Aperiodic composite crystals belong to a new state of matter that possesses long-range order without translational symmetry. We report measurements of low-lying phonon branches in an $n$-alkane/urea compound that provide insight into the urea sublattice and the commensurate basal plane dynamics. Focusing on the thoroughly studied $n$-nonadecane/urea compound makes a comparison with other inelastic scattering results possible, allowing the observation of two distinct aperiodic elastic signatures. Using three techniques, a slight but reproducible difference in sound velocities is observed between the transverse mode propagating along the aperiodic direction and polarized in the commensurate basal plane, and the one polarized along the aperiodic direction propagating in the basal plane.

Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel-symmetry-breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with ${\mathrm{\Gamma }}_3$ non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic order necessarily breaks time-reversal symmetry, but the spatial arrangement of the hybridization spinor can be either uniform (ferrohastatic) or break additional lattice symmetries (antiferrohastatic). The experimental signatures of both orders are presented in detail, and include tiny conduction electron magnetic moments. Interestingly, there can be several distinct antiferrohastatic orders with the same moment pattern that break different lattice symmetries, revealing a potential experimental route to detect the spinorial nature of the hybridization. We employ an $\mathrm{SU}\left(N\right)$ fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields.

Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices is studied analytically and numerically. The disordered medium is composed of layers with alternating refractive indices and with thickness disorder distributed according to the Pareto distribution $\sim 1/x^{(\alpha +1)}$. In Levy lattices the variance (or both variance and mean) of a random parameter does not exist, which leads to a different functional form for the localization length. In this study an equation for the localization length is obtained, and it is found to be in excellent agreement with the numerical calculations throughout the spectrum. The explicit asymptotic equations for the localization lengths for both short and long wavelengths have been deduced. It is shown that the localization length tends to a constant at short wavelengths and it is determined by the layer interface Fresnel coefficient. At the long wavelengths the localization length is proportional to the power of the wavelength $\ell \sim {\lambda }^{\alpha }$ for $1<\alpha <2$, and it has a transcendental behavior $\ell \sim {\lambda }^2/ln\lambda$ for $\alpha =2$. For $\alpha >2$, where the variance of the random distribution exists, the localization length attains its classical long-wavelength asymptotic form $\ell \sim {\lambda }^2$.

We investigate the use of variational wave functions that mimic stochastic recurrent neural networks, specifically, unrestricted Boltzmann machines, as guiding functions in projective quantum Monte Carlo (PQMC) simulations of quantum spin models. As a preliminary step, we investigate the accuracy of such unrestricted neural network states as variational Ansätze for the ground state of the ferromagnetic quantum Ising chain. We find that by optimizing just three variational parameters, independently on the system size, accurate ground-state energies are obtained, comparable to those previously obtained using restricted Boltzmann machines with few variational parameters per spin. Chiefly, we show that if one uses optimized unrestricted neural network states as guiding functions for importance sampling, the efficiency of the PQMC algorithms is greatly enhanced, drastically reducing the most relevant systematic bias, namely, the one due to the finite random-walker population. The scaling of the computational cost with the system size changes from the exponential scaling characteristic of PQMC simulations performed without importance sampling, to a polynomial scaling, apparently even at the ferromagnetic quantum critical point. The important role of the protocol chosen to sample hidden-spin configurations, in particular at the critical point, is analyzed. We discuss the implications of these findings for what concerns the problem of simulating adiabatic quantum optimization using stochastic algorithms on classical computers.

We demonstrate that combining standing wave (SW) excitation with resonant inelastic x-ray scattering (RIXS) can lead to depth resolution and interface sensitivity for studying orbital and magnetic excitations in correlated oxide heterostructures. SW-RIXS has been applied to multilayer heterostructures consisting of a superconductor $\mathrm{L}{\mathrm{a}}_{1.85}\mathrm{S}{\mathrm{r}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$ (LSCO) and a half-metallic ferromagnet $\mathrm{L}{\mathrm{a}}_{0.67}\mathrm{S}{\mathrm{r}}_{0.33}\mathrm{Mn}{\mathrm{O}}_3$ (LSMO). Easily observable SW effects on the RIXS excitations were found in these LSCO/LSMO multilayers. In addition, we observe different depth distribution of the RIXS excitations. The magnetic excitations are found to arise from the LSCO/LSMO interfaces, and there is also a suggestion that one of the $dd$ excitations comes from the interfaces. SW-RIXS measurements of correlated-oxide and other multilayer heterostructures should provide unique layer-resolved insights concerning their orbital and magnetic excitations, as well as a challenge for RIXS theory to specifically deal with interface effects.

We analyze the robustness of topological order in the toric code in an open boundary setting in the presence of perturbations. The boundary conditions are introduced on a cylinder, and are classified into condensing and noncondensing classes depending on the behavior of the excitations at the boundary under perturbation. For the noncondensing class, we see that the topological order is more robust when compared to the case of periodic boundary conditions while in the condensing case topological order is lost as soon as the perturbation is turned on. In most cases, the robustness can be understood by the quantum phase diagram of a equivalent Ising model.

We show the resonant behavior of ∼0.5-THz longitudinal acoustic (LA) phonons in an acoustic nanocavity of thickness ∼28 nm sandwiched between two GaAs/AlAs superlattices (SLs). One of the SLs, upon excitation with an ultrafast optical pulse, acts as a source of coherent LA phonons. These phonons, generated outside the cavity, resonantly drive the cavity mode. The phonon dynamics can be modeled using a driven-damped harmonic oscillator. The confinement and enhancement of phonons in the acoustic nanocavity opens up possibilities in the field of nanophononics.

The Bott index is an index that discerns among pairs of unitary matrices that can or cannot be approximated by a pair of commuting unitary matrices. It has been successfully employed to describe the approximate integer quantization of the transverse conductance of a system described by a short-range, bounded, and spectrally gapped Hamiltonian on a lattice on a finite two-dimensional torus and to describe the invariant of the Bernevig-Hughes-Zhang model even with disorder. This paper shows the constancy in time of the Bott index and the Chern number related to the time-evolved Fermi projection of a system described by a short-range, bounded, and time-dependent Hamiltonian that is initially gapped. The general situation of a ramp of a time-dependent perturbation is considered, a section is dedicated to time-periodic perturbations.

Through first-principles calculations, we report on the phonon-limited transport properties of two-dimensional (2D) hexagonal MSe (M = Ge, Sn, and Pb) compounds, which can be seen as a new family of 2D group-IV selenides established by the isovalent substitutions of germanium and tellurium in layered ${\mathrm{Ge}}_4{\mathrm{Se}}_3\mathrm{Te}$ phase [Angew. Chem. Inter. Edit. 56 10204 (2017)]. We find that 2D PbSe exhibits low values of sound velocity (800–2030 m/s), large $\mathrm{Gr}\ddot{\mathrm{u}}\mathrm{neisen}$ parameters $\left(\sim 1.93\right)$, low-lying optical modes $\left(\sim 20.02{\mathrm{cm}}^{-1}\right)$, and strong optical-acoustic phonon coupling. These intrinsic properties mainly stem from strong phonon anharmonicity, which greatly suppress the phonon transport and therefore give rise to an ultralow thermal conductivity $\left(\sim 0.26\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}\right)$ for 2D PbSe at room temperature. Our studies may offer perspectives for applications of thermoelectricity and motivate further experimental efforts to synthesize MSe compounds.

We measure transport through a Ga[Al]As heterostructure at temperatures between $32\mathrm{mK}$ and $30\mathrm{K}$. Increasing the temperature enhances the electron-electron scattering rate and viscous effects in the two-dimensional electron gas arise. To probe this regime we measure so-called vicinity voltages and use a voltage-biased scanning tip to induce a movable local perturbation. We find that the scanning gate images differentiate reliably between the different regimes of electron transport. Our data are in good agreement with recent theories for interacting electron liquids in the ballistic and viscous regimes stimulated by measurements in graphene. However, the range of temperatures and densities where viscous effects are observable in Ga[Al]As are very distinct from the graphene material system.

We report the separate response of the critical temperature of the nematic phase transition $T_{\mathrm{S}}$ to symmetric and antisymmetric strains for the prototypical underdoped iron pnictide $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.975}{\mathrm{Co}}_{0.025}\right)}_2{\mathrm{As}}_2$. This decomposition is achieved by comparing the response of $T_{\mathrm{S}}$ to in-plane uniaxial stress and hydrostatic pressure. In addition to quantifying the two distinct linear responses to symmetric strains, we find a quadratic variation of $T_{\mathrm{S}}$ as a response to antisymmetric strains ${\varepsilon }_{{\mathrm{B}}_{1\mathrm{g}}}=\frac{1}{2}({\varepsilon }_{\mathrm{xx}}-{\varepsilon }_{\mathrm{yy}})$, exceeding the nonlinear response to symmetric strains by at least two orders of magnitude. These observations establish orthogonal antisymmetric strain as a powerful tuning parameter for nematic order.

One-dimensional systems with topological order are intimately related to the appearance of zero-energy modes localized on their boundaries. The most common example is the Kitaev chain, which displays Majorana zero-energy modes and it is characterized by a twofold ground-state degeneracy related to the global ${\mathbb{Z}}_2$ symmetry associated with fermionic parity. By extending the symmetry to the ${\mathbb{Z}}_N$ group, it is possible to engineer systems hosting topological parafermionic modes. In this work, we address one-dimensional systems with a generic discrete symmetry group $G$. We define a ladder model of gauge fluxes that generalizes the Ising and Potts models and displays a symmetry broken phase. Through a non-Abelian Jordan-Wigner transformation, we map this flux ladder into a model of dyonic operators, defined by the group elements and irreducible representations of $G$. We show that the so-obtained dyonic model has topological order, with zero-energy modes localized at its boundary. These dyonic zero-energy modes are in general weak topological modes, but strong dyonic zero modes appear when suitable position-dependent couplings are considered.

We provide detailed comparisons between experimental findings and numerical simulations of large cooperatively interacting, spatially disordered metamaterial arrays, consisting of asymmetrically split rings. Simulation methods fully incorporate strong field-mediated inter-meta-atom interactions between discrete resonators and statistical properties of disorder, while approximating the resonators' internal structure. Despite the large system size, we find a qualitative agreement between the simulations and experiments and characterize the microscopic origins of the observed disorder response. Our microscopic description of macroscopic electrodynamics reveals how the response of disordered arrays with strong field-mediated interactions is inherently linked to their cooperative response to electromagnetic waves where the multiple scattering induces strong correlations between the excitations of individual resonators. Whereas for a regular array the response can be overwhelmingly dominated by a spatially extended collective eigenmode with subradiant characteristics, a gradual increase of the positional disorder rapidly leads to a spatial localization of both the electric and magnetic dipolar excitation profile of this eigenmode. We show how the effects of disorder and cooperative interactions are mapped onto the transmission resonance in the far field spectrum and measure the “cooperative Lamb shift” of the resonance that is shifting toward the red as the disorder increases. The interplay between the disorder and interactions generally is most dramatic in the microwave arrays, but we find that in suitable regimes the strong disorder effects can be achieved also for plasmonic optical systems.

The high-throughput screening of periodic inorganic solids using machine learning methods requires atomic positions to encode structural and compositional details into appropriate material descriptors. These atomic positions are not available a priori for new materials, which severely limits exploration of novel materials. We overcome this limitation by using only crystallographic symmetry information in the structural description of materials. We show that for materials with identical structural symmetry, machine learning is trivial, and accuracies similar to that of density functional theory calculations can be achieved by using only atomic numbers in the material description. For machine learning of formation energies of bulk crystalline solids, this simple material descriptor is able to achieve prediction mean absolute errors of only 0.07 eV/at on a test dataset consisting of more than 85 000 diverse materials. This atomic-position independent material descriptor presents a new route of materials discovery wherein millions of materials can be screened by training a machine learning model over a drastically reduced subspace of materials.

In this study, we examine the thermodynamics and spin dynamics of spin-1/2 and spin-3/2 heptamers. Through an exact diagonalization of the isotropic Heisenberg Hamiltonian, we find the closed-form, analytical representations for thermodynamic properties, spin excitations, and neutron-scattering structure factors. Furthermore, we investigate the clusterlike excitations of quantum spin heptamer in the three-dimensional pyrochlore lattice material ${\mathrm{MgCr}}_2{\mathrm{O}}_4$. Using a spin mapping of the spin-1/2 heptamer excitations, the calculated structure factors of the spin-3/2 heptamer are to be determined, which provides clarification for the spin excitations in ${\mathrm{MgCr}}_2{\mathrm{O}}_4$. Overall, this study demonstrates the ability to use the spin mapping of structure factors for small spin systems to analyze more complex structures.

Following our previous results, which provide evidence for the emergence of a chiral p-wave triplet-pairing component in superconducting Nb upon the adsorption of chiral molecules, we turned to investigate whether such an effect can take place in a proximal superconductor consisting of metal on superconductor bilayer. Note that in such proximity systems, correlated electron-hole (Andreev) pairs exist in the normal metal rather than genuine Cooper pairs. To that end, we used scanning tunneling spectroscopy (STS) on thin Au films grown in-situ on NbN (a conventional s-wave superconductor) before and after adsorbing helical chiral, alpha-helix polyalanine molecules. The tunneling spectra measured on the pristine Au surface showed conventional (s-wave like) proximity gaps. However, upon molecules adsorption the spectra significantly changed, all exhibiting a zero-bias conductance peak embedded inside a gap, indicating unconventional superconductivity. The peak reduced with magnetic field but did not split, consistent with equal-spin triplet-pairing p-wave symmetry. In contrast, adsorption of nonhelical chiral cysteine molecules did not yield any apparent change in the order parameter, and the tunneling spectra exhibited only gaps free of in-gap structure.

We present the results of broadband dielectric spectroscopy of $\mathrm{GaM}{\mathrm{o}}_4{\mathrm{S}}_8$, a lacunar spinel system that recently was shown to exhibit non canonical, orbitally driven ferroelectricity. Our study reveals complex relaxation dynamics of this multiferroic material, both above and below its Jahn-Teller transition at $T_{\mathrm{JT}}=47\mathrm{K}$. Above $T_{\mathrm{JT}}$, two types of coupled dipolar-orbital dynamics seem to compete: relaxations within cluster-like regions with short-range polar order as in relaxor ferroelectrics and critical fluctuations of only weakly interacting dipoles, the latter resembling the typical dynamics of order-disorder type ferroelectrics. Below the Jahn-Teller transition, the onset of orbital order drives the system into long-range ferroelectric order and dipolar dynamics within the ferroelectric domains is observed. The coupled dipolar and orbital relaxation behavior of $\mathrm{GaM}{\mathrm{o}}_4{\mathrm{S}}_8$ above the Jahn-Teller transition markedly differs from that of the skyrmion host $\mathrm{Ga}{\mathrm{V}}_4{\mathrm{S}}_8$, which seems to be linked to differences in the structural distortions of the two systems on the unit-cell level.

Quantum phases of matter have many relevant applications in quantum computation and quantum information processing. Current experimental feasibilities in diverse platforms allow us to couple two or more subsystems in different phases. In this paper, we investigate the situation in which one couples two domains of a periodically driven lattice of interacting particles, where one of them is ergodic while the other is fully localized. By combining tools of both graph and Floquet theory, we show that the localized domain remains stable for strong disorder, but as this disorder decreases, the localized domain becomes ergodic.

Here, we resolve the nature of the moment coupling between 10-nm dimercaptosuccinic acid–coated magnetic nanoparticles. The individual iron oxide cores were composed of $>95\%$ maghemite and agglomerated to clusters. At room temperature the ensemble behaved as a superparamagnet according to Mössbauer and magnetization measurements, however, with clear signs of dipolar interactions. Analysis of temperature-dependent ac susceptibility data in the superparamagnetic regime indicates a tendency for dipolar-coupled anticorrelations of the core moments within the clusters. To resolve the directional correlations between the particle moments we performed polarized small-angle neutron scattering and determined the magnetic spin-flip cross section of the powder in low magnetic field at 300 K. We extract the underlying magnetic correlation function of the magnetization vector field by an indirect Fourier transform of the cross section. The correlation function suggests nonstochastic preferential alignment between neighboring moments despite thermal fluctuations, with anticorrelations clearly dominating for next-nearest moments. These tendencies are confirmed by Monte Carlo simulations of such core clusters.