We present an efficient method for the design of anomalous reflectors for acoustic waves. The approach is based on the fact that the anomalous reflector is actually a diffraction grating in which the amplitude of all the modes is negligible except for the one traveling towards the desired direction. A supercell of drilled cavities in an acoustically rigid surface is proposed as the basic unit cell, and analytical expressions for an inverse diffraction problem are derived. It is found that the the number of cavities required for the realization of an anomalous reflector is equal to the number of diffracted modes to cancel, and this number depends on the relationship between the incident and reflected angles. Then, the “retroreflection” effect is obtained by just one cavity per unit cell; also, with only two cavities it is possible to change the reflection angle of a normally incident wave, and five cavities are enough to design a general retroreflector changing the incident and reflected angles at oblique incidence. Finally, the concept of Snell's law violation is extended not only to the incident and reflected angles, but also to the plane in which it happens, and a device based on a single cavity in a square lattice is designed in such a way that the reflection plane is rotated $\pi /4$ with respect to the plane of incidence. Numerical simulations are performed to support the predictions of the analytical expressions, and an excellent agreement is found.

We present a microscopic theory of the orbital magnetic quadrupole moment density ${\mathcal{Q}}_{ij}$ in periodic crystals with combined time-reversal ($\mathbf{T}$) and inversion ($\mathbf{I}$) symmetry. We obtain a gauge-invariant expression with a clear physical interpretation and demonstrate the typical behavior of ${\mathcal{Q}}_{ij}$ in a minimal two-band model that hosts a tilted Dirac cone. We then show that ${\mathcal{Q}}_{ij}$ leads to an intrinsic nonlinear anomalous thermoelectric current. As an example, we calculate the nonlinear Nernst and Hall current in the loop-current model for cuprate superconductors, and demonstrate their unique behavior and capability of indicating $\mathbf{TI}$ invariance.

With a full set of experimentally obtained self- and interdiffusion coefficients, we are able to verify the relation between different transport coefficients in binary glass-forming Zr-Ni liquids. Despite a thermodynamic strong tendency of mixing, the interdiffusion is up to a factor of 2 slower than that predicted by the Darken equation. With the help of mode-coupling theory calculations, we identify that this is due to a slow, dominating kinetic contribution, arising from the dense packing of the melt, and the coupling of dynamics due to the strong Zr-Ni affinity. As a consequence, the cross correlation is on the order of 0.5 or less, whose contribution cannot be neglected, which seems to be a general feature of the glass-forming melts.

Using a combination of quantum Monte Carlo and exact methods, we study the field-driven saturation transition of the two-dimensional $J\text{−}Q$ model, in which the antiferromagnetic Heisenberg exchange $\left(J\right)$ coupling competes with an additional four-spin interaction $\left(Q\right)$ that favors valence-bond solid order. For small values of $Q$, the saturation transition is continuous and is expected to be governed by zero-scale-factor universality at its upper critical dimension, with a specific form of logarithmic corrections to scaling (first proposed by Sachdev et al. [Phys. Rev. B 50, 258 (1994)]). Our results conform to this expectation, but the logarithmic corrections to scaling do not match the form predicted by Sachdev et al. We also show that the saturation transition becomes first order above a critical coupling ratio ${(Q/J)}_{\min }$ and is accompanied by magnetization jumps—metamagnetism. We obtain an exact solution for ${(Q/J)}_{\min }$ using a high magnetization expansion, and confirm the existence of the magnetization jumps beyond this value of coupling using quantum Monte Carlo simulations.

Using Raman and infrared spectroscopies, spontaneous ferriquadrupolar ordering has been observed in the rare-earth-based system $\mathrm{KDy}{\left({\mathrm{MoO}}_4\right)}_2$. Ordered quadrupoles in the electron subsystem attend nonequivalent distortions of rare-earth ions in the ordered phase. A mean-field theory explaining the onset of such a type of ordering has been constructed.

Using a combination of neutron diffraction with XYZ polarization analysis and magnetization measurements, the noncollinear magnetism in nanosized cobalt chromite, a potential multiferroic material, is revealed. For noninteracting 26.9(1) nm nanoparticles, a bulklike behavior is identified, including a ferrimagnetic Curie temperature of 99 K and a transition to the spin spiral magnetic phase at 27 K with a temperature-dependent, incommensurate propagation vector. A lock-in transition towards a commensurate propagation vector is not observed. Much smaller, 3.1(2) nm, nanoparticles reveal a strong cluster glass behavior, characterized by ferrimagnetic behavior below the Curie temperature of 43 K and a transition to asperomagnetic behavior at 18 K, with the absence of any magnetic reflections at a base temperature of 5 K.

We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride, and transition-metal dichalcogenides based on Wannier transformation of ab initio density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration and are beyond the central force approximation which assumes only pairwise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our ab initio approaches complement the symmetry group representation construction for such effective low-energy Hamiltonians and provide the values of the coefficients for each symmetry-allowed term. These models are relevant for the design of electronic device applications since they provide the framework for describing the coupling of electrons to other degrees of freedom including phonons, spin, and the electromagnetic field. The models can also serve as the basis for exploring the physics of many-body systems of interesting quantum phases.

We introduce the concept of sparse stochastic compression, an efficient stochastic sampling of any general function. The technique uses sparse stochastic orbitals (SSOs), short vectors that sample a small number of space points. As a first demonstration, SSOs are applied in conjunction with simple direct projection to accelerate our recent stochastic $GW$ technique; the new developments enable accurate prediction of $G_0{W}_0$ quasiparticle energies and gaps for systems with up to $N_e>10,000$ electrons, with small statistical errors of $\pm 0.05\mathrm{eV}$ and using less than 2000 core CPU hours. Overall, stochastic $GW$ scales now linearly (and often sublinearly) with $N_e.$

An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved to be efficient and accurate. The approach can also be efficiently used when the constraint is not a scalar quantity but a spatially varying function such as the charge density distribution.

We present the electronic band structures of states with the same symmetry as the three-sublattice planar antiferromagnetic order of the triangular lattice. Such states can also be defined on the honeycomb lattice provided the spin density waves lie on the bonds. We identify cases which are consistent with observations on twisted bilayer graphene: a correlated insulator with an energy gap, yielding a single doubly degenerate Fermi surface upon hole doping. We also discuss extensions to metallic states which preserve spin-rotation invariance, with fluctuating spin density waves and bulk ${\mathbb{Z}}_2$ topological order.

We develop a theory of the direct interband and indirect intraband photogalvanic effects in Weyl semimetals belonging to the gyrotropic classes with improper symmetry operations. At zero magnetic field, an excitation of such a material with circularly polarized light leads to a photocurrent whose direction depends on the light helicity. We show that in the semimetals of the ${\mathrm{C}}_{2v}$ symmetry, an allowance for the tilt term in the effective Hamiltonian is enough to prevent cancellation of the photocurrent contributions from the Weyl cones of opposite chiralities. In the case of the ${\mathrm{C}}_{4v}$ symmetry, in addition to the tilt, it is necessary to include terms of the second- or third-order in the electron quasimomentum. For indirect intraband transitions, the helicity-dependent photocurrent generated within each Weyl node takes on a universal value determined by the fundamental constants, the light frequency and electric field. We have complementarily investigated the magneto-gyrotropic photogalvanic effect, i.e., an appearance of a photocurrent under unpolarized excitation in a magnetic field. In quantized magnetic fields, the photocurrent is caused by optical transitions between the one-dimensional magnetic subbands. A value of the photocurrent is particularly high if one of the photocarriers is excited to the chiral subband with the energy below the cyclotron energy.

This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. We extend a recently developed Fermi liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, $c_A$, describing its leading $\sim {\varepsilon }^2$ term, and the transport coefficients $c_V$ and $c_T$, describing the leading $\sim V^2$ and $\sim T^2$ terms in the nonlinear differential conductance. A sign change in $c_A$ or $c_V$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. We find that the fields $B_A$, $B_T$, and $B_V$ at which $c_A$, $c_T$, and $c_V$ change sign, respectively, are all of order $T_K$, as expected, with $B_A=B_T=B_V=0.75073T_K$ in the Kondo limit.

We studied the spin and valley transports and magnetoresistance effect in a ${\mathrm{MoS}}_2$ junction with a quantum well inserted between the gate voltage and the ferromagnetic ${\mathrm{MoS}}_2$, which can apply generally to other transition metal dichalcogenides with the same crystal structure. In the absence of a quantum well, the broken inversion symmetry and spin-orbit coupling for ${\mathrm{MoS}}_2$ could give rise to a fully spin- and valley-polarized conductance for the parallel configuration, while there is no spin and valley polarization for the antiparallel configuration. The general condition of pure polarization and the position of resonant conductance are achieved. The magnetoresistance is positive and oscillates with the gate voltage. Dramatically, the presence of a quantum well can lead to the formation of spin-polarized quantum well states. As a result, the conductances for opposite spin and valley indices have a steady phase shift, making them oscillate in antiphase with the well width. Therefore, the high spin and valley polarization could be obtained for the antiparallel and parallel configurations. In particular, the spin-polarized quantum well states directly result in negative polarization and negative magnetoresistance.

While double perovskites $A_{2}B{B}^{\prime }{\mathrm{O}}_6$, if ordered, usually form a rock-salt–type structure with a checkerboard $B\text{−}{B}^{\prime }$ ordering, it is surprising that ${\mathrm{Ca}}_2{\mathrm{FeMnO}}_6$ has alternate ${\mathrm{FeO}}_2$ and ${\mathrm{MnO}}_2$ layers in its perovskite structure. Here, by using density functional calculations, we demonstrate that this unusual layered ordering facilitates, and is largely helped by, the ${\mathrm{Fe}}^{3+}\text{−}{\mathrm{Fe}}^{5+}$ charge disproportionation (CD) of the formal ${\mathrm{Fe}}^{4+}$ ions, which would otherwise be frustrated in the common rock-salt structure. To further verify the important role of the CD for stabilization of this layered ordering, we carry out a comparative study for the isostructural ${\mathrm{Ca}}_2{\mathrm{TiMnO}}_6$ which has a simple ${\mathrm{Ti}}^{4+}\text{−}{\mathrm{Mn}}^{4+}$ state free of the CD. Our calculations indicate that ${\mathrm{Ca}}_2{\mathrm{TiMnO}}_6$ instead prefers the standard rock-salt structure to the layered one. Thus our study shows a nontrivial interplay between the CD and the type of ion ordering and proves that the CD is strongly involved in stabilizing the unusual layered order of ${\mathrm{Ca}}_2{\mathrm{FeMnO}}_6$.

We present the first-principles investigation of the structural, electronic, and magnetic properties of ${\mathrm{SrCoO}}_{3-\delta }$ ($\delta =0,0.25,0.5$) to understand the multivalent nature of Co ions in ${\mathrm{SrCoO}}_{3-\delta }$ along the line of topotactic transition between perovskite ${\mathrm{SrCoO}}_3$ and brownmillerite ${\mathrm{SrCoO}}_{2.5}$. From the onsite Coulomb interaction $U$-dependent ground state of stoichiometric ${\mathrm{SrCoO}}_3$, we show the proximity of its metallic ferromagnetic ground state to other antiferromagnetic states. The structural and magnetic properties of ${\mathrm{SrCoO}}_{3-\delta }$ depending on their oxygen content provide an interesting insight into the relationship between the Co-Co distances and the magnetic couplings so that the spin-state transition of Co spins can be understood by the change of $pd$ hybridization depending on the Co-Co distances. The strong suppression of the $dp\sigma$ hybridization between Co $d$ and O $p$ orbitals in brownmillerite ${\mathrm{SrCoO}}_{2.5}$ brings on the high-spin state of ${\mathrm{Co}}^{3+}{d}^6$ and is responsible for the antiferromagnetically ordered insulating ground state. The increase of effective Co-Co distances driven by the presence of oxygen vacancies in ${\mathrm{SrCoO}}_{3-\delta }$ is consistent with the reduction of the effective $pd$ hybridization between Co $d$ and O $p$ orbitals. We conclude that the configuration of neighboring Co spins is shown to be crucial to their local electronic structure near the metal-to-insulator transition along the line of the topotactic transition in ${\mathrm{SrCoO}}_{3-\delta }$. Incidentally, we also find that the I2mb symmetry of ${\mathrm{SrCoO}}_{2.5}$ is energetically stable and exhibits ferroelectricity via the ordering of ${\mathrm{CoO}}_4$ tetrahedra, where this polar lattice can be stabilized by the presence of a large activation barrier.

Physical systems evolve from one state to another along paths of least energy barrier. Without a priori knowledge of the energy landscape, multidimensional search methods aim to find such minimum energy pathways between the initial and final states of a kinetic process. However, in many cases, the user has to repeatedly provide initial guess paths, thus implying that the reliability of the final result is heavily user-dependent. Recently, the idea of “distortion symmetry groups” as a complete description of the symmetry of a path has been introduced. Through this, a new framework is enabled that provides a powerful means of classifying the infinite collection of possible pathways into a finite number of symmetry equivalent subsets, and then exploring each of these subsets systematically using rigorous group theoretical methods. The method, which we name the distortion symmetry method, is shown to lead to the discovery of previously hidden pathways for the case studies of bulk ferroelectric switching and domain wall motion in proper and improper ferroelectrics, as well as in multiferroic switching. These provide novel physical insights into the nucleation of switching pathways at experimentally observed domain walls in ${\mathrm{Ca}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$, as well as how polarization switching can proceed without reversing magnetization in ${\mathrm{BiFeO}}_3$. Furthermore, we demonstrate how symmetry-breaking from a highly symmetric pathway can be used to probe the non-Ising (Bloch and Néel) polarization components integral to transient states involved in switching in ${\mathrm{PbTiO}}_3$. The distortion symmetry method is applicable to a wide variety of physical phenomena ranging from structural, electronic and magnetic distortions, diffusion, and phase transitions in materials.

Metal halide perovskites exhibit a materials physics that is distinct from traditional semiconductors. While materials such as ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ are nonmagnetic, the presence of heavy elements (Pb and I) in a noncentrosymmetric crystal environment result in a spin splitting of the frontier electronic bands through the Rashba-Dresselhaus effect. We show, from a combination of ab initio molecular dynamics, density-functional theory, and quasiparticle $\mathit{GW}$ theory, that the nature (magnitude and orientation) of the band splitting depends on the local asymmetry around the Pb and I sites in the perovskite structure. The potential fluctuations vary in time as a result of thermal disorder. We show that the same physics emerges both for the organic-inorganic ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ and the inorganic ${\mathrm{CsPbI}}_3$ compound. The results are relevant to the photophysics of these compounds and are expected to be general to other lead iodide containing perovskites.

We theoretically study the electromagnetic response of type-I and type-II centrosymmetric Weyl metals. We derive an anisotropic permittivity tensor with off-diagonal elements to describe such gyrotropic media. Our findings reveal that for appropriate Weyl cones tilts, the real part of the transverse component of the permittivity can exhibit an $\epsilon$-near-zero response. The tilt parameter can also control the amount of loss in the medium, ranging from lossless to dissipative when transitioning from type-I to type-II. Similarly, by tuning either the frequency of the electromagnetic field or the chemical potential in the system, an $\epsilon$-near-zero response can appear as the permittivity of the Weyl semimetal transitions between positive and negative values. Employing the obtained permittivity tensor, we consider a setup where the Weyl semimetal is deposited on a perfect conductive substrate and study the refection and absorption characteristics of this nano-layered configuration. We show that by choosing the proper geometrical and material parameters, devices can be created that perfectly absorb electromagnetic energy over a wide angular range of incident electromagnetic waves.

We introduce a coupled wire model for a sequence of non-Abelian quantum Hall states that generalize the $Z_4$ parafermion Read-Rezayi state. The $Z_4$ orbifold quantum Hall states occur at filling factors $\nu =2/(2m-p)$ for odd integers $m$ and $p$, and have a topological order with a neutral sector characterized by the orbifold conformal field theory with central charge $c=1$ at radius $R=\sqrt{p/2}$. When $p=1$ the state is Abelian. The state with $p=3$ is the $Z_4$ Read-Rezayi state, and the series of $p\ge 3$ defines a sequence of non-Abelian states that resembles the Laughlin sequence. Our model is based on clustering of electrons in groups of four, and is formulated as a two fluid model in which each wire exhibits two phases: a weak clustered phase, where charge $e$ electrons coexist with charge $4e$ bosons and a strong clustered phase where the electrons are strongly bound in groups of four. The transition between these two phases on a wire is mapped to the critical point of the four-state clock model, which in turn is described by the orbifold conformal field theory. For an array of wires coupled in the presence of a perpendicular magnetic field, strongly clustered wires form a charge $4e$ bosonic Laughlin state with a chiral charge mode at the edge, but no neutral mode and a gap for single electrons. Coupled wires near the critical state form quantum Hall states with a gapless neutral mode described by the orbifold theory. The coupled wire approach allows us to employ the Abelian bosonization technique to fully analyze the physics of single wire, and then to extract most topological properties of the resulting non-Abelian quantum Hall states. These include the list of quasiparticles, their fusion rules, the correspondence between bulk quasiparticles and edge topological sectors, and most of the phases associated with quasiparticles winding one another.