We present a detailed theoretical and experimental study to show how a model system for the investigation of classic electrolyte theory emerges in a nonelectrical context. In particular we develop the thermodynamic treatment of spin ice as a “magnetolyte,” a fluid of singly and doubly charged magnetic monopoles. This is equivalent to the electrochemical system $2{\mathrm{H}}_2\mathrm{O}={\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{OH}}^{-}={\mathrm{H}}_4{\mathrm{O}}^{2+}+{\mathrm{O}}^{2-}$, but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis going beyond Debye-Hückel theory to include Bjerrum pairs. This is accurate at all temperatures and incorporates “Dirac strings” imposed by the microscopic ice rule constraints at the level of Pauling's approximation. Our theory is in close agreement with the specific heat from numerical simulations as well as new experimental measurements with an improved lattice correction, which we present here, on the spin ice materials ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Our results provide new experimental tests of Debye-Hückel theory and its extensions and yield insights into the electrochemical behavior of water ice and liquid water, which are closely related to the spin ice magnetolyte.

$\mathrm{S}{\mathrm{r}}_2\mathrm{C}{\mathrm{a}}_2\mathrm{CoM}{\mathrm{n}}_2{\mathrm{O}}_9$ is made of Ising spin chains distributed on a triangular lattice, with antiferromagnetic coupling between them. In spite of a unique interchain distance, this compound exhibits two peculiarities making it deviate from the textbook case of geometrical frustration expected in ideal triangular lattices: first, there are three subclasses of chains shifted from each other along the chain direction; second, these chains fall into two categories which differ by some of the intrachain distances between spins. These features are found to confer a character of centered honeycomb lattice on this system of spin chains. Experimental investigation of the magnetism of $\mathrm{S}{\mathrm{r}}_2\mathrm{C}{\mathrm{a}}_2\mathrm{CoM}{\mathrm{n}}_2{\mathrm{O}}_9$ reveals a peculiar pretransitional regime, which is manifested by a frequency-dependent peak of susceptibility. We put this behavior in relation with the formation of short-range one-dimensional ferromagneticlike segments taking place a few degrees above the $T_N$. This phenomenon is itself regarded as a precursor effect of the long-range ordering, induced by the particular topology of the spin system.

In the present paper, we address a long-standing problem of the magnetic ground state and magnetic excitations in underdoped cuprates. Modeling cuprates by the extended $t-J$ model, we show that there is a dimensionless parameter $\lambda$ which drives quantum magnetic criticality at low doping $x$. Hence we derive the zero temperature $\lambda -x$ phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point $x=0,\lambda =1$. The three phases “meet” at the tricritical point: (i) Néel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave vector, (iii) algebraic spin liquid. We argue that underdoped cuprates belong either to the spin-liquid phase or they are on the borderline between the spin liquid and the spin spiral. We calculate the energy position $E_{\text{cross}}$ of the inelastic neutron scattering response maximum at $\mathit{q}=(\pi ,\pi )$ and compare our results with experiments. We also explain softening of magnons in the intermediate regime observed in inelastic neutron scattering.

We present a complete numerical calculation and an experimental data analysis of the universal conductance fluctuations in quasi-one-dimensional nanowires. The conductance peak density model, introduced in nanodevice research by Ramos et al. [Phys. Rev. Lett. 107, 176807 (2011)], is applied successfully to obtain the coherence length of InAs nanowire magnetoconductance and we prove its equivalence with correlation methods. We show the efficiency of the method and therefore a prominent alternative to obtain the phase-coherence length. The peak density model can be similarly applied to spintronic setups, graphene, and topological isolators where phase-coherence length is a relevant experimental parameter.

Since the discovery of graphene, the localization physics has been studied extensively, and both weak antilocalization (WAL) and weak localization (WL) have been observed. A graphene superlattice (GSL) with multiple Dirac cones has emerged as a focus point in condensed-matter physics in recent years. However, the localization physics at multiple Dirac cones has not been studied to date. Here, we study the magnetoconductance in hexagonal boron nitride-graphene moiré-superlattice devices. Our magnetoconductance results show a clear signature of WL at the cloned Dirac cone (CDC) over one decade of variation of both carrier concentration and temperature in the two devices. In contrast, the WAL becomes stronger at the primary Dirac cone (PDC) with increasing temperature and lower carrier concentration in one device, in agreement with previous studies, whereas the other device shows stronger WAL for both lower temperature and carrier concentration. Since the observation of WAL at PDC is expected in a cleaner device due to the $\pi$ Berry phase, it is natural to ask whether the observation of WL at CDC in our GSL devices has any connection to Berry phase change or not. In order to address this issue we measure the Shubnikov–de Haas (SdH) resistance oscillations, which show a shift of the Berry phase by $\pi$ from PDC to CDC, indicating the role of the Berry phase for observing WL at CDC. We further corroborate our results with realistic electronic band structure calculations, which suggest a change in the Fermi surface topology from that with a small Fermi pocket enclosing a single PDC in each valley to a large Fermi surface shared by all the CDCs, in accordance with the change in oscillation frequency from PDC to CDC in the SdH measurements.

Heterostructures of ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices have shown the formation of “polar vortices,” in which a continuous rotation of ferroelectric polarization spontaneously forms. Recently, Shafer et al. [Proc. Natl. Acad. Sci. USA (PNAS) 115, 915 (2018)] reported strong nonmagnetic circular dichroism (CD) in resonant soft x-ray diffraction at the Ti $L_3$ edge from such superlattices. The authors ascribe the CD to the chiral rotation of a polar vector. However, a polar vector is invisible to the parity-even electric-dipole transition which governs absorption in the soft x-ray region. A realistic, nonmagnetic explanation of the observed effect is found in Templeton-Templeton scattering. Following this route, the origin of the CD in Bragg diffraction is shown by us to be the chiral array of charge quadrupole moments that forms in these heterostructures. While there is no charge quadrupole moment in the spherically symmetric $3d^0$ valence state of ${\mathrm{Ti}}^{4+}$, the excited state $2p^{5}3d^1\left(t_{2g}\right)$ at the Ti $L_3$ resonance is known to have a quadrupole moment. Our expressions for intensities of satellite Bragg spots in resonance-enhanced diffraction of circularly polarized x rays, including their harmonic content, account for all observations reported by Shafer et al. We predict both intensities of Bragg spots for the second harmonic of a chiral superlattice and circular polarization created from unpolarized x rays, in order that our successful explanation of existing diffraction data can be further scrutinized through renewed experimental investigations. The increased understanding of chiral dipole arrangements could open the door to switchable optical polarization.

We use magnetization measurements, high-resolution angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) calculations to study the electronic properties of $\mathrm{Au}{}_2\mathrm{Pb}$, a topological superconductor candidate. The magnetization measurements reveal three discontinuities at 40, 51, and 99 K that agree well with reported structural phase transitions. To measure the band structure along desired crystal orientations, we utilized polishing, sputtering, and annealing to obtain clean flat sample surfaces. ARPES measurements of the $\mathrm{Au}{}_2\mathrm{Pb}$ (111) surface at 110 K shows a shallow hole pocket at the center and flower-petal-like surface states at the corners of the Brillouin zone. These observations match the results of DFT calculations relatively well. The flower-petal-like surface states appear to originate from a Dirac-like dispersion close to the zone corner. For the $\mathrm{Au}{}_2\mathrm{Pb}$ (001) surface at 150 K, ARPES reveals at least one electron pocket between the $\mathrm{\Gamma }$ and $M$ points, consistent with the DFT calculations. Our results provide evidence for the possible existence of a Dirac state in this material.

We report spin-split Landau levels of quasi-two-dimensional Dirac fermions in a layered antiferromagnet ${\mathrm{EuMnBi}}_2$, as revealed by interlayer resistivity measurements in a tilted magnetic field up to $\sim 35$ T. The amplitude of Shubnikov–de Haas (SdH) oscillation in interlayer resistivity is strongly modulated by changing the tilt angle of the field, i.e., the Zeeman-to-cyclotron energy ratio. The effective $g$ factor estimated from the tilt angle, where the SdH oscillation exhibits a phase inversion, differs by approximately 50% between two antiferromagnetic phases. This observation signifies a marked impact of the magnetic order of Eu sublattice on the Dirac-like band structure. The origin may be sought in strong exchange coupling with the local Eu moments, as verified by the first-principles calculation.

The tunability of topological surface states and the controllable opening of the Dirac gap are two keys for the study of topological crystalline insulators (TCIs). By constructing PbTe/SnTe heterostructures, we discover giant linear magnetoresistance (GLMR) $(2150\%$ under a magnetic field of 14 T at 2 K) and strong metallic behavior that are likely induced by Dirac fermions with a high carrier mobility. By decreasing the hole density in SnTe, a much weaker metallic behavior and two-dimensional weak antilocalization are exhibited in PbTe/SnTe heterostructures. This striking transport difference is attributed to the cubic-rhombohedral structural phase transition in SnTe and broken mirror symmetry effect. The revelation of lattice structural distortion and mirror symmetry breaking in a PbTe/SnTe heterostructure's transport properties is very significant to the fundamental research in topological matter, magnetoelectronics, and spintronics.

We address the question of how the time-resolved bulk Hall response of a two-dimensional honeycomb lattice develops when driving the system with a pulsed perturbation. A simple toy model that switches a valley Hall signal by breaking inversion symmetry is studied in detail for slow quasiadiabatic ramps and sudden quenches, obtaining an oscillating dynamical response that depends strongly on doping and time-averaged values that are determined both by the out of equilibrium occupations and the Berry curvature of the final states. On the other hand, the effect of irradiating the sample with a circularly-polarized pump pulse that breaks time reversal symmetry and thus ramps the system into a nontrivial topological regime is probed. Even though there is a nonquantized average signal due to the breakdown of the Floquet adiabatical picture, some features of the photon-dressed topological bands are revealed to be present even in a few femtosecond timescale. Small frequency oscillations during the transient response evidence the emergence of dynamical Floquet gaps which are consistent with the instantaneous amplitude of the pump envelope. On the other hand, a characteristic heterodyning effect is manifested in the model. The presence of a remnant Hall response for ultrashort pulses that contain only a few periods of the radiation field is briefly discussed.

Magnetotransport measurements on antidot lattices with square and hexagonal geometries are reported. The resistivity shows a superposition of the classical commensurability resonances and Shubnikov–de Haas type oscillations. In this range of magnetic fields, quantum Hall plateaus are already developed, but shifted to lower fields. The transitions between these plateaus are found to be in-phase with an additional small-amplitude oscillation in the resistivity. This is interpreted with the help of numerical simulations as a quantum signature of the competition between skipping and hopping transport in antidot superlattices.

A two-dimensional (2D) $J$-resolved magic-angle spinning nuclear magnetic resonance (NMR) spectrum of silica glass at ${}^{29}\mathrm{Si}$ natural abundance levels, 4.7%, was measured using the shifted-echo phase-incremented echo train acquisition (SE-PIETA) pulse sequence. At ${}^{29}\mathrm{Si}$ natural abundance levels the $J_{\text{Si-O-Si}}$ coupling splittings appear as overlapping doublet patterns arising from isolated ${}^{29}\mathrm{Si}-\mathrm{O}-{}^{29}\mathrm{Si}$ linkages. The experimental 2D $J$-resolved spectrum is analyzed to obtain a bivariate probability distribution correlating the central Si-O-Si angle of a ${\mathrm{Q}}^4-{\mathrm{Q}}^4$ linkage to its mean Si-O-Si angle (seven angles) using relationships between ${}^{29}\mathrm{Si}$ isotropic chemical shifts and geminal $J_{\text{Si-O-Si}}$ coupling of a ${\mathrm{Q}}^4-{\mathrm{Q}}^4$ to its local structure. To obtain a self-consistent bivariate probability distribution it was necessary to introduce an additional dependence of the ${}^{29}\mathrm{Si}$ chemical shift of a ${\mathrm{Q}}^4$ on mean Si-O distance as well as mean Si-O-Si angle. The implication of this necessary modification is a positive correlation between Si-O-Si angle and Si-O distance in the silica glass, consistent with recent ${}^{17}\mathrm{O}$ NMR measurements on ambient and densified silica glasses but running opposite to the trend generally found in crystalline silica polymorphs. From the analysis of the ${}^{29}\mathrm{Si}$ 2D $J$-resolved spectrum we determine a Si-O-Si bond angle distribution in silica glass as having a mean at $147.8^{\circ }$, a mode at ${147}^{\circ }$, and a standard deviation of $10.7^{\circ }$. Our statistical model for analyzing the experimental ${}^{29}\mathrm{Si}$ 2D $J$-resolved spectrum also indicates that the individual Si-O-Si bond angle distributions are relatively uncorrelated.

We study the real-time dynamics of local occupation numbers in a one-dimensional model of spinless fermions with a random on-site potential for a certain class of initial states. The latter are thermal (mixed or pure) states of the model in the presence of an additional static force but become nonequilibrium states after a sudden removal of this static force. For this class and high temperatures, we show that the induced dynamics is given by a single correlation function at equilibrium, independent of the initial expectation values being prepared close to equilibrium (by a weak static force) or far away from equilibrium (by a strong static force). Remarkably, this type of universality holds true in both the ergodic phase and the many-body localized regime. Moreover, it does not depend on the specific choice of a unit cell for the local density. We particularly discuss two important consequences. First, the long-time expectation value of the local density is uniquely determined by the fluctuations of its diagonal matrix elements in the energy eigenbasis. Thus, the validity of the eigenstate thermalization hypothesis is not only a sufficient but also a necessary condition for thermalization. Second, the real-time broadening of density profiles is always given by the current autocorrelation function at equilibrium via a generalized Einstein relation. In the context of transport, we discuss the influence of disorder for large particle-particle interactions, where normal diffusion is known to occur in the disorder-free case. Our results suggest that normal diffusion is stable against weak disorder, while they are consistent with anomalous diffusion for stronger disorder below the localization transition. Particularly, for weak disorder, Gaussian density profiles can be observed for single disorder realizations, which we demonstrate for finite lattices up to 31 sites.

We study scrambling in connection with multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well-defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are found to be very different: up to the Ehrenfest time, they rise side by side, departing only afterward. Entanglement saturates and becomes extensively multipartite, while scrambling, characterized by the dynamic of the square commutator of initially commuting variables, continues its growth up to the recurrence time. Remarkably, the exponential growth of the latter emerges not only in the chaotic case but also in the regular one, when the dynamics occurs at a dynamical critical point.

The theoretical finding on chiral phonons at Brillouin-zone corners (valleys) of two-dimensional honeycomb lattices and its experimental verification in monolayer tungsten diselenide [H. Zhu, J. Yi, M. Li, J. Xiao, L. Zhang, C. Yang, R. A. Kaindl, L. Li, Y. Wang, and X. Zhang, Science 359, 579 (2018)], have attracted wide attention in the study of phonon chirality very recently. In this paper, to make chiral phonons more measurable, the valley phonons were folded to Brillouin-zone center in $\sqrt{3}\times \sqrt{3}$ honeycomb superlattices, and near the center topological chiral phonons can be observed. The chiral phonons which are not the superposition of linear modes are nondegenerate and can be optically excited in helicity-resolved Raman scattering. Moreover, by adjusting the doping mass, the topological chiral phonons can be engineered in specific branches. Finally, in deformed $\sqrt{3}\times \sqrt{3}$ honeycomb superlattices, topological chiral phonons can also be found near the Brillouin-zone center. We believe that the findings of nondegenerate topological chiral phonons in the Brillouin-zone center help to enrich our understanding of chiral phonons and promote future applications in phononics.

The confinement and deconfinement of spinons in the square-lattice antiferromagnetic $J_1-J_2$ Heisenberg model are elaborated by exploring the evolution of the whole excitation spectra with $J_2$, based on the spin cluster perturbation theory. We find that deconfined spin-$1/2$ spinons beyond the conventional spin-1 magnons have already emerged partially even in the limit $J_2=0$ and develop with $J_2$, exhibiting as a continuum close to $(\pi ,0)$ in the Brillouin zone. In the region near $J_2=0.5J_1$, the entire spectrum is characterized by a broad continuum in which all magnons are deconfined into spinons, whose ground state is attributed to a $Z_2$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis. The spinon continua are also found in the stripe phase with $J_2>0.6J_1$. Our study provides spectroscopic evidences for the fractionalized excitations and quantum spin liquid and highlights the rising field to explore the exotic quantum phases from a perspective of excitation spectrum.

Giant spin Hall effect (GSHE) in heavy metals can convert charge current into spin current with a high efficiency characterized by a spin Hall angle. In this paper, we prepare a set of multilayer systems of $\beta -\mathrm{W}$/CoFeB/MgO/Ta with the different $\beta -\mathrm{W}$ thickness up to 18 nm. Using a direct-current magneto-transport method and relying on the anomalous Hall effect of CoFeB, we observed a large spin Hall angle of 64% in the bulk limit of $\beta -\mathrm{W}$ solid at room temperature and a weak temperature dependence of the spin Hall angle. Additionally, we also studied the crystal structure, magnetization, magnetic anisotropy, electrical transport, spin diffusion, and interfacial spin current transmission in this exemplary GSHE system over a broad temperature range of 10 to 300 K, which would benefit fundamental studies and potential spintronics applications of $\beta -\mathrm{W}$.

Noncollinear two-dimensional triangular lattice antiferromagnets (2D TLAFs) are currently an area of very active research due to their unique magnetic properties, which lead to nontrivial quantum effects that experimentally manifest themselves in the spin excitation spectra. Recent examples of such insulating 2D TLAFs include $(\mathrm{Y},\mathrm{Lu}){\mathrm{MnO}}_3, {\mathrm{LiCrO}}_2$, and ${\mathrm{CuCrO}}_2$. Hexagonal ${\mathrm{LuFeO}}_3$ is a recently synthesized 2D TLAF which exhibits properties of an ideal multiferroic material, partially because of the high spin ($S=5/2$) and strong magnetic superexchange interactions. We report the full range of spin dynamics in a bulk single crystal of $\left({\mathrm{Lu}}_{0.6}{\mathrm{Sc}}_{0.4}\right){\mathrm{FeO}}_3$ (Sc doping to stabilize the hexagonal structure) measured via time-of-flight inelastic neutron scattering. Modeling with linear spin-wave theory yields a nearest-neighbor exchange coupling of $J=4.0\left(2\right)\mathrm{meV}$ (density functional theory calculations for $h-{\mathrm{LuFeO}}_3$ predicted a value of 6.31 meV) and anisotropy values of $K_D=0.17\left(1\right)\mathrm{meV}$ (easy plane) and $K_A=-0.05\left(1\right)\mathrm{meV}$ (local easy axis). It is observed that the magnon bandwidth of the spin-wave spectra is twice as large for $h-(\text{Lu},\mathrm{Sc}){\mathrm{FeO}}_3$ as it is for $h-{\mathrm{LuMnO}}_3$.

We study the modulations of the superconducting order parameter in the vicinity of edges, and magnetic and nonmagnetic impurities by self-consistently solving the gap equations of a system with competing interactions in the Cooper channel. It is shown that the presence or absence of Friedel-like oscillations of the superconducting order parameter crucially depends on its symmetry and can, hence, be used to obtain information about the symmetry properties of the condensate. Furthermore, the appearance of competing order parameters at inhomogeneities is discussed. We show that this can lead to the presence of a topologically trivial region close to the boundary of a system that is topologically nontrivial in its bulk. The resulting shift in position of the Majorana bound states is demonstrated to significantly affect its signatures in Josephson-junction experiments. We discuss Josephson scanning tunneling microscopy as a probe to resolve the Friedel-like oscillations as well as the spatial texture of competing $s$-wave superconductivity and Majorana bound states in the vicinity of the edge of the system.

We discuss how the collective magnetic resonance response of the monoaxial chiral helimagnetic crystal ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ can be tailored by changing the area of its magnetization plane. Micrometer-sized samples of this crystal yield a number of resonance modes occurring at frequencies ranging from 15 to 20 GHz, even in the absence of a magnetic field. Changes in the resonance bandwidth, of the order of several GHz, are attributed to the effect of the spatially nonuniform demagnetization fields on standing spin wave modes. This material hosts a chiral spin soliton lattice phase, whose field robustness, degree of controllability, and the relatively unexplored polarization-dependent microwave absorption make way for novel microwave applications.