Results regarding spin glass models are, to this day, mainly confined to models with discrete (usually Ising) spins. Spin glass models with continuous spins exhibit interesting new physical behaviors related to the additional degrees of freedom, but have been primarily studied on fully connected topologies. Only recently some advancements have been made in the study of continuous models on sparse graphs. In this work we partially fill this void by introducing a method to solve numerically the belief propagation equations for systems of Heisenberg spins on sparse random graphs via a discretization of the sphere. We introduce techniques to study the finite-temperature, finite-connectivity case as well as algorithms to deal with the zero-temperature and large-connectivity limits. As an application, we locate the de Almeida–Thouless line for this class of models and the critical field at zero temperature, showing the full consistency of the methods presented. Beyond the specific results reported for Heisenberg models, the approaches presented in this paper have a much broader scope of application and pave the way to the solution of strongly disordered models with continuous variables.

The results of extensive combined experimental and theoretical investigations of static and dynamic properties of an Ir/Co/Pt multilayer with low uniaxial anisotropy and asymmetric Ir/Co and Co/Pt interfaces responsible for large interfacial Dzyaloshinskii-Moriya interaction (IDMI) are presented. Within longitudinal magneto-optical Kerr effect-based microscopy and magnetic force microscopy studies a complex magnetic configuration was detected: Large in-plane magnetized domains several dozen micrometers in size were modulated by a weak stripe domain pattern with periods of about 100 nm. Using Brillouin light scattering spectrometry, the hysteresis of the Stokes and anti-Stokes peaks frequencies was observed as a function of the magnetic field. This hysteretic behavior associated with IDMI-induced asymmetry of spin wave dispersion is correlated with the switching of the large macrodomains. Using micromagnetic simulations, we determine field-dependent magnetization distributions and dispersion relations, proposing an explanation of the observed behavior. The investigated nanostructure can be used as a nonvolatile spin wave velocity switcher.

We report the magnetic properties of $\mathrm{CaC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$ as a Kitaev candidate. $\mathrm{CaC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$ was synthesized through a topochemical process, wherein all $\mathrm{N}{\mathrm{a}}^{+}$ ions in $\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$ were replaced with half the amount of $\mathrm{C}{\mathrm{a}}^{2+}$ ions. This substitution brings the $\mathrm{Co}{\mathrm{O}}_6$ octahedra closer to an approximate cubic symmetry. $\mathrm{CaC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$ exhibits antiferromagnetic ordering at $T_{\mathrm{N}}\sim 13$ K, which is lower than ∼27 K observed for $\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$. Notably, its magnetic order is suppressed in a relatively low magnetic field of approximately 4 T, indicating that non-Kitaev interactions can be restrained by reducing trigonal distortion. Our findings highlight the potential of $\mathrm{CaC}{\mathrm{o}}_2\mathrm{Te}{\mathrm{O}}_6$ as a viable platform for exploring Kitaev quantum spin liquids, and they pave the way for a deeper understanding of the fundamental mechanisms in Kitaev physics.

We present the results of microscopic investigations of antiferromagnetic ${\mathrm{CeNiGe}}_3$ using neutron powder diffraction (NPD), inelastic neutron scattering (INS), and muon spin relaxation ($\mu \mathrm{SR}$) measurements. ${\mathrm{CeNiGe}}_3$ crystallizes in a centrosymmetric orthorhombic crystal structure (space group $Cmmm$) and undergoes antiferromagnetic (AFM) ordering. The occurrence of long-range AFM ordering at $T_{\mathrm{N}}\simeq 5.2\mathrm{K}$ is confirmed by magnetic susceptibility, heat capacity, neutron diffraction, and $\mu \mathrm{SR}$ measurements. The NPD data characterize the AFM state with an incommensurate helical magnetic structure having a propagation vector k = (0, 0.41, 1/2). In addition, INS measurements at 10 K identified two crystal electric field (CEF) excitations at 9.17 meV and 18.42 meV. We analyzed the INS data using a CEF model for an orthorhombic environment of ${\mathrm{Ce}}^{3+}$ ($J=5/2$) and determined the CEF parameters and ground state wave functions of ${\mathrm{CeNiGe}}_3$. Moreover, zero-field $\mu \mathrm{SR}$ data for ${\mathrm{CeNiGe}}_3$ at $T<T_{\mathrm{N}}$ show long-range AFM ordering with three distinct oscillation frequencies corresponding to three different internal fields at the muon sites. The internal fields at the muon-stopping sites have been further investigated using density functional theory calculations.

We theoretically demonstrate that in a nonhysteretic Josephson junction (JJ) with a $2\pi$ periodic supercurrent in the presence of radio-frequency (RF) radiation one or several low-lying Shapiro steps could be absent in the voltage-current $\left(VI\right)$ characteristic. The effect exists at low RF power and at frequencies $f$ approximately ten times smaller than $f_0=I_c{R}_N/{\mathrm{\Phi }}_0$ (where $I_c$ is the critical current, $R_N$ is the normal-state resistance of the Josephson junction, and ${\mathrm{\Phi }}_0$ is the magnetic flux quantum). The origin of the effect is related to the large differential resistance $R_{\mathrm{diff}}=dV/dI$ near $I\simeq I_c$, which is significantly greater than the value predicted by the resistively capacitance shunted junction (RCSJ) model in the overdamped limit. Our theoretical results are supported by experiments on Nb/NbSi/Nb Josephson junctions with nonhysteretic $VI$ curves, where we observe the absence of one or more low-lying Shapiro steps, depending on the frequency and power of the RF radiation.

J. E. Hirsch and F. Marsiglio in their publication [Phys. Rev. B 103, 134505 (2021)], assert that hydrogen-rich compounds under high pressures do not exhibit superconductivity. Their argument hinges on the absence of broadening of resistive superconducting transitions in applied magnetic fields. We argue that this assertion is incorrect, as it relies on a flawed analysis and a selective and inaccurate report of published data, where data supporting the authors’ perspective are highlighted while data demonstrating clear broadening are disregarded.

In our paper [Phys. Rev. B 103, 134505 (2021)] we surveyed the known hydride superconductors, and compared their resistive behavior to that of typical known superconductors, including conventional (e.g., NbN and ${\mathrm{MgB}}_2$) and unconventional (e.g., YBCO) superconductors, and concluded that the behavior of the hydrides was indicative of nonstandard or no superconductivity. In the preceding Comment, Talantsev, Minkov, Balakirev, and Eremets claim that we presented a “flawed analysis and a selective and inaccurate report of published data.” Here, we show that this claim is wrong.

We study two-dimensional systems with Galilean invariance gapped under magnetic fields. When such quantum Hall systems are coupled with external sources for charge, energy, and momentum currents, they exhibit invariance under the Milne boost as well as under the gauge and general coordinate transformations. We construct the most general effective action consistent with all the symmetries in the derivative expansion, where an electric field is regarded as order of unity so as to allow for nonlinear responses. The resulting action is shown to consist of four terms proportional to the Hall conductivity and viscosity and the energy density and magnetization. We then compute the local currents induced by electromagnetic fields, revealing universal relations among distinct kinds of responses. In particular, we find the Hall conductivity determining the longitudinal conductivity at nonzero frequency and the Hall viscosity contributing to the nonlinear electrothermal conductivity at nonzero wave number.

The one-dimensional $p$-wave superconductor, characterized by boundary Majorana modes, has attracted significant interest owing to its potential application in topological quantum computation. Similarly, spin-1/2 Kitaev ladder systems with bond-dependent Ising interactions, featuring Majorana fermions coupled with $Z_2$ flux, exhibit boundary Majorana modes when in a topological phase. However, the ground-state degeneracy, inherent in these systems, may result in the annihilation of Majorana modes due to the superposition of the degenerate states. To avoid this issue, here we introduce a projective measurement that selects one of the degenerate $Z_2$ sectors, enabling the revival of Majorana modes. Once the state is selected, we show that the application of the local spin operators on a bond flips the sign of the adjacent $Z_2$ flux. Repeating such operators enables the system to reach a desired $Z_2$ flux configuration. The Majorana zero modes can be manipulated and fused by tuning the flux sectors achievable through applying local spin operators. We also discuss the engineering of the Kitaev ladder and open questions for future studies.

Chiral anomaly engineering has been established as one of the mechanisms for achieving energy efficient dissipationless transport. Here we show how to design tunable chiral anomalies in a honeycomb lattice free of any magnetic fields. By applying an external electric field to a flat band material with a broken inversion symmetry, we generate electronic modes exhibiting chiral anomalies capable of disorder resilient transport in the bulk of the material. As the electric field increases, the system exhibits an unusual cubic-like dispersion. By providing a performance comparable to other honeycomb lattice-based ballistic conductors such as armchair nanotube, zigzag nanoribbon and hypothetical cumulenic carbyne, this scheme opens a new research avenue for the design of energy efficient information processing and higher-order dispersion materials.

The precise direction of the off-cut of a vicinal crystal surface determines the azimuth (in-plane angle) of the surface steps and thus their kink density. Here we develop a Burton-Cabrera-Frank (BCF) theory for step-flow crystal growth that includes the effects of step azimuth. We focus on the basal-plane surfaces of hexagonal close-packed (hcp) and related crystal structures, for which surface steps have alternating properties that depend on azimuth. We build on a previous treatment that considered only a single-step azimuth, $\varphi =0$, that gives alternating steps of pure A and B type. As $\varphi$ increases from zero, the density of kinks on the steps increases. For hcp-type crystals, in addition the structural difference between alternating steps decreases, until they become equivalent at $\varphi ={30}^{\circ }$. We consider the azimuth dependence of the step transparency, attachment, and repulsion parameters of the BCF model, including the effects of both geometrically required and thermally generated kinks. Example calculations are presented that demonstrate the overall effect of step azimuth on BCF predictions for step spacings during steady-state growth and for their dynamics during growth transients. Effects of symmetric and asymmetric step-step repulsion are discussed.

Confining charge carriers of materials into a geometrical configuration is expected to destabilize their intrinsic ground electronic states. Especially for the many-body interacting systems, understanding the underlying physics of quantum confined behaviors at the atomic scale is critical for the advancement of nanoscience and nanotechnology. Here we report scanning tunneling microscopy experiments on anomalous quantum confinement effects in triangularlike nanostructures of monolayer $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$, a prototypical two-dimensional (2D) charge-density-wave (CDW) metal, as well as their modulation by substrate engineering. Domain boundaries usually appear in monolayer $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ nanostructures as they are directly placed onto graphene, while they are absent with insertion of a metallic $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ or insulating $T\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ monolayer. Moreover, both $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ and $T\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ substrates can effectively induce striped charge states in $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ nanostructures. Our spectroscopic measurements further reveal unique electron confinements in monolayer $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ nanostructures on $H\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ substrates, where the confined electrons can be visualized either along the nanostructure edges or within the nanostructures, dependent on the electron energies. Our results provide a fruitful playground for investigating the intertwined quantum confinement effects in CDW nanostructures under the 2D limit.

The residual entropy of ice systems has long been a significant and intriguing issue in condensed-matter physics and statistical mechanics. Exact solutions for the residual entropy of realistic three-dimensional ice systems remain unknown. This study focuses on two typical realistic ice systems: hexagonal ice (ice Ih) and cubic ice (ice Ic). We present a transfer-matrix description of the number of ice-ruled configurations for these systems. A transfer matrix $\mathbf{M}$ is constructed for ice Ic, where each element represents the number of ice-ruled configurations of a hexagonal monolayer under certain conditions. The product of $\mathbf{M}$ and its transpose corresponds to a bilayer unit in the ice Ih lattice, thus forming an exact transfer matrix for ice Ih. Utilizing this, we show that the residual entropy of ice Ih is not less than that of ice Ic in the thermodynamic limit, first proved by Onsager in the 1960s. Additionally, we introduce an alternative transfer matrix ${\mathbf{M}}^{\prime }$ for ice Ih based on a monolayer periodic unit. Various interesting properties of $\mathbf{M}$, ${\mathbf{MM}}^T$, and ${\mathbf{M}}^{\prime }$ are analyzed, including the summation of all elements, the element in the first row and first column, and the trace. Each property corresponds to the residual entropy of a certain two-dimensional ice model. This work provides an effective description, based on transfer matrices, for the residual entropies of various two-dimensional ice models.

Voltage is a sensitive quantity to quantum interference in coherent electronic transport. We study the voltage fluctuations in disordered graphene nanoribbons with zigzag and armchair edge terminations in a four-terminal configuration. We show that the average and standard deviation of the voltage oscillates with the separation of the attached voltage probes and depend on the coupling strength of the probes. The voltage fluctuations can be large enough to observe negative voltages for weakly coupled probes. As we numerically verified, the voltage fluctuations are described within a random matrix approach for weakly disordered nanoribbons at energies away from the Fermi energy. However, near the Fermi energy, zigzag nanoribbons exhibit Anderson localization, whereas electrons are anomalously localized in armchair nanoribbons. This distinction leads to different voltage statistics for zigzag and armchair nanoribbons.

We present a thorough study of the complexity of optical localized modes in two-dimensional disordered photonic crystals. Direct experimental measurements of complexity were made using an interferometric setup that allowed for the extraction of phases and hence complex-valued wave functions. The comparison of experimental and theoretical results allows us to propose a metric for Anderson localization based on the average value and statistical distribution of complexity. Being an alternative to other known criteria of localization, the proposed metric exploits the openness of the disordered medium and provides a quantitative characterization of the degree of localization allowing for determining the localization length.

We study the spectral properties of the adjacency matrix in the giant connected component of Erdös-Rényi random graphs, with average degree $p$ and randomly distributed hopping amplitudes. By solving the self-consistent cavity equations satisfied by the matrix elements of the resolvent, we compute the probability distribution of the local density of states, which governs the scaling with the system size of the moments of the eigenvectors' amplitudes, as well as several other observables related to the spectral statistics. For small values of $p>1$ above the percolation threshold, we unveil the presence of an exotic delocalized but (weakly) multifractal phase in a broad region of parameter space, which separates the localized phase found for $p\le 1$ from the fully delocalized and Gaussian orthogonal ensemble-like phase expected for $p\to \infty$. We explore the fundamental physical mechanism underlying the emergence of delocalized multifractal states, rooted in the pronounced heterogeneity in the topology of the graph. This heterogeneity arises from the interplay between strong fluctuations in local degrees and hopping amplitudes, and leads to an effective fragmentation of the graph. We further support our findings by characterizing the level statistics and the two-point spatial correlations within the multifractal phase, and address the ensuing anomalous transport and relaxation properties affecting the quantum dynamical evolution.

The frustration-induced interplay of competing degrees of freedom and quantum fluctuations can evade long-range magnetic ordering and result in novel quantum states with exotic fractionalized excitations. Herein, a comprehensive investigation of $\mathrm{YbTa}{\mathrm{O}}_4$ is carried out, where the magnetic $\mathrm{Y}{\mathrm{b}}^{3+}$ ions form a quasi-two-dimensional deformed square lattice. Our studies reveal the absence of long-range magnetic ordering and spin freezing down to 1.8 K. Analysis of magnetization and heat capacity confirms that the $\mathrm{Y}{\mathrm{b}}^{3+}$ ions possess a spin orbit driven effective spin ($J_{\mathrm{eff}}$) = ${}^1/{}_2$ state with weak antiferromagnetic interactions in the Kramers doublet ground state. Muon spin relaxation measurements confirm the fluctuating nature of $\mathrm{Y}{\mathrm{b}}^{3+}$ spins, and also indicate a large energy separation between the ground state Kramers doublet state and the first excited state. Additionally, the muon spin relaxation rate reveals a plateau below 30 K owing to depopulation of excited crystal field levels which clearly signifies the development of a $J_{\mathrm{eff}}={}^1/{}_2$ doublet at low temperatures. Theoretical studies based on density functional theory point out the crucial role of spin orbit coupling (SOC) and support the $J_{\mathrm{eff}}={}^1/{}_2$ nature of $\mathrm{Y}{\mathrm{b}}^{3+}$ spins. Furthermore, DFT+$U$ calculations with and without the inclusion of SOC indicate that SOC gives rise to an insulating state, thereby suggesting $\mathrm{YbTa}{\mathrm{O}}_4$ to be a potential spin orbit driven Mott insulator candidate.