the self-assembled clusters.

Abstract: We discuss positron-annihilation lifetimes for a set of illustrative bulk materials within the framework of the weighted-density approximation (WDA). The WDA can correctly describe electron-positron correlations in strongly inhomogeneous systems, such as surfaces, where the applicability of (semi-)local approximations is limited. We analyze the WDA in detail and show that the electrons which cannot screen external charges efficiently, such as the core electrons, cannot be treated accurately via the pair correlation of the homogeneous electron gas. We discuss how this problem can be addressed by reducing the screening in the homogeneous electron gas by adding terms depending on the gradient of the electron density. Further improvements are obtained when core electrons are treated within the LDA and the valence electron using the WDA. Finally, we discuss a semiempirical WDA-based approach in which a sum rule is imposed to reproduce the experimental lifetimes.

Abstract: When subjected to the interfacially induced Dzyaloshinskii-Moriya interaction, the ground state in thin ferromagnetic films with high perpendicular anisotropy is cycloidal. The period of this cycloidal state depends on the strength of the Dzyaloshinskii-Moriya interaction. In this work, we have studied the effect of confinement on the magnetic ground state and excited states, and we determined the phase diagram of thin strips and thin square platelets by means of micromagnetic calculations. We show that multiple cycloidal states with different periods can be stable in laterally confined films, where the period of the cycloids does not depend solely on the Dzyaloshinskii-Moriya interaction strength but also on the dimensions of the film. The more complex states comprising skyrmions are also found to be stable, though with higher energy.

Abstract: In a recent paper [Phys. Rev. B 89, 125418 (2014)], the authors argue that it is possible to map the electronic properties of twisted bilayer graphene to those of bilayer graphene in an in-plane magnetic field. However, their description of the low-energy dynamics of twisted bilayer graphene is restricted to the extended zone scheme and therefore neglects the effects of the superperiodic structure. If the energy spectrum is studied in the supercell Brillouin zone, we find that the comparison with an in-plane magnetic field fails because (i) the energy spectra of the two situations exhibit different symmetries and (ii) the low-energy spectra are very different.