Using temperature-dependent and low-frequency Raman spectroscopy, we address the question of how the transition from bulk to a few atomic layers affects the charge density wave (CDW) phases in $1T\text{−}\mathrm{Ta}{\mathrm{S}}_2$. We find that for crystals with thickness larger than $\approx 10$ nm the transition temperatures between the different phases as well as the hysteresis that occurs in the thermal cycle correspond to the ones expected for a bulk sample. However, when the crystals become thinner than $\approx 10$ nm, the low-temperature commensurate CDW phases can be suppressed down to the experimentally accessible temperatures ($\sim 80$ K) upon cooling at moderate rates $\left(\sim 5\mathrm{K}\mathrm{mi}{\mathrm{n}}^{-1}\right)$. In addition, even the near commensurate CDW phase is not accessible in few-layer flakes below $\approx 4$ nm for even slower cooling rates $\left(\sim 1\mathrm{K}\mathrm{mi}{\mathrm{n}}^{-1}\right)$. We employ Raman hyperspectral imaging to statistically confirm these findings and consider the interlayer coupling and its dynamics to play significant roles in determining the properties of CDW systems consisting of a few unit cells in the vertical direction.

The structural and dielectric characterization of 30% Sn-doped ${\mathrm{BaTiO}}_3$ (${{\mathrm{BaSn}}_{0.3}{\mathrm{Ti}}_{0.7}\mathrm{O}}_3$) as a function of temperature is carried out combining, complementary probes to reveal structural modifications associated to the relaxor behavior. Dielectric data confirms the existence of relaxor-type behavior in ${{\mathrm{BaSn}}_{0.3}{\mathrm{Ti}}_{0.7}\mathrm{O}}_3$. The local and average structural changes as a function of temperature have been investigated in the region of broad changes of dielectric response. Local probes, such as x-ray absorption fine structure spectroscopy and Mössbauer spectroscopy reveal a special trend of the lattice related to the diffuse dielectric phase transition as observed from dielectric data. The analysis of Raman spectra as a function of temperature reveals a peculiar behavior in the temperature region corresponding to the dielectric transition. The analysis of x-ray diffraction patterns points out a pseudocubic structure throughout the temperature range while the volume exhibits a negative thermal expansion in the region of broad dielectric maximum. Our results suggest structural modifications occurring in the system throughout a wide temperature range, interestingly, associated with changes in macroscopic properties of relaxors such as dispersion in dielectric constants and raising of dipole moments.

We present experimental measurements and ab initio simulations of the crystalline and amorphous phases of ${\mathrm{P}}_2{\mathrm{O}}_5$. The calculated Raman, infrared, and vibrational density of states (VDOS) spectra are in excellent agreement with experimental measurements and contain the signatures of all the peculiar local structures of the amorphous phase, namely, bridging and nonbridging (double-bonded or terminal) oxygens and tetrahedral ${\mathrm{PO}}_4$ units associated with $Q^2, Q^3$, and $Q^4$ species ($Q^n$ denotes the various types of ${\mathrm{PO}}_4$ tetrahedra, with $n$ being the number of bridging oxygen atoms that connect the tetrahedra to the rest of the network). In order to reveal the internal structure of the vibrational spectrum, the characteristics of vibrational modes in different frequency ranges are investigated using a mode-projection approach at different symmetries based on the $T_d$ symmetry group. In particular, the VDOS spectrum in the range from $\sim 600$ to 870 ${\mathrm{cm}}^{-1}$ is dominated by bending ($F_{2b}$) motions related to bridging oxygen and phosphorus ($\sim 800 {\mathrm{cm}}^{-1}$ band) atoms, while the high-frequency doublet zone ($\sim 870$–1250 ${\mathrm{cm}}^{-1}$) is associated mostly with the asymmetric ($F_{2s}$) and symmetric ($A_1$) stretching modes, and most prominent peak around 1400 ${\mathrm{cm}}^{-1}$ (exp. 1380 ${\mathrm{cm}}^{-1}$) is mainly due to asymmetric stretching vibrations supported by double-bonded oxygen atoms. The lower-frequency range below 600 ${\mathrm{cm}}^{-1}$ is shown to arise from a mixture of bending ($E$ and $F_{2b}$) and rotation ($F_1$) modes. The scissors bending ($E$) and rotation ($F_1$) modes are well localized below 600 ${\mathrm{cm}}^{-1}$, whereas the $F_{2b}$ bending modes spread further into the range $\sim 600$–870 ${\mathrm{cm}}^{-1}$. The projections of the eigenmodes onto $Q^2, Q^3$, and $Q^4$ species yield well-defined contributions at frequencies in striking correspondence with the positions of the Raman and infrared bands.

Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle-point textures and energy barriers of large skyrmions. The sign of the spin stiffness and the sign of fourth-order derivative terms in the classical field theory determines the nature of the saddle point and thus the height of the energy barrier. In the most common case for DMI-stabilized skyrmions, positive stiffness and negative fourth-order term, the saddle-point energy approaches a universal upper limit described by an effective continuum theory. For skyrmions stabilized by frustrating interactions, the stiffness is negative and the energy barrier arises mainly from the core of a singular vortex configuration.

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematical model: It does not rely on assuming a particular distribution function of the particles.

We examine the magnetic ordering of UN and of a closely related nitride, ${\mathrm{U}}_2{\mathrm{N}}_3$, by preparing thin epitaxial films and using synchrotron x-ray techniques. The magnetic configuration and subsequent coupling to the lattice are key features of the electronic structure. The well-known antiferromagnetic (AF) ordering of UN is confirmed, but the expected accompanying distortion at ${\mathrm{T}}_N$ is not observed. Instead, we propose that the strong magnetoelastic interaction below ${\mathrm{T}}_N$ causes substantial changes in the strain in the sample being measured. These strains vary as a function of the sample form. As a consequence, the accepted AF configuration of UN may be incorrect. In the case of cubic $\alpha -{\mathrm{U}}_2{\mathrm{N}}_3$, no single crystals have been previously prepared, and we have determined the AF ordering wave vector. The AF ${\mathrm{T}}_N$ is close to that previously reported. In addition, resonant diffraction methods have identified an aspherical quadrupolar charge contribution in ${\mathrm{U}}_2{\mathrm{N}}_3$ involving the $5f$ electrons.

We classify topological defects in non-Hermitian systems with point, real, and imaginary gaps for all the Bernard-LeClair classes or generalized Bernard-LeClair classes in all dimensions. The defect Hamiltonian $H(\mathbf{k},\mathbf{r})$ is described by a non-Hermitian Hamiltonian with a spatially modulated adiabatical parameter $\mathbf{r}$ surrounding the defect. While the non-Hermitian system with a point gap belongs to any of 38 symmetry classes (Bernard-LeClair classes), for non-Hermitian systems with a linelike gap, we get 54 nonequivalent generalized Bernard-LeClair classes as a natural generalization of point gap classes. Although the classification of defects in Hermitian systems has been explored in the context of the standard tenfold Altland-Zirnbauer symmetry classes, a complete understanding of the role of the general non-Hermitian symmetries on the topological defects and their associated classification is still lacking. By continuous transformation and homeomorphic mapping, these non-Hermitian defect systems can be mapped to topologically equivalent Hermitian systems with associated symmetries, and we get the topological classification by classifying the corresponding Hermitian Hamiltonians. We discuss some nontrivial classes with a point gap according to our classification table and give explicitly the topological invariants for these classes. We also study some lattice or continuous models and discuss the correspondence between the topological number and zero modes at the topological defect.

An unusual exchange bias (EB) effect in single-crystalline $\mathrm{GdCr}{\mathrm{O}}_3$ compensated ferrimagnet (fM), composed of two antiferromagnetically coupled Gd and Cr sublattices, presenting two opposite ferromagnetic (FM) moments, is reported. It is shown that the temperature- or field-induced fast reversal of the net FM moment in $\mathrm{GdCr}{\mathrm{O}}_3$ may be identified as a switching between two opposite spin configurations, attendant with abrupt drop in Zeeman energy $\approx k_{\mathrm{B}}(7\times {10}^{-4}\mathrm{K})$ per formula unit. It was found that the FM moment reversal is exchange biased in the narrow temperature interval above the compensation temperature $T_{\mathrm{comp}}=144\mathrm{K}$. Namely, the EB field emerges and diverges upon approaching $T_{\mathrm{comp}}$ at temperatures $T>T_{\mathrm{comp}}$ while unexpectedly it collapses to zero below $T_{\mathrm{comp}}$. This is in contrast to experimental results obtained for compensated fMs $R\mathrm{Fe}{\mathrm{O}}_3(R=\mathrm{Nd}$, Sm, Er) orthoferrites showing EB in a narrow range, both above and below $T_{\mathrm{comp}}$. We suppose that breakdown of EB in $\mathrm{GdCr}{\mathrm{O}}_3$ may be linked to the lack of anisotropy of the spin-only Gd $S$-ion magnetic moment dominating below $T_{\mathrm{comp}}$.

The spin anomalous Hall effect (SAHE), generating spin angular momentum flow (spin current, ${\mathbf{J}}_{\mathrm{s}})$, in an $L{1}_0\text{−}\mathrm{FePt}$ ferromagnet was quantitatively evaluated by exploiting giant magnetoresistance devices composed of $L{1}_0\text{−}\mathrm{FePt}\left|\mathrm{Cu}\right|\mathrm{N}{\mathrm{i}}_{81}\mathrm{F}{\mathrm{e}}_{19}$. From the ferromagnetic resonance linewidth modulated by the charge current $\left({\mathbf{J}}_{\mathrm{c}}\right)$ injection, the spin anomalous Hall angle $\left({\alpha }_{\mathrm{SAHE}}\right)$ was obtained to be 0.25 ± 0.03. The evaluation of ${\alpha }_{\mathrm{SAHE}}$ at different configurations of ${\mathbf{J}}_{\mathrm{c}}$ and magnetization made it possible to discuss the symmetry of SAHE, giving the unambiguous evidence that SAHE is the source of ${\mathbf{J}}_{\mathrm{s}}$. Thanks to the large ${\alpha }_{\mathrm{SAHE}}$, the SAHE-induced magnetization switching was achieved.

We report on the temperature evolution of the infrared-active optical phonons in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ investigated by Fourier-transform infrared spectroscopy. The eigenfrequencies of the four triply degenerate infrared-active $T_{1u}$ phonons of the room-temperature cubic spinel structure shift when entering into the ferrimagnetically ordered state below $T_C=165\mathrm{K}$ indicating strong spin-phonon coupling as reported earlier. A new mode at 200 ${\mathrm{cm}}^{-1}$ emerges below a temperature $T^{*}\simeq 115\mathrm{K}$ and a splitting of the lowest-lying cubic phonon mode at about 120 ${\mathrm{cm}}^{-1}$ appears below the temperature $T_M\approx 60\mathrm{K}$ associated with the onset of an incommensurate modulation of the magnetic structure. At the transition to the orbitally ordered and ferroelectric ground state at $T_{\text{OO}}=9\mathrm{K}$ two more modes emerge at 146 and 253 ${\mathrm{cm}}^{-1}$ in very good agreement with the eigenfrequencies of two of the cubic Raman-active phonon modes reported by Choi et al. [J. Phys. Condens. Matter 19, 145260 (2007)]. These new modes are interpreted as signatures of a symmetry lowering with a loss of inversion symmetry to induce the multiferroic orbitally ordered ground state.

A growing body of literature suggests that odd-frequency superconducting pair amplitudes can be generated in normal-metal-superconductor junctions. The emergence of odd-frequency pairing in these systems is often attributed to the breaking of translation invariance. In this work, we study the pair symmetry of a one-dimensional $s$-wave superconductor in the presence of a single nonmagnetic impurity and demonstrate that translation-symmetry breaking is not sufficient for inducing odd-frequency pairing. We consider three kinds of impurities: a local perturbation of the chemical potential, an impurity possessing a quantum energy level, and a local perturbation of the superconducting gap. Surprisingly, we find local perturbations of the chemical potential do not induce any odd-frequency pairing, despite the fact that they break translation invariance. Moreover, although odd frequency can be induced by both the quantum impurity and the perturbation of the gap, we find these odd-frequency amplitudes emerge from entirely different kinds of scattering processes. The quantum impurity generates odd-frequency pairs by allowing one of the quasiparticles belonging to an equal-time Cooper pair to tunnel onto the impurity state and then back to the superconductor, giving rise to odd-frequency amplitudes with a temporal broadening inversely proportional to the energy level of the impurity. In contrast to this, the perturbation of the gap leads to odd-frequency pairing by “gluing together” normal-state quasiparticles from different points in space and time, leading to odd-frequency amplitudes which are very localized in the time domain.

We analyze the instability of an unpolarized uniform quantum plasma consisting of two oppositely charged fermionic components with varying mass ratios against charge and spin density waves. Using density functional theory, we treat each component with the local spin density approximation and a rescaled exchange-correlation functional. Interactions between different components are treated with a mean-field approximation. In both two and three dimensions, we find leading unstable charge density wave modes in the second-order expansion of the energy functional, which would induce the transition to quantum liquid crystals. The transition point and the length of the wave vector are computed numerically. Discontinuous ranges of the wave vector are found for different mass ratios between the two components, indicating exotic quantum phase transitions. Phase diagrams are obtained, and a scaling relation is proposed to generalize the results to two-component fermionic plasmas with any mass scale. We discuss the implications of our results and directions for further improvement in treating quantum plasmas.

Symmetry considerations are of extreme importance to the topological properties of crystals. A crystal field splitting $\delta$ yields Dirac nodes near the Brillouin zone center in $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$, but its value has yet to be determined with precision. We study the band structure of $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ using magnetooptical infrared spectroscopy measurements on epilayers with low carrier density grown by molecular beam epitaxy. By combining angular dependent cyclotron resonance with Landau level spectroscopy measurements in the Faraday geometry, we determine that $\delta$ is positive and equal to $15\pm 5$ meV in $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$. Our results lead to a more accurate knowledge of the details of the band structure of this Dirac semimetal such as the position its Dirac nodes in momentum space and their splitting into Weyl nodes under a magnetic field.

Semiconductor quantum dots with dimensions exceeding the free-exciton Bohr radius are appealing because of their high oscillator strengths. While this property has received much attention in the context of cavity quantum electrodynamics, little is known about the degree of indistinguishability of single photons consecutively emitted by such dots and on the proper excitation schemes to achieve high indistinguishability. A prominent example is represented by GaAs quantum dots obtained by local droplet etching, which recently outperformed other systems as triggered sources of entangled photon pairs. On these dots, we compare different single-photon excitation mechanisms, and we find (i) poor indistinguishability for conventional excitation via excited states and (ii) photon indistinguishablilities above 90% for both strictly resonant and for incoherent phonon-assisted excitation. Among the explored excitation schemes, optical phonon-assisted excitation allows straightforward laser rejection and is thus worth of further investigation and optimization for quantum dots embedded in high-brightness photonic structures.

Symmetry-protected phases are gapped phases of matter which are distinguished only in the presence of a global symmetry $G$. These quantum phases lack any symmetry-breaking or topological order and have short-range entangled ground states. Based on this short-range entanglement property, we give a general argument for the existence of an emergent antiunitary (and sometimes also a unitary) ${\mathbb{Z}}_2$ symmetry at a critical point separating two different bosonic symmetry-protected phases in any dimension. Often, the emergent symmetry group at criticality has a mixed global anomaly. For those phases classified by group cohomology, we identify a criterion for when such a mixed global anomaly is present, and write down representative cocycles for the corresponding anomaly class. We illustrate our results with a series of examples and make connections to recent results on $(2+1)$-dimensional beyond-Landau critical points.

We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder models in which long-wavelength fluctuations are increasingly suppressed as a parameter $\alpha$ is tuned. For $\alpha =0$, one recovers the familiar infinite-randomness critical point. For $0<\alpha <1$, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at $\alpha =0$ are absent at any $\alpha >0$. When $\alpha >1$, randomness is a dangerously irrelevant perturbation at the clean Ising critical point, leading to a state we call the critical Ising insulator. In this state, thermodynamics and equilibrium correlation functions behave as in the clean system. However, all finite-energy excitations are localized, thermal transport vanishes, and autocorrelation functions remain finite in the long-time limit. We characterize this line of hyperuniform critical points using a combination of perturbation theory, renormalization-group methods, and exact diagonalization.

The implementation of a single magnon level quantum manipulation is one of the fundamental targets in quantum magnetism with a significant practical relevance for precision metrology, quantum information processing, and quantum simulation. Here we demonstrate theoretically the feasibility of using a hybrid ferromagnet-superconductor quantum system to prepare a single magnon source based on magnon blockade effects. By numerically solving the quantum master equation, we show that the second-order correlation function of the magnon mode depends crucially on the relation between the qubit-magnon coupling strength and the driving detuning, and simultaneously signatures of the magnon blockade appear only under quite stringent conditions of a cryogenic temperature. In addition to providing perception into the quantum phenomena of magnon, the study of magnon blockade effects will help to develop novel technologies for exploring the undiscovered magnon traits at the quantum level and may find applications in designing single magnon emitters.

In magnetic topological phases of matter, the quantum anomalous Hall (QAH) effect is an emergent phenomenon driven by ferromagnetic doping, magnetic proximity effects, and strain engineering. The realization of QAH states with multiple dissipationless edge and surface conduction channels defined by a Chern number $\mathcal{C}\ge 1$ was foreseen for the ferromagnetically ordered SnTe class of topological crystalline insulators (TCIs). From magnetotransport measurements on ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}(0.00\le x\le 0.08)$ (111) epitaxial thin films grown by molecular beam epitaxy on ${\mathrm{BaF}}_2$ substrates, hole-mediated ferromagnetism is observed in samples with $x\ge 0.06$ and the highest $T_{\mathrm{c}}\sim 7.5\mathrm{K}$ is inferred from an anomalous Hall behavior in ${\mathrm{Sn}}_{0.92}{\mathrm{Mn}}_{0.08}\mathrm{Te}$. The sizable anomalous Hall angle $\sim 0.3$ obtained for ${\mathrm{Sn}}_{0.92}{\mathrm{Mn}}_{0.08}\mathrm{Te}$ is one of the greatest reported for magnetic topological materials. The ferromagnetic ordering with perpendicular magnetic anisotropy, complemented by the inception of the anomalous Hall effect in the ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ layers for a thickness commensurate with the decay length of the top and bottom surface states, points at ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ as a preferential platform for the realization of QAH states in ferromagnetic TCIs.