A correction method for vertical transition levels (VTLs) involving defect states calculated with a supercell technique is formulated and its effectiveness is systematically verified with ten defects in prototypical materials: cubic-BN, GaN, MgO, and 3C-SiC. Without any corrections, the absolute errors are around 1 eV with moderate size supercells in most cases. In contrast, when our correction method is adopted, the absolute errors are reduced and become less than 0.12 eV in all the cases. Our correction scheme is general and will have the potential for wide application as it is adaptive for evaluating various quantities at fixed geometry, as represented by those relevant to the generalized Koopmans' theorem.

We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground state is characterized by noncollinear long-range order with nonzero vector chirality, and study the effects of quenched bond disorder, i.e., random exchange couplings. A single bond defect is known to induce a dipolar texture in the spin background independent of microscopic details. Using general analytical arguments as well as large-scale simulations for the classical triangular-lattice Heisenberg model, we show that any finite concentration of such defects destroys long-range order for spatial dimension $d\le 2$, in favor of a glassy state whose correlation length in $d=2$ is exponentially large for small randomness. Our results are relevant for a wide range of layered frustrated magnets.

We measure the dispersion of the Cu-O bond-stretching phonon mode in the high-temperature superconducting parent compound ${\mathrm{Ca}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$. Our density functional theory calculations predict a cosine-shaped bending of the dispersion along both the $(\xi 00$) and $(\xi \xi 0$) directions, while comparison with previous results on ${\mathrm{Ca}}_{1.84}{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ show it only along $(\xi 00$), suggesting an anisotropic effect which is not reproduced in calculation. Comparison with isostructural ${\text{La}}_{2-x}{\text{Sr}}_x{\text{CuO}}_4$ and literature suggests that these calculations reproduce well the dispersion in the overdoped regime.

Intrinsic donor point defects and electron polarons are investigated in bulk ${\mathrm{AmO}}_2$ using density functional theory $+U$ calculations. Oxygen vacancies are deep double-donor defects, with transition energy levels closer to the valence band maximum than to the conduction band minimum. Americium interstitials are unlikely, due to prohibitive formation energies. Self-trapped electron polarons (which locally correspond to reducing one ${\mathrm{Am}}^{4+}$ in ${\mathrm{Am}}^{3+}$) are found extremely stable (self-trapping energy $=-1.01\mathrm{eV}$). The electron is even more stable in the self-trapped state (far from an oxygen vacancy) rather than in association with an oxygen vacancy, indicating that oxygen vacancies have the tendency to spontaneously ionize, and thus automatically liberate electron polarons in the lattice. This large stability of the electron polarons confines the accessible range of Fermi levels to a very narrow interval between the valence band maximum $E_{\text{VBM}}$ and $\sim E_{\text{VBM}}+0.09\mathrm{eV}$. In oxygen-poor conditions, oxygen vacancies may be formed in rather large concentration in ${\mathrm{AmO}}_2$ and have a strong probability to be doubly or singly ionized, with charge compensation being mostly ensured by a large number of electron polarons. The electron polaron hopping from an Am atom onto the nearest one involves a rather large activation energy of $\sim 0.6\mathrm{eV}$ and probably takes place by a nonadiabatic mechanism.

By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $\gamma$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid for SU(2) invariant systems, $\gamma =\mathrm{\Omega }/2$, where $\mathrm{\Omega }$ is the solid angle subtended by the local magnetic moments enclosed by the loop. The general form of $\gamma$ demonstrates that collinear and coplanar magnetic textures can also induce a Berry phase different from 0 or $\pi$, smoothly connecting the result for SU(2) invariant systems with the well-known result of Karplus and Luttinger for collinear ferromagnets with finite SOC. By taking the continuum limit of the theory, we also derive the corresponding generalized form of the real-space Berry curvature. The new expression is a generalization of the scalar spin chirality, which is presented in an explicitly covariant form. We finally show how these simple concepts can be used to understand the origin of the spontaneous topological Hall effect that has been recently reported in collinear and coplanar antiferromagnetic phases of correlated materials.

We report on a study of the structural and magnetic properties of single crystals of ${\mathrm{Ce}}_2{\mathrm{IrGa}}_{12}$. ${\mathrm{Ce}}_2{\mathrm{IrGa}}_{12}$ crystallizes in a layered tetragonal structure and undergoes an antiferromagnetic transition below 3.1 K. We characterize the temperature-field phase diagrams of ${\mathrm{Ce}}_2{\mathrm{IrGa}}_{12}$ for fields both within the $ab$ plane and along the $c$ axis, where the presence of a field-induced magnetic phase is found for in-plane fields. The ordering temperature is moderately enhanced upon the application of pressures up to 2.3 GPa, suggesting that ${\mathrm{Ce}}_2{\mathrm{IrGa}}_{12}$ corresponds to the well-localized region of the Doniach phase diagram.

We theoretically study the photoinduced topological phase transition of black phosphorene induced by laser light with moderate intensity, which can satisfy the experimentally realistic requirement to preserve the quality of the sample. By deriving the effective Floquet Hamiltonian in terms of pseudospin $S=1/2$ degrees of freedom, we calculate the Chern number and the optical conductivity of the system with varying laser frequency $\mathrm{\Omega }$. As one can expect from the photon-assisted transport, the longitudinal optical conductivity has a threshold frequency at $\mathrm{\Omega }=\mathrm{\Delta }/\hslash$, with $\mathrm{\Delta }$ being the band gap of black phosphorene. Unlike the longitudinal optical conductivity, the optical Hall conductivity sharply increases when $\hslash \mathrm{\Omega }$ goes beyond one-half of the band gap $\mathrm{\Delta }/2$. We also show that the Chern number changes from trivial to nontrivial upon increasing frequency $\mathrm{\Omega }$ beyond $\hslash \mathrm{\Omega }=\mathrm{\Delta }/2$.

We consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$j$ symbol, $\left\{\begin{array}{ccc}2& 2& 2\\ \frac{3}{2}& \frac{3}{2}& \frac{3}{2}\end{array}\right\}=0$. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $p$-type semiconductors.

Structured environment controls dynamics of light-matter interaction processes via modified local density of electromagnetic states. In typical scenarios, where nanosecond-scale fluorescent processes are involved, mechanical conformational changes of the environment during the interaction processes can be safely neglected. However, slow decaying phosphorescent complexes (e.g., lanthanides) can efficiently probe micro- and millisecond scale motion via near-field interactions with nearby structures. As the result, lifetime statistics can inherit information about nanoscale mechanical motion. Here we study light-matter interaction dynamics of phosphorescent dyes, diffusing in a proximity of a plasmonic nanoantenna. The interplay between time-varying Purcell enhancement and stochastic motion of molecules is considered via a modified diffusion equation, and collective decay phenomena is analysed. Fluid properties, such as local temperature and diffusivity, are mapped on phosphorescent lifetime distribution and then extracted with the help of inverse Laplace transformation. The presented photonic platform enables performing contactless all-optical thermometry and diffusion measurements, paving a way for a range of possible applications. In particular, detailed studies of nanofluidic processes in lab-on-a-chip devices, challenging for analysis with other optical methods, can be performed with time-dependent phosphorescence.

We report quantum Hall effect breakdown of a local filling factor $v_{\mathrm{local}}=1$ state formed in a bulk $v_{\mathrm{bulk}}=2$ system in an AlGaAs/GaAs heterostructure. When a finite source-drain bias is applied across the local system, the breakdown occurs in two steps. At low bias, quantized conductance through the $v_{\mathrm{local}}=1$ system breaks down due to interedge electron tunneling. At high bias, the incompressibility of the $v_{\mathrm{local}}=1$ system breaks down because the spin gap closes. The two steps are resolved by combining measurements of resistively detected nuclear magnetic resonance and shot noise, which allows one to evaluate electron spin polarization in the local system and spin-dependent charge transport through the system, respectively.

In sufficiently clean metals, it is possible for electrons to collectively flow as a viscous fluid at finite temperature. These viscous effects have been predicted to give a notable magnetoresistance, but whether the magnetoresistance is positive or negative has been debated. We argue that regardless of the strength of inhomogeneity, bulk magnetoresistance is always positive in the hydrodynamic regime. We also compute transport in weakly inhomogeneous metals across the ballistic-to-hydrodynamic crossover, where we also find positive magnetoresistance. The nonmonotonic temperature dependence of resistivity in this regime (a bulk Gurzhi effect) rapidly disappears upon turning on any finite magnetic field, suggesting that magnetotransport is a simple test for viscous effects in bulk transport, including at the onset of the hydrodynamic regime.

In this paper, a topological classification of molecules and their chemical reactions is proposed on a single-particle level. We consider zero-dimensional electronic Hamiltonians in a real-space tight-binding basis with spinless time-reversal symmetry and an additional spatial reflection symmetry. The symmetry gives rise to a perplectic structure and suggests a ${\mathbb{Z}}_2$ invariant in form of a Pfaffian, which can be captured by an entanglement cut. We apply our findings to a class of chemical reactions studied by Woodward and Hoffmann, where a reflection symmetry is preserved along a one-dimensional reaction path and argue that the topological classification should contribute to the rate constants of these reactions. More concretely, we find that a reaction takes place experimentally whenever the reactants and products can be adiabatically deformed into each other, while reactions that require a change of topological invariants have not been observed experimentally.

Understanding physics of high-$T_c$ cuprate superconductors remains one of the important problems in materials science. Though a number of diverse theories argue about the superconductivity and competing orders, ab initio and quantitative understanding is lacking. Here, we reproduce the experimental phase diagram of ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+y}$ by solving its ab initio low-energy effective Hamiltonian without adjustable parameters. It shows a superconducting phase in a wide range of hole density $\delta$, and its competition with charge period-4 plus spin period-8 stripe order near $\delta \sim 0.1$, in agreement with experimental results including recent x-ray scattering. Then a crucial role of off-site interactions in stabilizing the superconductivity is elucidated with emphasis on charge fluctuations. It also clarifies the condensation energy mainly contributed from the on-site Coulomb interaction. The present achievement will enable deeper, predictable understanding on open issues of the high-$T_c$ superconducting mechanism and promote ab initio studies on strongly correlated electrons beyond parametrized model studies.

Aluminum oxide nanoparticles are increasingly sought in numerous technological applications. However, as the nanoparticles grow during the synthesis, two phase transitions occur. At the nanoscale, numerical simulation of the stability of the alumina phases requires the use of empirical potentials that are reliable over a large range of system sizes going from a few atoms to several hundred thousand atoms. In this work, we confronted four different empirical potentials that are currently employed for bulk alumina. We found that only two of them are correct at the molecular level when compared to density functional theory calculations. Furthermore, the two potentials remain the best at the nanoscale as they reproduce one or two phase transitions that were observed experimentally: from amorphous solid to cubic crystal ($\gamma$) and from cubic to hexagonal ($\alpha$, i.e., corundum) crystal.

We study the Anderson transition for three-dimensional (3D) $N\times N\times N$ tightly bound cubic lattices where both real and imaginary parts of on-site energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r\left(W\right)$ crosses from 0.72 to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r\left(W\right)$ cross at $W_c=6.0\pm 0.1$ (in units of nearest-neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.

We introduce a two-dimensional generalization of the quasiperiodic Aubry–André model. Even though this model exhibits the same duality relation as the one-dimensional version, its localization properties are found to be substantially more complex. In particular, partially extended single-particle states appear for arbitrarily strong quasiperiodic modulation. They are concentrated on a network of low-disorder lattice lines, while the rest of the lattice hosts localized states. This spatial separation protects the localized states from delocalization, so no mobility edge emerges in the spectrum. Instead, localized and partially extended states are interspersed, giving rise to an unusual type of mixed spectrum and enabling complex dynamics even in the absence of interactions. A striking example is ballistic transport across the low-disorder lines while the rest of the system remains localized. This behavior is robust against disorder and other weak perturbations. Our model is thus directly amenable to experimental studies and promises fascinating many-body localization properties.

We present a time-resolved ultrafast optical spectroscopy study on thermoelectric material ${\mathrm{ZrTe}}_5$, regarding its carrier decay dynamics and anharmonic decay of coherent optical phonons at 5–280 K. A reflectivity time series consists of a single exponential decay due to the relaxation of carriers via electron-phonon coupling and decaying oscillations due to coherent phonon vibration of the $A_g$ mode. The carrier decay characteristics follow the temperature-induced electronic transitions of ${\mathrm{ZrTe}}_5$. The coherent optical phonon vibrations can be well described with the anharmonicity model including lattice thermal expansion and phonon-phonon coupling. The phonon vibration frequency and dephasing time are obtained as a function of temperature, and decrease with increasing temperature. The effects of pump fluence are also explored.

In this paper, we perform a systematic calculation of the Fe-Ta phase diagram to discover hard magnetic phases. By using structure prediction methods based on evolutionary algorithms, we identify two energetically stable magnetic structures: a tetragonal ${\mathrm{Fe}}_3\mathrm{Ta}$ (space group 122) and a cubic ${\mathrm{Fe}}_5\mathrm{Ta}$ (space group 216) binary phase. The tetragonal structure is estimated to have both high saturation magnetization (${\mu }_0{\mathrm{M}}_s=1.14$ T) and magnetocrystalline anisotropy (${\mathrm{K}}_1=2.17 \mathrm{MJ}/{\mathrm{m}}^3$) suitable for permanent magnet applications. The high-throughput screening of magnetocrystalline anisotropy also reveals two low-energy metastable hard magnetic phases: ${\mathrm{Fe}}_5{\mathrm{Ta}}_2$ (space group 156) and ${\mathrm{Fe}}_6\mathrm{Ta}$ (space group 194), that may exhibit intrinsic magnetic properties comparable to ${\mathrm{SmCo}}_5$ and ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$, respectively.