We reveal how to exploit joint spatial-electromagnetic duality symmetries to obtain invariant scattering properties (including extinction, scattering, absorption) of self-dual scattering systems for incident waves of arbitrary polarizations. The electromagnetic duality ensures the helicity preservation along all scattering directions and thus intrinsically eliminates the interferences between the two scattering channels originating from the circularly polarized components of incident waves. This absence of interference directly secures invariant scattering properties for all polarizations located on the same latitude circle of the Poincaré sphere, which are characterized by polarization ellipses of the same eccentricity and handedness. Further incorporations of mirror and/or inversion symmetries would lead to such invariance throughout the whole Poincaré sphere, guaranteeing invariant scattering properties for all polarizations. Simultaneous exploitations of composite symmetries of different natures render an extra dimension of freedom for scattering manipulations, offering new insights for both fundamental explorations and optical device engineering related to symmetry-dictated light-matter interactions.

In the tight-binding description of electronic, photonic, or cold atomic dynamics in a periodic lattice potential, particle motion is described in terms of hopping amplitudes and potentials on an abstract network of discrete sites corresponding to physical orbitals in the lattice. The physical attributes of the orbitals, including their locations in three-dimensional space, are independent pieces of information. In this paper we identify a notion of geometry independence: any physical quantity or observable that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be “geometry independent.” The band structure itself and, for example, the Chern numbers of the bands in a two-dimensional system, are geometry independent, while the Bloch-band Berry curvature is geometry dependent. Careful identification of geometry dependent versus independent quantities can be used as a novel principle for constraining a variety of results. By extending the notion of geometry independence to certain classes of interacting systems, where the many-body energy gap is evidently geometry independent, we shed light on a hypothesized relation between many-body energy gaps of fractional Chern insulators and the uniformity of Bloch-band Berry curvature in the Brillouin zone. We furthermore explore the geometry dependence of semiclassical wave-packet dynamics, and use this principle to show how two different types of Hall response measurements may give markedly different results due to the fact that one is geometry dependent, while the other is geometry independent. Similar considerations apply for anomalous thermal Hall response, in both electronic and spin systems.

Herein, we introduce the framework of gauge-invariant variables to describe fractional quantum Hall (FQH) states, and prove that the wave function can always be represented by a unique holomorphic multivariable complex function. As a special case, within the lowest Landau level, this function reduces to the well-known holomorphic coordinate representation of wave functions in the symmetric gauge. Using this framework, we derive an analytic guiding center Schrödinger's equation governing FQH states; it has a novel structure. We show how the electronic interaction is parametrized by generalized pseudopotentials, which depend on the Landau level occupancy pattern; they reduce to the Haldane pseudopotentials when only one Landau level is considered. Our formulation is apt for incorporating a new combination of techniques, from symmetric functions, Galois theory and complex analysis, to accurately predict the physics of FQH states using first principles.

Optimally chiral electromagnetic fields with maximized helicity density, recently introduced by Hanifeh et al. [M. Hanifeh, M. Albooyeh, and F. Capolino, ACS Photonics 7, 2682 (2020)], enable chirality characterization of optically small nanoparticles. Here we demonstrate a technique to obtain optimally chiral near fields that leads to the maximization of helicity density under the constraint of constant energy density, beyond the diffraction limit. We show how optimally chiral illumination induces balanced electric and magnetic dipole moments in an achiral dielectric nanoantenna, which leads to generating optimally chiral scattered and total near fields. In particular, we explore helicity and energy densities in the near field of a spherical dielectric nanoantenna illuminated by an optimally chiral combination of azimuthally and radially polarized beams. This beam combination generates parallel induced electric and magnetic dipole moments in the nanoantenna that in turn generate an optimally chiral scattered field with the same helicity sign of the incident field. The application of helicity maximization to near fields results in helicity enhancement at the nanoscale, which is of great advantage in the detection of nanoscale chiral samples, microscopy, and optical manipulation of chiral nanoparticles.

Two-dimensional materials exhibit a variety of mechanical instabilities accompanied by spontaneous symmetry breaking. Here, we develop a continuum description of the buckling instability of antimonene sheets. Regions of oppositely directed buckling constitute domains separated by domain walls that are solitons in our model. Perturbations about equilibrium propagate as waves with a gapped dispersion in the bulk, but there is a gapless mode with linear dispersion that propagates along the domain walls in a manner reminiscent of the electronic modes of topological insulators. We establish that monolayer antimonene is a mechanical topological insulator by demonstrating a mapping between our continuum model and an underlying Dirac equation of the symmetry class BDI, which is known to be a topological insulator in one dimension and a weak topological insulator in two dimensions. Monolayer antimony can be produced by exfoliation as well as epitaxy, and the effects predicted in this paper should be accessible to standard experimental tools such as scanning probe microscopy and Raman spectroscopy. We surmise that the effects studied here (namely, low-scale symmetry breaking, strain solitons, and gapless edge modes) are not limited to antimonene but are common features of two-dimensional materials.

We study thermal fluctuations of freestanding bilayer graphene subject to vanishing external tension. Within a phenomenological theory, the system is described as a stack of two continuum crystalline membranes, characterized by finite elastic moduli and a nonzero bending rigidity. A nonlinear rotationally invariant model guided by elasticity theory is developed to describe interlayer interactions. After neglection of in-plane phonon nonlinearities and anharmonic interactions involving interlayer shear and compression modes, an effective theory for soft flexural fluctuations of the bilayer is constructed. The resulting model, neglecting anisotropic interactions, has the same form of a well-known effective theory for out-of-plane fluctuations in a single-layer membrane, but with a strongly wave-vector-dependent bare bending rigidity. Focusing on AB-stacked bilayer graphene, parameters governing interlayer interactions in the theory are derived by first-principles calculations. Statistical-mechanical properties of interacting flexural fluctuations are then calculated by a numerical iterative solution of field-theory integral equations within the self-consistent screening approximation. The bare bending rigidity in the considered model exhibits a crossover between a long-wavelength regime governed by in-plane elastic stress and a short wavelength region controlled by monolayer curvature stiffness. Interactions between flexural fluctuations drive a further crossover between a harmonic and a strong-coupling regime, characterized by anomalous scale invariance. The overlap and interplay between these two crossover behaviors is analyzed at varying temperatures.

Intricate topographical patterns can form on the surface of crystalline Ge(001) subject to low-energy ion irradiation in the reverse epitaxy regime, i.e., at elevated temperatures which enable dynamic recrystallization. We compare such nanoscale patterns produced by irradiation from varied polar and azimuthal ion incidence angles with corresponding calculated surface topographies. To this end, we propose a continuum equation including both anisotropic erosive and anisotropic diffusive effects. Molecular dynamics simulations provide the coefficients of angle-dependent sputter erosion for the calculations. By merely changing these coefficients accordingly, the experimentally observed surface morphologies can be reproduced, except for extreme ion incidence angles. Angle-dependent sputter erosion is thereby identified as a dominant mechanism in ion-induced pattern formation on crystalline surfaces under irradiation from off-normal incidence angles.

We propose a general and easy-to-use method of the ab initio calculation of the higher-order elastic constants, which is based on the analytical formulas for the deformation-gradient tensors as functions of the Lagrangian strain. The method allows for elimination of the truncation errors in the Taylor expansion series of the deformation gradients and is particularly useful to calculate the fourth-order elastic constants, where large strains have to be applied. It also facilitates the calculation of the Lagrangian stress, which is helpful in determination of the strain-stress relations. To demonstrate the application of our approach, we derive the analytic formulas for the deformation gradients as functions of the Lagrangian strain tensors, which are used in calculations of the third-order elastic constants in trigonal crystals and the fourth-order elastic constants in cubic crystals. Then, we perform the ab initio calculations of the fourth-order elastic constants in face-centered-cubic aluminum. We discuss the results obtained using the strain-energy and strain-stress relations and analyze the errors of the fourth-order elastic constants which would be incurred when approximating the deformation gradients by the Taylor polynomials. We show that the relatively small truncation errors in the Taylor expansion series of the deformation gradients can cause significant deviations of the fourth-order elastic constants. This effect is larger for the strain-energy method than for the strain-stress approach. We find that in both methods, the deviations are particularly significant for the $C_{1155}$, $C_{1266}$, $C_{4455}$, $C_{1255}$, and $C_{1456}$ elastic constants and are mainly caused by the truncation errors in the nondiagonal elements of the Taylor expansion series of the deformation gradients.

We present a combined theoretical and experimental study of solid-state spin decoherence in an electronic spin bath, focusing specifically on ensembles of nitrogen-vacancy (NV) centers in diamond and the associated substitutional nitrogen spin bath. We perform measurements of NV spin free-induction decay (FID) times $T_2^{*}$ and spin-echo coherence times $T_2$ in 25 diamond samples with nitrogen concentrations [N] ranging from 0.01 to 300 ppm. We introduce a microscopic model and perform numerical simulations to quantitatively explain the degradation of both $T_2^{*}$ and $T_2$ over four orders of magnitude in [N]. Our analysis enables us to describe the NV ensemble spin coherence decay shapes as emerging consistently from the contribution of many individual NV centers.

We perform ab initio calculations on ${\mathrm{Bi}}_{\mathrm{Se}}$ antisite defects in the surface of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, finding strong low-energy defect resonances with a spontaneous ferromagnetism, fixed to an out-of-plane orientation due to an exceptionally large magnetic anisotropy energy. For antisite defects in the surface layer, we find semi-itinerant ferromagnetism and strong hybridization with the Dirac surface state, generating a finite energy gap. For deeper lying defects, such hybridization is largely absent, the magnetic moments become more localized, and no energy gap is present.

We demonstrate that antiferromagnet-superconductor (AF-S) junctions show qualitatively different transport properties than normal metal–superconductor (N-S) and ferromagnet-superconductor (F-S) junctions. We attribute these transport features to the presence of two different scattering processes in AF-S junctions, i.e., specular reflection of holes and retroreflection of electrons. Using the Blonder-Tinkham-Klapwijk formalism, we find that the electrical and thermal conductances depend nontrivially on antiferromagnetic exchange strength, voltage, and temperature bias. Furthermore, we show that the interplay between the Néel vector direction and the interfacial Rashba spin-orbit coupling leads to a large anisotropic magnetoresistance. The unusual transport properties make AF-S interfaces unique among the traditional condensed-matter-system-based superconducting junctions.

The late-stage ordering of interacting magnetic skyrmions is studied numerically through extensive Langevin molecular dynamics simulations. Defining skyrmion displacements that change the connectivity of cells obtained in a Voronoi tesselation as events, we investigate event histograms as a function of the time elapsed since preparing the system as well as the histograms of consecutive events as a function of the time separating these two events. These histograms, which provide unique insights into the transient properties during the ordering process of skyrmion matter, show a characteristic behavior that allows the Magnus-force-dominated regime, where the Magnus force accelerates the relaxation process, to be distinguished from the noise-dominated regime, where the Magnus force enhances the effects of thermal noise. In the Magnus-force-dominated regime, the different histograms display power-law tails with exponents that depend on the strength of the Magnus force.

The magnetic proximity effect in top and bottom Pt layers induced by Co in Ta/Pt/Co/Pt multilayers has been studied by interface-sensitive, element-specific x-ray resonant magnetic reflectivity. The asymmetry ratio for circularly polarized x-rays of left and right helicity has been measured at the Pt $L_3$ absorption edge (11 567 eV) with an in-plane magnetic field ($\pm 158$ mT) to verify its magnetic origin. The proximity-induced magnetic moment in the bottom Pt layer decreases with the thickness of the Ta buffer layer. Grazing incidence x-ray diffraction has been carried out to show that the Ta buffer layer induces the growth of Pt(011) rather than Pt(111), which in turn reduces the induced moment. A detailed density functional theory study shows that an adjacent Co layer induces more magnetic moments in Pt(111) than in Pt(011). The manipulation of the magnetism in Pt by the insertion of a Ta buffer layer provides a way to control the magnetic proximity effect, which is of huge importance in spin-transport experiments across similar kinds of interfaces.

We study a spin-ice Kondo lattice model on a breathing pyrochlore lattice with classical localized spins. The highly efficient kernel polynomial expansion method, together with a classical Monte Carlo method, is employed in order to study the magnetic phase diagram at four representative values of the number density of itinerant electrons. We tune the breathing mode by varying the hopping ratio—the ratio of hopping parameters for itinerant electrons along inequivalent paths. Several interesting magnetic phases are stabilized in the phase diagram parameterized by the hopping ratio, Kondo coupling, and electronic filling fraction, including an “all-in/all-out” ordered spin configuration phase, spin-ice, ordered phases containing 16 and 32 spin sites in the magnetic unit cell, as well as a disordered phase at small values of the hopping ratio.

Recently, it has been proposed that higher-spin analogs of the Kitaev interactions $K>0$ may also occur in a number of materials with strong Hund's and spin-orbit coupling. In this work, we use Lanczos diagonalization and density matrix renormalization group methods to investigate numerically the $S=1$ Kitaev-Heisenberg model. The ground-state phase diagram and quantum phase transitions are investigated by employing local and nonlocal spin correlations. We identify two ordered phases at negative Heisenberg coupling $J<0$: a ferromagnetic phase with $\langle S_i^z{S}_{i+1}^z\rangle >0$ and an intermediate left-left-right-right phase with $\langle S_i^x{S}_{i+1}^x\rangle \ne 0$. A quantum spin liquid is stable near the Kitaev limit, while a topological Haldane phase is found for $J>0$.

The optical properties of a large, detwinned single crystal of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ have been examined over a wide frequency range above and below the structural and magnetic transition at $T_{\mathrm{N}}\simeq 138\mathrm{K}$. Above $T_{\mathrm{N}}$ the real part of the optical conductivity and the two infrared-active lattice modes are almost completely isotropic; the lattice modes show a weak polarization dependence just above $T_{\mathrm{N}}$. For $T<T_{\mathrm{N}}$, the optical conductivity due to the free-carrier response is anisotropic, being larger along the $a$ axis than the $b$ axis below $\simeq 30$ meV; above this energy the optical conductivity is dominated by the interband contributions, which appear to be isotropic. The splitting of the low-energy infrared-active mode below $T_{\mathrm{N}}$ is clearly observed, and the polarization modulation of the new modes may be used to estimate that the crystal is $\simeq 70\%$ detwinned. The high-frequency mode, with a threefold increase in strength of the lower branch below $T_{\mathrm{N}}$ and the nearly silent upper branch, remains enigmatic.

The effect of a hexagonal boron nitride (hBN) layer closely aligned with twisted bilayer graphene (TBG) is studied. At sufficiently low angles between twisted bilayer graphene and hBN, ${\theta }_{hBN}\lesssim 2^{\circ }$, the graphene electronic structure is strongly disturbed. The width of the low-energy peak in the density of states changes from $W\sim 5–10$ meV for a decoupled system to $\sim 20–30$ meV. Spikes in the density of states due to van Hove singularities are smoothed out. We find that for a realistic combination of the twist angle in the TBG and the twist angle between the hBN and the graphene layer the system can be described using a single moiré unit cell.

Copper monotelluride CuTe is of current interest due to the discovery of the quasi-one dimensional charge density wave (CDW) behavior below the transition temperature $T_{\mathrm{CDW}}\simeq 335\mathrm{K}$. To explore the transport and thermodynamic properties and provide experimental insights into the underlying origins of the CDW, we have carried out a combined study by means of the electrical resistivity, Seebeck coefficient, thermal conductivity, as well as specific heat measurements on single crystalline CuTe. The CDW phase transition has been characterized by marked features near $T_{\mathrm{CDW}}$ from all measured physical quantities. In particular, the observed Seebeck coefficient and electronic thermal conductivity exhibit a pronounced reduction as cooling the temperature across $T_{\mathrm{CDW}}$, indicative of the partially gapped Fermi surfaces associated with the CDW formation. From the examination of the excess specific heat in the vicinity of $T_{\mathrm{CDW}}$, we obtained evidence for the strong-coupling character of the CDW, suggesting that the electron-phonon coupling plays an important role for the CDW instability in CuTe.

${\mathrm{ZrTe}}_5$ is considered a potential candidate for either a Dirac semimetal or a topological insulator in close proximity to a topological phase transition. Recent optical conductivity results motivated a two-band model with a conical dispersion in 2D, in contrast to density-functional-theory calculations. Here, we reconcile the two by deriving a four-band model for ${\mathrm{ZrTe}}_5$ using $\mathbf{k}·\mathbf{p}$ theory, and fitting its parameters to the ab initio band structure. The optical conductivity with an adjusted electronic structure matches the key features of experimental data. The chemical potential varies strongly with temperature, to the point that it may cross the gap entirely between zero and room temperature. The temperature-dependent resistivity displays a broad peak and confirms theoretically the conclusions of recent experiments attributing the origin of the resistivity peak to the large shift of the chemical potential with temperature.