We present a detailed micromagnetic study of the synchronization dynamics of two spin-torque nano-oscillators which are dynamically coupled by the emission of spin waves through an extended magnetic layer. We show that the intercontact distance and the wavelength of the emitted spin waves have a large impact on the possible synchronization states. Depending on the intercontact distance, there exist three different synchronization regions which can be characterized as in-phase and antiphase synchronization as well as a bistability region with both in-phase and antiphase synchronization. We demonstrate under which conditions bistability can be achieved and how the system can be switched from one to the other synchronization state. Finally, we develop a reduced semianalytical model which reproduces the simulation results and allows us to understand the physical origin of the bistability. It turns out that the bistability is caused by time-delay effects.

We present an approach based on colloidal epitaxy to obtain three-dimensional colloidal quasicrystals, i.e., structures with long-range order but no periodicity. In contrast to other attempts to obtain soft-matter quasicrystals by design, no fine tuning of the colloid-colloid interactions is required. By using Monte Carlo simulations, we explore the development of multiple layers with the desired quasicrystalline symmetry when the colloidal particles sediment onto suitable quasicrystalline substrates. In addition, well-defined defect lines can be induced in the grown colloidal quasicrystal by constructing substrates with well-chosen defects that lead to induced defect lines. We present a study of the three-dimensional course of such dislocation lines by inducing and analyzing stable lines that bend, unstable ones that split up, or defect lines that merge with other defects. Dislocations are characterized by Burgers vectors that are composed of a phononic part as in a periodic crystal and an additional phasonic part that is unique to quasicrystals. As in a periodic crystal, the sum of all Burgers vectors is conserved along defect lines and at all forks. However, unlike in a periodic crystal, the course of a dislocation line in a quasicrystal depends on its position. Furthermore, although in a quasicrystal all Burgers vectors can always be written as sum of Burgers vectors with a smaller phononic part, we find dislocations that do not decompose into dislocations with smaller phononic Burgers vectors. For quasicrystals with eightfold and twelvefold rotational symmetry, we identify basis Burgers vectors that denote stable dislocations. Our results can be verified in experiments and are important for applications of colloidal quasicrystals, e.g., for the development of photonic quasicrystals.

Cooperative Jahn-Teller ordering is well known to drive the cubic $Fd\overline{3}m$ to tetragonal $I{4}_1/amd$ structural distortion in ${\mathrm{Mn}}_3{\mathrm{O}}_4$ at $1170{}^{\circ }\mathrm{C}$. Further structural distortion occurs in ${\mathrm{Mn}}_3{\mathrm{O}}_4$ upon magnetic ordering at 42 K. Employing high-resolution variable-temperature synchrotron x-ray diffraction we show that tetragonal $I{4}_1/amd$ and orthorhombic $Fddd$ phases coexist with nearly equal fractions below the Néel temperature of ${\mathrm{Mn}}_3{\mathrm{O}}_4$. Significant variation in the orthorhombic $a$ and $b$ lattice constants from the tetragonal $a$ lattice constant is observed. Structural phase coexistence in ${\mathrm{Mn}}_3{\mathrm{O}}_4$ is attributed to large strains due to the lattice mismatch between the tetragonal $I{4}_1/amd$ and the orthorhombic $Fddd$ phases. Strain tensors determined from Rietveld refinement show a highly strained matrix of the $I{4}_1/amd$ phase that accommodates the nucleated orthorhombic $Fddd$ phase in the phase coexistence regime. A comparison of the deformation observed in ${\mathrm{Mn}}_3{\mathrm{O}}_4$ to structural deformations of other magnetic spinels shows that phase coexistence may be a common theme when structural distortions occur below 50 K.

We investigate the dynamical properties of the classical antiferromagnetic Heisenberg model on the kagome lattice using a combination of Monte Carlo and molecular dynamics simulations. We find that frustration induces a distribution of time scales in the cooperative paramagnetic regime (i.e., far above the onset of coplanarity), as recently reported experimentally in deuterium jarosite. At lower temperature, when the coplanar correlations are well established, we show that the weather-vane loop fluctuations control the system relaxation: the time distribution observed at higher temperatures splits into two distinct time scales associated with fluctuations in the plane and out of the plane of coplanarity. The temperature and wave-vector dependencies of these two components are qualitatively consistent with loops diffusing in the entropically dominated free energy landscape. Numerical results are discussed and compared with the $O\left(N\right)$ model and recent experiments for both classical and quantum realizations of the kagome magnets.

We study the Shannon and Rényi mutual information (MI) in the ground state (GS) of different critical quantum spin chains. Despite the apparent basis dependence of these quantities we show the existence of some particular basis (we will call them conformal basis) whose finite-size scaling function is related to the central charge $c$ of the underlying conformal field theory of the model. In particular, we verified that for large index $n$, the MI of a subsystem of size $\ell$ in a periodic chain with $L$ sites behaves as $\frac{c}{4}\frac{n}{n-1}ln[\frac{L}{\pi }sin\left(\frac{\pi \ell }{L}\right)]$, when the ground-state wave function is expressed in these special conformal basis. This is in agreement with recent predictions. For generic local basis, we will show that, although in some cases $b_{n}ln[\frac{L}{\pi }sin\left(\frac{\pi \ell }{L}\right)]$ is a good fit to our numerical data, in general, there is no direct relation between $b_n$ and the central charge of the system. We will support our findings with detailed numerical calculations for the transverse field Ising model, $Q=3,4$ quantum Potts chain, quantum Ashkin-Teller chain, and the XXZ quantum chain. We will also present some additional results of the Shannon mutual information ($n=1$), for the parafermionic $Z_Q$ quantum chains with $Q=5,6,7$, and 8.

Scanning photocurrent maps of gapless materials, such as graphene, often exhibit complex patterns of hot spots positioned far from current-collecting contacts. We develop a general formalism that helps to explain the unusual features of the observed patterns, such as the directional effect and the global character of photoresponse. We show that this behavior is captured by a simple Shockley-Ramo-type framework. We examine specific examples and show that the photoresponse patterns can serve as a powerful tool to extract information about symmetry breaking, inhomogeneity, chirality, and other local characteristics of the system.

Scanning tunneling microscopy (STM) and grazing-incidence x-ray diffraction (GIXD) have been used to follow in situ the growth and the structure of Au-Cu nanoparticles (NPs) formed on $\mathrm{Ti}{\mathrm{O}}_2$(110) by successive metal evaporations. STM observations of the same area of the substrate highlight the strong dependence between the sequence of deposition and the final result. Deposition of Cu first leads to a system where both Au-Cu and pure Au NPs coexist. Deposition of Au first ensures growing mostly bimetallic NPs. GIXD results show that Cu alloys instantaneously with Au NPs at room temperature. Similar observations during evaporation of Au on Cu NPs show that some of the Au atoms alloy with Cu whereas the rest remain at the NP shell. This is attributed both to kinetics and thermodynamics origins.

Starting from a three-dimensional Hamiltonian, we study the optical properties of ultrathin topological insulator slabs for which the coupling between Dirac fermions on opposite surfaces results in two degenerated gapped hyperbolic bands. The gap is a threshold for the optical absorption and translates in a peak in the imaginary part of the optical conductivity. An exchange field applied perpendicular to the slab splits the degenerated hyperbolic bands and a double step structure comes out in the optical absorption, whereas a double peak structure appears in the imaginary part of the longitudinal optical conductivity. The exchange field breaks time-reversal symmetry and for exchange fields larger than the surfaces coupling gap, the zero frequency Hall conductivity is quantized to $e^2/h$. This result implies large values of the Kerr rotation angle and a quantization of the Faraday angle. In ultrathin slabs, the absence of light multiple scattering and bulk conductivity makes the Kerr angle remain rather large in a wide range of frequencies.

Quantum gates for the manipulation of topological qubits rely on interactions between non-Abelian anyonic quasiparticles. We study the collective behavior of systems of anyons arising from such interactions. In particular, we study the effect of favoring different fusion channels of the screened Majorana spins appearing in the recently proposed topological Kondo effect. Based on the numerical solution of a chain of $SO{\left(5\right)}_2$ anyons we identify two critical phases whose low-energy behavior is characterized by conformal field theories with central charges $c=1$ and $c=8/7$, respectively. Our results are complemented by exact results for special values of the coupling constants which provide additional information about the corresponding phase transitions.

We shed light on the interplay between structure and many-body effects relevant for itinerant ferromagnetism in $\mathrm{La}\mathrm{Al}{\mathrm{O}}_3$/$\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ heterostructures. The realistic correlated electronic structure is studied by means of the (spin-polarized) charge self-consistent combination of density-functional theory with dynamical mean-field theory beyond the realm of static correlation effects. Though many-body behavior is also active in the defect-free interface, a ferromagnetic instability occurs only with oxygen vacancies. A minimal Ti two-orbital $e_g-t_{2g}$ description for the correlated subspace is derived. Magnetic order affected by quantum fluctuations builds up from effective double exchange between modified nearly localized $e_g$ and mobile $xy$ electrons.

In the continuum low-energy model, we calculate the one-loop dynamical polarization functions in ABC-stacked (rhombohedral) $n$-layer graphene in a magnetic field. Neglecting the trigonal warping effects, they are derived as functions of wave vector and frequency at finite chemical potential, temperature, band gap, and the width of Landau levels. The analytic results are given in terms of digamma functions and generalized Laguerre polynomials and have the form of double sums over Landau levels. Various particular limits for polarization functions (static, clean, etc.) are discussed. The intralayer and interlayer screened Coulomb potentials are numerically calculated as functions of momentum and frequency.

High-resolution atomic force microscopy (AFM) and scanning tunneling microscopy (STM) imaging with functionalized tips is well established, but a detailed understanding of the imaging mechanism is still missing. We present a numerical STM/AFM model, which takes into account the relaxation of the probe due to the tip-sample interaction. We demonstrate that the model is able to reproduce very well not only the experimental intra- and intermolecular contrasts, but also their evolution upon tip approach. At close distances, the simulations unveil a significant probe particle relaxation towards local minima of the interaction potential. This effect is responsible for the sharp submolecular resolution observed in AFM/STM experiments. In addition, we demonstrate that sharp apparent intermolecular bonds should not be interpreted as true hydrogen bonds, in the sense of representing areas of increased electron density. Instead, they represent the ridge between two minima of the potential energy landscape due to neighboring atoms.

First principles calculations are done for a $\sqrt{2}\times 4\times 2\sqrt{2} Pnma$ structure, which has been recently discussed in several attempts to describe experiments in complex magnetoelectric perovskites and which experimentally was shown to compete with several ferroelectric phases. This makes these materials extremely attracting as switchers, starters, field-stimulated capacitors, high-voltage converters, transmitters, etc. The relative energies of the $\sqrt{2}\times 4\times 2\sqrt{2} Pnma$ structure have been calculated from first principles and analyzed as a function of pressure in ${\mathrm{BiFeO}}_3$. The stability of two polymorphs of the $\sqrt{2}\times 4\times 2\sqrt{2} Pnma$ structure has been studied for solid solution ${\mathrm{BiFe}}_{1/2}{\mathrm{Sc}}_{1/2}{\mathrm{O}}_3$. The main distortions and relative energies of these two polymorphs in ${\mathrm{BiFe}}_{1/2}{\mathrm{Sc}}_{1/2}{\mathrm{O}}_3$, in terms of $Pm\overline{3}m$ parent symmetry, have been calculated from first principles as well.

We investigate the scattering and localization properties of edge and bulk states in a disordered two-dimensional topological insulator when they coexist at the same Fermi energy. Due to edge-bulk backscattering (which is not prohibited a priori by topology or symmetry), Anderson disorder makes the edge and bulk states localized indistinguishably. Two methods are proposed to effectively decouple them and to restore robust transport. The first kind of decouple is from long-range disorder since edge and bulk states are well separated in $k$ space. The second one is from an edge gating, owing to the edge nature of edge states in real space. The latter can be used to electrically tune a system between an Anderson insulator and a topologically robust conductor, i.e., a realization of a topological transistor.

We report the appearance of ferromagnetism in thin films of Pd(100), which depends on film thickness in the range of $3\text{–}5$ nm on ${\mathrm{SrTiO}}_3$(100) substrates. X-ray magnetic circular dichroism measurement shows the intrinsic nature of ferromagnetism in Pd(100) films. The spontaneous magnetization in Pd(100) films, corresponding to is $0.61{\mu }_B$/atom, is comparable to Ni, and it changes in an oscillatory manner depending on film thickness, where the period quantitatively agrees with the theoretical prediction based on the two-dimensional quantum well in the film. This indicates that the discrete electronic states in the quantum well shift to Fermi energy to satisfy the condition for ferromagnetism (Stoner criterion) at a specific film thickness.

We investigate the chiral magnetic order in freestanding planar $3d-5d$ biatomic metallic chains $(3d$: Fe, Co; $5d$: Ir, Pt, Au) using first-principles calculations based on density functional theory. We find that the antisymmetric exchange interaction, commonly known as the Dzyaloshinskii-Moriya interaction (DMI), contributes significantly to the energetics of the magnetic structure. For the Fe-Pt and Co-Pt chains, the DMI can compete with the isotropic Heisenberg-type exchange interaction and the magnetocrystalline anisotropy energy, and for both cases a homogeneous left-rotating cycloidal chiral spin-spiral with a wavelength of 51 Å and 36 Å, respectively, was found. The sign of the DMI, which determines the handedness of the magnetic structure, changes in the sequence of the $5d$ atoms $\mathrm{Ir}(+)$, $\mathrm{Pt}(-)$, $\mathrm{Au}(+)$. We use the full-potential linearized augmented plane wave method and perform self-consistent calculations of homogeneous spin spirals, calculating the DMI by treating the effect of spin-orbit interaction in the basis of the spin-spiral states in first-order perturbation theory. To gain insight into the DMI results of our ab initio calculations, we develop a minimal tight-binding model of three atoms and four orbitals that contains all essential features: the spin canting between the magnetic $3d$ atoms, the spin-orbit interaction at the $5d$ atoms, and the structure inversion asymmetry facilitated by the triangular geometry. We find that spin canting can lead to spin-orbit active eigenstates that split in energy due to the spin-orbit interaction at the $5d$ atom. We show that the sign and strength of the hybridization, the bonding or antibonding character between $d$ orbitals of the magnetic and nonmagnetic sites, the bandwidth, and the energy difference between occupied and unoccupied states of different spin projection determine the sign and strength of the DMI. The key features observed in the trimer model are also found in the first-principles results.

We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling dynamics in the form of a synthesized magnetic field for the photon-like excitations of the system allows the implementation of a parent Hamiltonian whose ground state is the Pfaffian wave function. Furthermore, we show that the addition of the next-nearest-neighbor tunneling stabilizes the ground state, recovering the expected topological degeneracy even for small lattices. Finally, we discuss the implementation of these ideas with the current technology.