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In conventional \textit{ab initio} methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with non-zero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange's equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general, and can be applied to determine the adiabatic dynamics of any mixed set of slow variables., Comment: Added a discussion section on the role of SOC and fixed some typos. This article has been accepted by Physical Review X

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this work, we develop a first-principles method to calculate this velocity-force coupling in extended solids, and show via the example of ferromagnetic CrI$_3$ that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.

The group-IV diamond-structure elements are known to host a variety of planar defects, including {001} planar defects in C and {001}, {111} and {113} planar defects in Si and Ge. Among the {001} planar defects, the Humble defect, known for some time to occur in Ge, has recently also been observed in Si/Ge alloys, but the details of its electronic structure remain poorly understood. Here we perform first-principles density functional calculations to study Humble defects in both Ge and Ge$_{0.8}$Si$_{0.2}$. We also measure the Si L$_{2,3}$-edge electron energy loss spectra both at the defect and in a bulk-like region far from the defect, and compare with theoretical calculations on corresponding Si sites in our first-principles calculations. We find that inclusion of core-hole effects in the theory is essential for reproducing the observed L$_{2,3}$ edge spectra, and that once they are included, the results provide a set of fingerprints for different types of local atomic bonding environments in Ge$_{0.8}$Si$_{0.2}$. Our first-principles calculations reveal that the Humble defects have a tendency to enlarge the electronic band gap, which may have potential uses in band engineering. The use of hybrid functionals for an improved description of the band gap in these systems is also discussed., Comment: 11 pages, 10 figures; Comments are welcome

We report a new \{001\} planar defect found in SiGe nanopillars. The defect structure, determined by atomic resolution electron microscopy, matches the Humble defect model proposed for diamond. We also investigated several possible variants of the Humble structure using first principles calculations and found that the one lowest in energy was also in best agreement with the STEM images. The pillar composition has been analyzed with electron energy loss spectroscopy, which hints at how the defect is formed. Our results show that the structure and formation process of defects in nanostructured group IV semiconductors can be different from their bulk counterparts.

Non-reciprocal photonic devices are essential components of classical optical information processing. It is interesting and important to investigate their feasibility in the quantum world. In this work, the quantum properties of an on-chip silicon nitride (SiN)-based magneto-optical (MO) isolator were studied using a single-photon non-reciprocal dynamical transmission experiment. The measured isolation ratio for single photons achieved was 12.33 dB, which proved the functionality of our on-chip isolator. The quantum coherence of the passing single photons was further verified using high-visibility quantum interference. Our work will promote on-chip isolators within the integrated quantum circuits and help introduce novel phenomena in quantum information processes., Comment: 5 pages, 4figures

The quantum confinement of Bloch waves is fundamentally different from the well-known quantum confinement of plane waves. Unlike that obtained in the latter are all stationary states only; in the former, there is always a new type of states -- the boundary dependent states. This distinction leads to interesting physics in low-dimensional systems., Comment: 8 pages

The modern theory of polarization allows for the determination of the macroscopic end charge of a truncated one-dimensional insulator, modulo the charge quantum $e$, from a knowledge of bulk properties alone. A more subtle problem is the determination of the corner charge of a two-dimensional insulator, modulo $e$, from a knowledge of bulk and edge properties alone. While previous works have tended to focus on the quantization of corner charge in the presence of symmetries, here we focus on the case that the only bulk symmetry is inversion, so that the corner charge can take arbitrary values. We develop a Wannier-based formalism that allows the corner charge to be predicted, modulo $e$, only from calculations on ribbon geometries of two different orientations. We elucidate the dependence of the interior quadrupole and edge dipole contributions upon the gauge used to construct the Wannier functions, finding that while these are individually gauge-dependent, their sum is gauge-independent. From this we conclude that the edge polarization is not by itself a physical observable, and that any Wannier-based method for computing the corner charge requires the use of a common gauge throughout the calculation. We satisfy this constraint using two Wannier construction procedures, one based on projection and another based on a gauge-consistent nested Wannier construction. We validate our theory by demonstrating the correct prediction of corner charge for several tight-binding models. We comment on the relations between our approach and previous ones that have appeared in the literature., Comment: 21 pages, 10 figures, typo fixed, references updated, published version

A first principle prediction of the binary nanoparticle phase diagram assembled by solvent evaporation has eluded theoretical approaches. In this paper, we show that a binary system interacting through Lennard-Jones (LJ) potential contains all experimental phases in which nanoparticles are effectively described as quasi hard spheres. We report a phase diagram consisting of 53 equilibrium phases, whose stability is quite insensitive to the microscopic details of the potentials, thus giving rise to some type of universality. Furthermore, we show that binary lattices may be understood as consisting of certain particle clusters, i.e. motifs, which provide a generalization of the four conventional Frank-Kasper polyhedral units. Our results show that meta-stable phases share the very same motifs as equilibrium phases. We discuss the connection with packing models, phase diagrams with repulsive potentials and the prediction of likely experimental superlattices.

We study crystal nucleation of the Weeks-Chandler-Andersen (WCA) model, using the recently introduced Persistent Embryo Method (PEM). The method provides detailed characterization of pre-critical, critical and post-critical nuclei, as well as nucleation rates that compare favorably with those obtained using other methods (umbrella sampling, forward flux sampling or seeding). We further map our results to a hard sphere model allowing to compare with other existing predictions. Implications for experiments are also discussed., Comment: 27 pages, 11 figures

First-principles total-energy calculations of the H/Si(001)-2x1 surfaces reveals a dual diffusion process for the Si adatoms: single along the dimer row while pairing up across the row. The calculated diffusion barrier along the dimer row is 1.1 eV, which is, however, too small to account for the hydrogen-induced growth disruption seen by experiments. Instead, we find that the adatom diffusion, in the presence of H, leads to the formation of immobile fourfold-ring Si tetramers which are difficult to break. This could explain the adverse effects of H on Si homoepitaxy., Comment: 4 pages 4 figures

This work investigates the existence and properties of a certain class of solutions of the Hill's equation truncated in the interval [tau, tau + L] - where L = N a, a is the period of the coefficients in Hill's equation, N is a positive integer and tau is a real number. It is found that the truncated Hill's equation has two different types of solutions which vanish at the truncation boundaries tau and tau + L: There are always N-1 solutions in each stability interval of Hill's equation, whose eigen value is dependent on the truncation length L but not on the truncation boundary tau; There is always one and only one solution in each finite conditional instability interval of Hill's equation, whose eigen value might be dependent on the boundary location tau but not on the truncation length L. The results obtained are applied to the physics problem on the electronic states in one dimensional crystals of finite length. It significantly improves many known results and also provides more new understandings on the physics in low dimensional systems., Comment: 16 pages, 1 figure

Electronic States of Si and Ge QDs of 5 to 3127 atoms with saturated shapes in a size range of 0.57 to 4.92 nm for Si and 0.60 to 5.13 nm for Ge are calculated by using an empirical tight binding model combined with the irreducible representations of the group theory. The results are compared with those of Si and Ge quantum dots with spherical shape. The effects of the shapes on electronic states in QDs are discussed., Comment: 11 pages, 5 figures

Exact and general results on the electronic states in ideal free standing films are presented. In many interesting cases, such as in FCC (001) films and in FCC (110) films, the energies of most electronic states in the film can be analytically obained from the corresponding energy band structure of the bulk. This approach can be further extended to obtain exact and general results on the electronic states in quantum wires and quantum dots., Comment: 15 pages