Icosahedral quasicrystals (IQCs) with extremely high degrees of translational order have been produced in the laboratory and found in naturally occurring minerals, yet questions remain about how IQCs form. In particular, the fundamental question of how locally determined additions to a growing cluster can lead to the intricate long-range correlations in IQCs remains open. In answer to this question, we have developed an algorithm that is capable of producing a perfectly ordered IQC yet relies exclusively on local rules for sequential, face-to-face addition of tiles to a cluster. When the algorithm is seeded with a special type of cluster containing a defect, we find that growth is forced to infinity with high probability and that the resultant IQC has a vanishing density of defects. The geometric features underlying this algorithm can inform analyses of experimental systems and numerical models that generate highly ordered quasicrystals.

Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\langle \langle S_0^a{S}_1^a{S}_r^b{S}_{r+1}^b\rangle \rangle ={(-1)}^{r}d/\left(r{ln}^{\frac{3}{2}}r\right)+(3{\delta }_{a,b}-1){ln}^{2}r/\left(12{\pi }^4{r}^4\right)$, and estimate the numerical prefactor as $d\simeq 0.067$. The relevance of our results for ground-state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition points in one-dimensional systems is discussed at the end of our work.

We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a $4\times 4$ matrix and six types of $k$-independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and $d$ vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the interorbital attraction is dominant, an unconventional superconducting state with point nodes appears. To verify the experimental signature of possible superconducting states, we calculate the temperature dependence of bulk physical properties such as electronic specific heat and spin susceptibility and surface state. In the unconventional superconducting phase, either dispersive or flat Andreev bound states appear between point nodes, which leads to double peaks or a single peak in the surface density of states, respectively. As a result, possible superconducting states can be distinguished by combining bulk and surface measurements.

We propose a systematic magnetic-flux-free approach to detect, manipulate, and braid Majorana fermions in a semiconductor-nanowire-based topological Josephson junction by utilizing the Majorana spin degree of freedom. We find an intrinsic $\pi$-phase difference between spin-triplet pairings enforced by the Majorana zero modes (MZMs) at the two ends of a one-dimensional spinful topological superconductor. This $\pi$ phase is identified to be a spin-dependent superconducting phase, referred to as the spin phase, which we show to be tunable by controlling spin-orbit coupling strength via electric gates. This electric controllable spin phase not only affects the coupling energy between MZMs but also leads to a fractional Josephson effect in the absence of any applied magnetic flux, which enables the efficient topological qubit readout. We thus propose an all-electrically controlled superconductor-semiconductor hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding statistics properties. Our work on spin properties of topological Josephson effects potentially opens up a new thrust for spintronic applications with Majorana-based semiconductor quantum circuits.

Muon spin rotation measurements have been performed on a powder sample of $\alpha -{\mathrm{RuCl}}_3$, a layered material in which Ru ions are arranged on a honeycomb lattice and which previously has been proposed to be close to a quantum spin liquid ground state. Our data reveal two distinct transitions at 11 and 14 K, which we interpret as originating from the onset of three-dimensional order and in-plane magnetic order, respectively. We identify, with the help of density functional theory calculations, likely muon stopping sites and combine these with dipolar field calculations to show that the two measured muon rotation frequencies are consistent with two inequivalent muon sites within a zigzag antiferromagnetic structure proposed previously.

The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science, spanning the broadest wealth of research areas that range from quantum optics to living organisms. Focusing on nonequilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. We reveal the spin-transfer torque-driven parity-time symmetry-breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. Our findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.

We present a model for nonadiabatic classical molecular dynamics simulations that captures with high accuracy the wave-vector $q$ dependence of the phonon lifetimes, in agreement with quantum mechanics calculations. It is based on a local view of the $e$-ph interaction where individual atom dynamics couples to electrons via a damping term that is obtained as the low-velocity limit of the stopping power of a moving ion in a host. The model is parameter free, as its components are derived from ab initio-type calculations, is readily extended to the case of alloys, and is adequate for large-scale molecular dynamics computer simulations. We also show how this model removes some oversimplifications of the traditional ionic damped dynamics commonly used to describe situations beyond the Born-Oppenheimer approximation.

We have considered the effect of different spin-orbit interaction mechanisms on the process of demagnetization under the influence of short-pulse lasers. All-optical magnetization reversal of perpendicularly magnetized thin films can occur if there are sufficient strong spin-Hall, skew scattering, and Rashba interactions. In the presence of spin-orbit interactions, the transient charge currents provide the generation of transverse-spin currents and accumulations, which eventually exert spin-transfer torque on the magnetization. By combining the optically excited spin-dependent diffusive transport with the spin and charge currents due to skew scattering, spin-Hall, inverse spin-Hall, and Rashba interactions into a numerical model, we demonstrate a possibility of ultrafast all-optical magnetization reversal. This understanding provokes intriguing, more in-depth experimental studies on the role of spin-orbit interaction mechanisms in optimizing structures for all-optical magnetization reversal.

The local atomic environments and magnetic properties were investigated for a series of ${\mathrm{Co}}_{1+x}{\mathrm{Fe}}_{2-x}\mathrm{Si}$ $\left(0\le x\le 1\right)$ Heusler compounds. While the total magnetic moment in these compounds increases with the number of valance electrons, the highest Curie temperature $\left(T_C\right)$ in this series was found for ${\mathrm{Co}}_{1.5}{\mathrm{Fe}}_{1.5}\mathrm{Si}$, with a $T_C$ of 1069 K (24 K higher than the well-known ${\mathrm{Co}}_2\mathrm{FeSi})$. ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy was used to characterize the local atomic order and to estimate the Co and Fe magnetic moments. Consideration of the local magnetic moments and the exchange integrals is necessary to understand the trend in $T_C$.

The phase boundary between the quantum solid and the liquid phases of ${}^4\mathrm{He}$ is strongly modified in a porous material. However the phase diagram at very low temperatures remains unexplored. We have used a variable-volume experimental cell with optical access to visualize the crystallization of ${}^4\mathrm{He}$ in silica aerogels with independent control of the pressure and temperature. The onset of crystallization was investigated in two aerogel samples with differing porosity both by pressurization at constant temperature and by cooling at constant pressure. With isothermal pressurization we have established a low-temperature phase diagram for each aerogel, and we find that the equilibrium crystallization pressure is reduced with increasing aerogel porosity. Crystals also began to grow in the aerogel on cooling at fixed pressure below an onset temperature $T_{\mathrm{grow}}$. We found that below this temperature the crystallization rate increased with decreasing temperature. The aerogel in our cell was surrounded by bulk crystals of ${}^4\mathrm{He}$, and surprisingly $T_{\mathrm{grow}}$ was found to be widely distributed when the surrounding bulk crystals were repressurized. In this experimental arrangement, crystallization within the aerogel on cooling requires mass flow from these exterior bulk crystals and is strongly influenced by the disordered structure at the interface between the bulk solid and the helium within the aerogel.

We perform current ($I$)-voltage ($V$) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex depinning current, and a broad linear $I-V$ region with an extrapolated $I$ intercept equal to the depinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history-dependent dissipative force. This approach has not been considered previously, to our knowledge, yet it is crucial for obtaining a correct description of the vortex dynamics in superconducting arrays.

We revisit the problem of a BCS superconductor in the regime where the Fermi energy is smaller than the Debye energy. This regime is relevant for low-density superconductors such as ${\mathrm{SrTiO}}_3$ that are not in the BEC limit, as well as in the problem of “shape resonances” associated with the confinement of a three-dimensional superconductor. While the problem is not new, exact results were lacking in the low-density limit. In two dimensions, we find that the initial rise of the pairing temperature $T_c$ at low density $n$ is nonanalytic and faster than any power of $n$. In three dimensions, we also find that $T_c$ is nonanalytic, but starts with zero slope at weak coupling and infinite slope at strong coupling. Self-consistent treatment of the chemical potential and energy dependence of the density of states are crucial ingredients to obtain these results. We also present exact results for multiband systems and confirm our analytical expressions by numerical simulations.

Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the fractional quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich commensurate structures also emerge, at certain filling fractions, in high temperature superconductors and other electronic systems. A natural question concerns the character of these and other electronic systems at irrational filling fractions. Here we demonstrate that quasicrystalline structures naturally emerge in these situations, and trigger behaviors not typically expected of periodic systems. We first show that irrationally filled quantum Hall systems cross over into quasiperiodically ordered configuration in the thin-torus limit. Using known properties of quasicrystals, we argue that these states are unstable against the effects of disorder, in agreement with the existence of quantum Hall plateaux. We then study analogous physical situations in a system of cold Rydberg atoms placed on an optical lattice. Such an experimental setup is generally disorder free, and can therefore be used to detect the emergent quasicrystals we predict. We discuss similar situations in the Falicov-Kimball model, where known exact results can be used to establish quasicrystalline structures in one and two dimensions. We briefly speculate on possible relations between our theoretical findings and the existence of glassy dynamics and other features of strongly correlated electronic systems.

Using a combination of first-principles density functional theory (DFT) calculations and exact diagonalization studies of a first-principles derived model, we carry out a microscopic analysis of the magnetic properties of the half-metallic double perovskite compound ${\mathrm{Sr}}_2{\mathrm{CrMoO}}_6$, a sister compound of the much discussed material ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$. The electronic structure of ${\mathrm{Sr}}_2{\mathrm{CrMoO}}_6$, though appearing similar to ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ at first glance, shows nontrivial differences with that of ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ on closer examination. In this context, our study highlights the importance of charge transfer energy between the two transition metal sites. The change in charge transfer energy due to a shift of Cr $d$ states in ${\mathrm{Sr}}_2{\mathrm{CrMoO}}_6$ compared to Fe $d$ in ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ suppresses the hybridization between Cr $t_{2g}$ and Mo $t_{2g}$. This strongly weakens the hybridization-driven mechanism of magnetism discussed for ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$. Our study reveals that, nonetheless, the magnetic transition temperature of ${\mathrm{Sr}}_2{\mathrm{CrMoO}}_6$ remains high since an additional superexchange contribution to magnetism arises with a finite intrinsic moment developed at the Mo site. We further discuss the situation in comparison to another related double perovskite compound, ${\mathrm{Sr}}_2{\mathrm{CrWO}}_6$. We also examine the effect of correlation beyond DFT, using dynamical mean field theory.

Low-energy electron excitation spectra were measured on a single crystal of a typical iron-based superconductor ${\mathrm{PrFeAsO}}_{0.7}$ using resonant inelastic x-ray scattering (RIXS) at the $\mathrm{Fe}-L_3$ edge. Characteristic RIXS features are clearly observed around 0.5, 1–1.5, and 2–3 eV energy losses. These excitations are analyzed microscopically with theoretical calculations using a 22-orbital model derived from first-principles electronic structure calculation. Based on the agreement with the experiment, the RIXS features are assigned to Fe-$d$ orbital excitations which, at low energies, are accompanied by spin flipping and dominated by Fe $d_{yz}$ and $d_{xz}$ orbital characters. Furthermore, our calculations suggest dispersive momentum dependence of the RIXS excitations below 0.5 eV, and predict remarkable splitting and merging of the lower-energy excitations in momentum space. Those excitations, which were not observed in the present experiment, highlight the potential of RIXS with an improved energy resolution to unravel new details of the electronic structure of the iron-based superconductors.

We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B 89, 161306 (2014); Phys. Rev. B 93, 115318 (2016)] have found, for a resonant electronic level interacting with a thermal free-electron wide-band bath, that the expectation value for the energy of the interacting subsystem can be correctly calculated by considering a symmetric splitting of the interaction Hamiltonian between the subsystem and the bath. However, the general implications of this approach were questioned [Phys. Rev. B 92, 235440 (2015)]. Here, we show that, already at equilibrium, such splitting fails to describe the energy fluctuations, as measured here by the second and third central moments (namely, width and skewness) of the energy distribution. Furthermore, we find that when the wide-band approximation does not hold, no splitting of the system-bath interaction can describe the system thermodynamics. We conclude that in general no proper division subsystem of the Hamiltonian of the composite system can account for the energy distribution of the subsystem. This also implies that the thermodynamic effects due to local changes in the subsystem cannot in general be described by such splitting.

Strong Fermi-level pinning (FLP) near the valence-band maximum on $n$-type Ge surfaces has been a long-standing challenge in semiconductor physics, and the nature of this phenomenon has been heavily debated for years. Here, we report a systematic synchrotron-based photoemission study of atomically well-defined Ge(100) surfaces and interfaces to elucidate the origin of FLP in such systems. It is experimentally shown that the FLP on $n$-Ge is not due to the dangling-bond, back-bond, and defect states, but is strongly contributed by the evanescent state of the Ge bulk. The conditions required for alleviating the FLP and even the implementation of a flatband structure on Ge(100) are formulated. Such a structure is realized in the BaO/Ge(100) system where one can obtain control over the Fermi-level position in the Ge gap. These findings are not only important from a fundamental viewpoint, but also open a route to producing Ohmic metal-insulator-semiconductor contacts for $n$-type Ge-based technology.

Atomistic calculations of the electronic stopping power in liquid water for protons and α particles from first principles are demonstrated without relying on linear response theory. The computational approach is based on nonequilibrium simulation of the electronic response using real-time time-dependent density functional theory. By quantifying the velocity dependence of the steady-state charge of the projectile proton and α particle from nonequilibrium electron densities, we examine the extent to which linear response theory is applicable. We further assess the influence of the exchange-correlation approximation in real-time time-dependent density functional theory on the stopping power with range-separated and regular hybrid functionals with exact exchange.