The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual unidirectional charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different CDW contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.

Isotope-shift spectroscopy with narrow optical transitions provides a benchmark for atomic structure calculations and has also been proposed as a way to constrain theories predicting physics beyond the standard model. Here we measure frequency shifts of the ${}^{1}S_0\to {}^{3}P_1$ and ${}^{1}S_0\to {}^{3}P_0$ transitions between ${}^{84}\mathrm{Sr},{}^{86}\mathrm{Sr}$, and ${}^{87}\mathrm{Sr}$, relative to ${}^{88}\mathrm{Sr}$. Using the isotope-shift measurements of the two transitions, a King plot analysis is performed, revealing a nonlinearity in the measured values.

We identify theoretically the geometric phases of the electrons' spinor that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers threaded by a magnetic flux $\mathrm{\Phi }$ (in units of the flux quantum) where Rashba spin-orbit and Zeeman interactions are active. We show that the combined effect of these two interactions produces a $sin\left(\mathrm{\Phi }\right)$ [in addition to the usual $cos\left(\mathrm{\Phi }\right)$] dependence of the magnetoconductance, whose amplitude is proportional to the Zeeman field. Therefore, although the magnetoconductance is an even function of the magnetic field, it is not a periodic function of it, and the widely used concept of a phase shift in the Aharonov-Bohm oscillations, as indicated in previous work, is not applicable. We find the directions of the spin polarizations in the system and show that in general (even without the Zeeman term) the spin currents are not conserved, implying the generation of magnetization in the terminals attached to the interferometer.

Magnetic excitations of long-range ordered localized spin systems are generally well described by the linear spin-wave theory which accounts for phase fluctuations of the order parameter. In contrast, quasiparticles associated with amplitude fluctuations are only observed in a few quantum antiferromagnets close to a quantum critical point (QCP), where the ordered moment is suppressed significantly from its fully saturated value. Via inelastic neutron scattering measurements and extended spin-wave calculations, we present the observation and explanation of amplitude modes in the magnetic excitation spectra of three-dimensional $S=3/2$ spin dimers $\mathrm{C}{\mathrm{r}}_2\mathrm{Te}{\mathrm{O}}_6$ and $\mathrm{C}{\mathrm{r}}_2\mathrm{W}{\mathrm{O}}_6$, which nevertheless are away from the QCP with the ordered moment reduced by only ∼24%. We show that the large spin of $\mathrm{C}{\mathrm{r}}^{3+}$ and narrow bandwidth of the amplitude modes render their detection even in polycrystalline samples. This paper suggests that amplitude modes are not the privilege of ordered spin systems in the vicinity of a QCP, but may be common excitation modes that can survive even away from the QCP, paving a way to search for and understand the physics of amplitude fluctuations in antiferromagnets beyond the quantum spin limit ($S=1/2$).

We present an exactly solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p+ip$ Richardson-Gaudin fermionic model, such as a third-order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.

A high-aspect ratio flexible filament suspended in a viscous fluid is unstable to a symmetry-breaking whirling motion when axially rotated beyond a critical velocity. We present experiments of this behavior and uncover a rich diversity of plectoneme formation soon after the initial instability, including multiple plectonemes for especially long filaments. A physical model extending Timoshenko's theory of elastic instability is presented which captures the fundamental physics involved in the instability. Additionally, we consider the effects of an axial flow that acts to tension the filament and control the onset of whirling without adjusting the physical properties of the filament itself. Such a setup could be employed to selectively engineer plectoneme formation at specified locations and lengths, and in fibers with submicron diameters, potentially to create superelastic ropes and fabrics.

We report on the microwave analysis of the interplay between magnetism and superconductivity in single crystals of ${\mathrm{EuFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$, accomplished by means of a coplanar waveguide resonator technique. The bulk complex magnetic susceptibility ${\chi }_m$ extracted through a cavity perturbation approach is demonstrated to be highly sensitive to the magnetic structure and dynamics, revealing two distinct magnetic transitions below the superconducting critical temperature. By a comparison with magnetic force microscopy maps, we ascribe the ${\chi }_m^{\prime \prime }$ peak observed at about 17 K to the transition from the ferromagnetic domain Meissner phase to the domain vortex-antivortex state, with the subsequent evolution of the domain structure at lower temperatures. The second ${\chi }_m^{\prime \prime }$ peak observed at 11 K reflects a specific high-frequency feature, connected to vortex-antivortex dynamics and eventual spin reorientation transition of the ${\mathrm{Eu}}^{2+}$ canted ferromagnetic subsystem. The two peaks merge and vanish upon application of an in-plane magnetic field, which is compatible with the presence of a quantum critical point below 1 T.

We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures particularly of the skyrmions, showing an excellent agreement with experiments and first-principles studies. An anisotropic Dzyaloshinskii-Moriya interaction suitable for thin films made with $C_{nv}$ symmetric materials is found to stabilize antiskyrmion and antimeron, which are prototypical for $D_{2d}$ symmetric systems, depending on the degree of anisotropy. Based on these solutions, we obtain a phase diagram by comparing the energies of various collinear and noncollinear competing phases.

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate (${\mathrm{Sr}}_2{\mathrm{RuO}}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al., Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

Determining the symmetry of the order parameter of unconventional superconductors remains a recurrent topic and nontrivial task in the field of strongly correlated electron systems. Here we show that the behavior of Dirac points away from the Fermi energy is a potential tool to unveil the orbital structure of a superconducting state. In particular, we show that gap openings in such Dirac crossings are a signature of nonunitary multiorbital superconducting order. Consequently, also spectral features at higher energy can help us to identify broken symmetries of superconducting phases and the orbital structure of nonunitary states. Our results show how angle-resolved photoemission spectroscopy measurements can be used to detect nonunitary multiorbital superconductivity.

It has been shown recently that extreme Reissner-Nordström black holes perturbed by a minimally coupled, free, massless scalar field have permanent scalar hair. The hair, a conserved charge calculated at the black hole's event horizon, can be measured by a certain expression at future null infinity: The latter approaches the hair inversely in time. We generalize this newly discovered hair also for extreme Kerr black holes. We study the behavior of nearly extreme black hole hair and its measurement at future null infinity as a transient phenomenon. For nearly extreme black holes the measurement at future null infinity of the length of the newly grown hair decreases quadratically in time at intermediate times until its length becomes short and the rate at which the length shortens further slows down. Eventually, the nearly extreme black hole becomes bald again like nonextreme black holes.

We propose a novel direct detection concept to search for dark matter with 100 keV to 100 MeV masses. Such dark matter can scatter off molecules in a gas and transfer an $\mathcal{O}\left(1\right)$ fraction of its kinetic energy to excite a vibrational and rotational state. The excited rovibrational mode relaxes rapidly and produces a spectacular multi-infrared-photon signal, which can be observed with ultrasensitive photodetectors. We discuss in detail a gas target consisting of carbon monoxide molecules, which enable efficient photon emission even at a relatively low temperature and high vapor pressure. The emitted photons have an energy in the range 180 to 265 meV. By mixing together carbon monoxide molecules of different isotopes, including those with an odd number of neutrons, we obtain sensitivity to both spin-independent interactions and spin-dependent interactions with the neutron. We also consider hydrogen fluoride, hydrogen bromide, and scandium hydride molecules, which each provide sensitivity to spin-dependent interactions with the proton. The proposed detection concept can be realized with near-term technology and allows for the exploration of orders of magnitude of new dark matter parameter space.

The existence of quasi-long-range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay.

The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization properties of a quantum-engineered system can be probed by spectroscopy, namely, by measuring its excitation rate upon a periodic drive. We apply this method to various examples that are of direct experimental relevance in ultracold atomic gases, including Anderson localization, topological edge modes, and interacting particles in a harmonic trap. Moreover, inspired by a relation between quantum fluctuations and the quantum metric, we describe how our scheme can be generalized in view of extracting the full quantum-geometric tensor of many-body systems. Our approach opens an avenue for probing localization, as well as quantum fluctuations, geometry and entanglement, in synthetic quantum matter.

This paper investigates the coexistence and interplay of spin and mass superfluidity in antiferromagnetic spin-1 Bose-Einstein condensates (BEC). The hydrodynamic theory describes the spin degree of freedom by equations similar to the Landau-Lifshitz-Gilbert theory for bipartite antiferromagnetic insulators. The variables in the spin space are two subspins with absolute value $\hslash /2$, which play the role of two sublattice spins in the antiferromagnetic insulators. As well as in bipartite antiferromagnetic insulators, in antiferromagnetic spin-1 BEC there are two spin-wave modes: One is a gapless Goldstone mode and the other is gapped. The Landau criterion shows that in limit of small total spin (two subspins are nearly antiparallel), the instability of supercurrents starts from the gapped mode. In the opposite limit of large total spin (two subspins are nearly parallel), the gapless modes become unstable earlier than the gapped one. Mass and spin supercurrents decay via phase slips, when vortices cross streamlines of the supercurrent. The vortices participating in phase slips are nonsingular bicirculation vortices. They are characterized by two topological charges, which are winding numbers describing circulations of two angles around the vortex axis. The winding numbers can be half-integers. A particular example of a half-integer vortex is a half-quantum vortex with the superfluid velocity circulation $h/2m$. However, the superfluid velocity circulation is not a topological charge, and in general the quantum of this circulation can be continuously tuned from 0 to $h/2m$.

Although Weyl semimetals have been extensively studied for exploring rich topological physics, the direct observation of the celebrated chiral magnetic effect (CME) associated with the so-called dipolar chiral anomaly has long intrigued and challenged physicists, still remaining elusive in nature. Here we propose a feasible scheme for experimental implementation of ultracold atoms that may enable us to probe the CME with a pure topological current in an artificial Weyl semimetal. The paired Weyl points with the dipolar chiral anomaly emerge in the presence of the well-designed spin-orbital coupling and laser-assisted tunneling. Both of the two artificial fields are readily realizable and highly tunable via current optical techniques using ultracold atoms trapped in three-dimensional optical lattices, providing a reliable way for manipulating Weyl points in the momentum-energy space. By applying a weak artificial magnetic field, the system processes an auxiliary current originated from the topology of a paired Weyl points, namely, the pure CME current. This topological current can be extracted from measuring the center-of-mass motion of ultracold atoms, which may pave the way to directly and unambiguously observe the CME in experiments.

Recently, ${\mathrm{Cd}}_3{\mathrm{As}}_2$ has attracted intensive research interest as an archetypical Dirac semimetal, hosting three-dimensional linear-dispersive electronic bands near the Fermi level. Previous studies have shown that single-crystalline ${\mathrm{Cd}}_3{\mathrm{As}}_2$ has an anomalously low lattice thermal conductivity, ranging from 0.3 to 0.7 W/mK at 300 K, which has been attributed to point defects. In this work, we combine first-principles lattice dynamics calculations and temperature-dependent high-resolution Raman spectroscopy of high-quality single-crystal thin films grown by molecular-beam epitaxy to reveal the existence of a group of soft optical phonon modes at the Brillouin-zone center of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. These soft phonon modes significantly increase the scattering phase space of heat-carrying acoustic phonons and are the origin of the low lattice thermal conductivity of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Furthermore, we show that the interplay between the phonon-phonon Umklapp scattering rates and the soft optical phonon frequency explains the unusual nonmonotonic temperature dependence of the lattice thermal conductivity of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Our results further suggest that the soft phonon modes are potentially induced by a Kohn anomaly associated with the Dirac nodes, in analogy to similar, nonetheless weaker, effects in graphene and Weyl semimetals.

We show that the exact ground state of the Lieb-Mattis Hamiltonian is an equal-weight superposition of all possible classical Néel states, and provide an exact formulation of this superposition in the $z$-spin basis for both $S=1/2$ and general $S$ using Schwinger bosons. In general, a superposition of possible rotations on a general initial state is symmetric if and only if the initial state has a nonzero overlap with a singlet state and is otherwise made up of states that vanish due to the symmetrization. Most notably, $|s,m=0\rangle$ states will vanish if symmetrized, which explains how a superposition of Néel states projects onto its singlet component.

Polarized neutron diffraction allows one to determine the local susceptibility tensor on the magnetic site both in single crystals and powders. It is widely used in the studies of single crystals, but it is still hardly applicable to a number of highly interesting powder materials, such as molecular magnets or nanoscale systems because of the low luminosity of existing instruments and the absence of appropriate data analysis software. We show that these difficulties can be overcome by using a large area detector in combination with the two-dimensional Rietveld method and powder samples with a magnetically induced preferred crystallite orientation. This is demonstrated by revisiting two test powder compounds, namely, the low anisotropy (soft) ferrimagnetic compound ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the spin-ice compound ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ with high local anisotropy. The values of the magnetic moments in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the susceptibility tensors of ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at various temperatures and fields were found in perfect agreement with these found earlier in single-crystal experiments. The magnetically induced preferred crystallite orientation was used to study the local susceptibility of a single-molecule magnet $\mathrm{Co}{\left({\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{N}\right]}_2\mathrm{CS}\right)}_2{\mathrm{Cl}}_2$. Hence, the studies of local magnetic anisotropy in powder systems might now become accessible.

We analyze structural properties of hydration for a biological membrane with the open boundary adaptive resolution molecular dynamics approach in its latest version. A large region of noninteracting pointlike particles (tracers) acts as a reservoir of molecules and energy for the atomistically resolved membrane-water interface. The drastic simplification of the environment and its simple coupling to the high-resolution region has been successfully tested in a previous work on pure liquid water, and this work represents the method's first application to a system with high structural complexity. The successful results and novel methodology allow us to suggest a complementary view to the controversial question of the definition of the hydration shell for a membrane. The adaptive resolution technique allows for a physically well-founded statistical mechanics definition of the hydration shell by quantifying the minimal size of the region where the atomistic resolution of the molecules is strictly required while the rest of the system plays the role of a generic, structureless thermodynamic reservoir.