The sawtooth lattice shares some structural similarities with the kagome lattice and may attract renewed research interest. Here we report a comprehensive study on the physical properties of ${\mathrm{Fe}}_2{\mathrm{SiSe}}_4$, an unexplored member in the olivine chalcogenides with the sawtooth lattice of Fe. Our results show that ${\mathrm{Fe}}_2{\mathrm{SiSe}}_4$ is a magnetic semiconductor with band gap of 0.66 eV. It first undergoes an antiferromagnetic transition at ${\mathrm{T}}_{m1}=110$ K, then an ferrimagneticlike one at ${\mathrm{T}}_{m2}=50$ K, and finally a magnetic transition at ${\mathrm{T}}_{m3}=25$ K, which is likely driven by the thermal populations of spin-orbit manifold on the Fe sites. Neutron diffraction analysis reveals a noncollinear antiferromagnetic structure with propagation vector ${\mathbf{q}}_{\mathbf{1}}=(0,0,0)$ at ${\mathrm{T}}_{m2}<\mathrm{T}<{\mathrm{T}}_{m1}$. Interestingly, below ${\mathrm{T}}_{m2}$, an additional antiferromagnetic structure with ${\mathbf{q}}_{\mathbf{2}}=(0,0.5,0)$ appears, and ${\mathrm{Fe}}_2{\mathrm{SiSe}}_4$ exhibits a complex double-$\mathbf{q}$ magnetic structure which has never been observed in sawtooth olivines. Density functional theory calculations suggest this complex noncollinear magnetic structure may originate from the competing antiferromagnetic interactions for both intra- and interchain in the sawtooth lattice. Furthermore, band-structural calculations show that ${\mathrm{Fe}}_2{\mathrm{SiSe}}_4$ has quasi-flat-band features near the valence and conduction band structure. Our results have shown that ${\mathrm{Fe}}_2{\mathrm{SiSe}}_4$ could serve as a new material playground for further research on magnetic devices and the flat-band effect through chemical doping.

A combined experimental and theoretical study of the layered antiferromagnetic compound ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ in the ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type structure is presented. The heat capacity shows two transitions upon cooling: The first one at the Néel temperature $T_{\mathrm{N}}=55\mathrm{K}$ and a second one at $T_{\mathrm{N}2}=12\mathrm{K}$. Using magnetization measurements, we study the canting process of the Dy moments upon changing the temperature and can assign $T_{\mathrm{N}2}$ to the onset of the canting of the magnetic moments towards the [100] direction away from the $c$ axis. Furthermore, we found that the field dependence of the magnetization is highly anisotropic and shows a two-step process for $H\parallel 001$. We used a mean-field model to determine the crystalline electric field as well as the exchange interaction parameters. Our magnetization data together with the calculations reveal a moment orientation close to the [101] direction in the tetragonal structure at low temperatures and fields. Applying photoemission electron microscopy, we explore the (001) surface of the cleaved ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ single crystal and visualize Si- and Dy-terminated surfaces. Our results indicate that the Si-Rh-Si surface protects the deeper lying magnetically active Dy layers and is thus attractive for investigation of magnetic domains and their properties in the large family of ${\mathrm{LnT}}_2{\mathrm{Si}}_2$ materials.

Magnetic adatoms at surfaces of superconductors may induce localized bound states within the superconducting energy gap referred to as Yu-Shiba-Rusinov (YSR) states. We solve the Kohn-Sham-Dirac Bogoliubov–de Gennes equations within the fully relativistic multiple scattering Green's function method to study the nature of the YSR states for $3d$ magnetic impurities (Cr, Mn, Fe, and Co) placed on a pristine Nb(110) surface, as well as capped by a monolayer of Bi, Re, or Ir. First, we perform self-consistent relativistic calculations in the normal state and determine the direction of the easy axis and the magnetic anisotropy energy. Then we study the relation between the electronic structure in the normal state and the YSR states. We show that the YSR states can be categorized according to the energy-resolved singlet and triplet order parameters as normal, superconducting singlet, or induced triplet states. Finally, we demonstrate that the rotation of the adatom magnetic moment shifts the energy of the YSR states as a consequence of the spin orbit coupling. During this rotation, some branches of the YSR states might cross the Fermi energy, implying that at certain paths in the configuration space a peak can be found at zero energy.

We analyze from a microscopic point of view the thermoelectric transport properties of a type-I Weyl semimetal driven by electron-electron interactions mediated by virtual phonons, particularly the feasibility of entering a hydrodynamic regime. Considering also the effects of impurities and the absorption/emission of real phonons, electric and thermal conductivities are obtained. At temperatures $T$ above the Bloch-Grüneisen temperature $T_{\mathrm{BG}}$, virtual phonons behave similarly to real phonons, but the Lorenz ratio is modified by a constant prefactor dependent on the Fermi surface geometry. For temperatures below $T_{\mathrm{BG}}$, virtual phonons induce a $T^2$ dependence in the resistivities, opening a window where momentum-conserving interactions could dominate transport signatures. We find that the onset of such a hydrodynamic regime requires impurity scattering whose inverse relaxation time is one or two orders of magnitude smaller than realistic values, depending on the electron-phonon coupling strength.

We study the vibrational and electronic excitations in cubic iridium halides (${\mathrm{NH}}_4{)}_2{\mathrm{IrCl}}_6, {\mathrm{K}}_2{\mathrm{IrCl}}_6$, and ${\mathrm{K}}_2{\mathrm{IrBr}}_6$ by infrared reflectivity and transmission measurements of single crystals. All three compounds show optical excitations in the energy range of 0.5–0.8 eV, which can be ascribed to $j_{\mathrm{eff}}=\frac{3}{2}$ to $j_{\mathrm{eff}}=\frac{1}{2}$ transitions (spin-orbit excitons), and $t_{2g}$-to-$e_g$ excitations above $\sim 1$ eV. We observe at least two peaks due to spin-orbit excitons in the bromide and four peaks in both chlorides, suggesting local deviations from the cubic symmetry already at room temperature. We further show that the $e_g$ states lie at lower energies in the bromide compared to the chlorides, in agreement with density-functional band-structure calculations.

Flat bands play a central role in the presence of correlated phases in moiré and other modulated two-dimensional systems. In this paper, flat bands are shown to exist in uniaxially periodic strained graphene. Such strain should be produced for example by a substrate. The model is thus mapped into a one-dimensional effective Hamiltonian and this allows to find the conditions for having flat bands, i.e., a long-wavelength modulation only on each one of the bipartite graphene sublattices, while having a tagged strain field between neighboring carbon atoms. The origin of such flat bands is thus tracked down to the existence of topological localized wavefunctions at domain walls separating different regions, each with a nonuniform Su-Schriffer-Hegger model (SSH) type of coupling. Thereafter, the system is mapped into a continuum model allowing to explain the numerical results in terms of the Jackiw-Rebbi model and of pseudo-Landau levels. Finally, the interplay between the obtained flat bands and electron-electron interaction is explored through the Hubbard model. The numerical results within the mean-field approximation indicate that the flat bands induce Néel antiferromagnetic and ferromagnetic domains even for a very weak Hubbard interaction, while the repulsive Hubbard interaction results in an effective electron-electron attraction. Thus this paper provides a simple, analytically solvable but realistic model to understand the physical origin of flat bands, pseudo-Landau levels and their effects on the effective electron-electron interaction.

We construct a microscopic model based on superexchange theory for a moiré bilayer in chromium trihalides $(\mathrm{Cr}{X}_3,$ $X=\mathrm{Br},\mathrm{I})$. In particular, we derive analytically the interlayer Heisenberg exchange and the interlayer Dzyaloshinskii-Moriya interaction with arbitrary distances $\left(\mathit{x}\right)$ between spins. Importantly, our model takes into account sliding and twisting geometries in the interlayer $X\text{−}X$ hopping processes. Our approach can directly access the $\mathit{x}$-dependent interlayer exchange without large unit-cell calculations. We argue that deducing interlayer exchange by various sliding bilayers may lead to an incomplete result in a moiré bilayer. Using the ab initio tight-binding Hamiltonian, we numerically evaluate the exchange interactions in ${\mathrm{CrI}}_3$. We find that our analytical model agrees with previous comprehensive density functional theory studies. Furthermore, our findings reveal the important role of the correlation effects in the $X\text{'}\mathrm{s}$ $p$ orbitals, which give rise to a rich interlayer magnetic interaction with remarkable tunability.

We report a nuclear magnetic resonance study of the spin correlations in the spin-cluster-based mineral ${\mathrm{Na}}_2{\mathrm{Cu}}_3\mathrm{O}{\left({\mathrm{SO}}_4\right)}_3$ with magnetic fields ranging from 1 to 33 T. The long-range magnetic order is observed from both the sudden spectral broadening at $T_N$ and the critical slowing down behavior in the temperature dependence of spin-lattice relaxation rates $[1/T_1\left(T\right)]$. The hump behavior of $1/T_1\left(T\right)$ persists to ${\mu }_{0}H=7.25$ T, above which a spin excitation gap is observed from the thermally activated temperature dependence of $1/T_1$. The gap size shows a linear field dependence, whose slope and intercept respectively yield an effective magnetic moment of 2.54 ${\mu }_B$ and a 0.94-meV spin excitation gap under zero magnetic field. These results indicate the existence of short-range order and prominent easy-plane spin anisotropy, which are important for understanding the spin excitation spectrum in $A_2{\mathrm{Cu}}_3\mathrm{O}{\left({\mathrm{SO}}_4\right)}_3$.

We study the anomalous Hall effect (AHE) in tilted Weyl metals with Gaussian disorder due to the crossed $X$ and $\mathrm{\Psi }$ diagrams in this work. The importance of such diagrams to the AHE has been demonstrated recently in two-dimensional (2D) massive Dirac model and Rashba ferromagnets. It has been shown that the inclusion of such diagrams dramatically changes the total AHE in such systems. In this work, we show that the contributions from the $X$ and $\mathrm{\Psi }$ diagrams to the AHE in tilted Weyl metals are of the same order of the noncrossing diagram we studied in a previous work, but with the opposite sign. The total contribution of the $X$ and $\mathrm{\Psi }$ diagrams cancels the majority of the contribution from the noncrossing diagram in tilted Weyl metals, similar to the 2D massive Dirac model. We also discuss the difference of the contributions from the crossed diagrams between the 2D massive Dirac model and the tilted Weyl metals. At last, we discuss the experimental relevance of observing the AHE due to the $X$ and $\mathrm{\Psi }$ diagrams in type-I Weyl metal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$.

We formulate the spin contribution to the inverse Faraday effect of nonmagnetic metals. We deal with the role of the inversion symmetry, which forces all electronic bands to be at least twice degenerate at every point in the Brillouin zone. We show both analytically and numerically that our formulation of the inverse Faraday effect is invariant under unitary rotation within the doubly degenerate set of bands. In addition, we show the importance of resonance-like features in the band structure for the inverse Faraday effect. Our first-principles computed spin component of the inverse Faraday effect in a simple metal such as Au is reminiscent of its optical absorption, with a characteristic $d–s$ resonance in the optical spectrum.

The weak ferromagnet $\mathrm{Fe}{\mathrm{BO}}_3$ is well known for being a unique system for modeling and testing magnetic dynamics primarily due to relatively simple and localized magnetic structure and its interesting spin wave dynamics. At room temperature, it has slightly canted iron moments lying in the $a\text{−}b$ plane that result in a strong antiferromagnetic moment and a weak ferromagnetic moment, which results in pronounced ferromagnetic and antiferromagnetic spin modes. However, some previous studies have shown unusual low-temperature behavior that suggests a phase transition. By performing low-temperature magnetization measurements, both in bulk and on the mesoscale, we have observed a low-temperature magnetic texture in this material in which a large $c$-axis magnetization occurs. Magnetic fields along the $c$ axis as high as 1300 Oe were observed close to the sample's surface. This presents evidence for the onset of a Morin transition or another type of spin-reorientation phase transition wherein the ${\mathrm{Fe}}^{3+}$ moments would acquire a $c$-axis component to their canting below a critical temperature. The observation of this $c$-axis magnetization suggests that there is a different ground state in this material than has been previously expected and could be due to as yet unexplored intricacies of the Dzyaloshinskii-Moriya interaction.

Itinerant spin polaron and metallic ferromagnetism are theoretically predicted in the Mott insulator in semiconductor moiré superlattices doped below and above half filling of the narrow moiré band, respectively. The existence of a spin polaron can be directly identified from the kink in the dependence of the charge gap on the magnetic field.

We study the behavior of nonlinear spin motion in one-dimensional magnetic chain models. We explore how the various parameters affect the phase transitions between linear and nonlinear behaviors both with and without the Dzyaloshinskii-Moriya interaction (DMI). A Fourier analysis method is employed to investigate the modes in the structure with DMI. In all cases, we find that uniaxial anisotropy is necessary for the Fermi-Pasta-Ulam effect to appear. We investigate the DMI influence through the use of phase diagrams that examine the transitions between the three fundamental states: linear, Fermi-Pasta-Ulam, and ergodic. The DMI does make significant changes in these phase diagrams because it allows for additional routes for the distribution of energy.

We report thermal conductivity and Seebeck effect measurements on $\text{Mn}{\left({\text{Bi}}_{1-x}{\text{Sb}}_x\right)}_2{\text{Te}}_4$ (MBST) with $x=0.26$ under applied magnetic fields below $50\mathrm{K}$. Our data shows clear indications of the electronic structure transition induced by the antiferromagnetic (AFM) to ferromagnetic (FM) transition driven by applied magnetic field as well as significant positive magnetothermal conductivity in the Weyl semimetal state of MBST. Further, by examining the dependence of magnetothermal conductivity on field orientation for MBST and comparison with the magnetothermal conductivity of ${\text{MnBi}}_2{\text{Te}}_4$, we see possible evidence of a contribution to thermal conductivity due to Weyl fermions in the FM phase of MBST. From the temperature dependence of the Seebeck coefficient under magnetic fields for MBST, we also observed features consistent with the Fermi surface evolution from a hole pocket in the paramagnetic state to a Fermi surface with coexistence of electron and hole pockets in the FM state. These findings provide further evidence for the field-driven topological phase transition from an AFM topological insulator to a FM Weyl semimetal.

Semiconductor quantum dots have emerged as an especially promising platform for the generation of polarization-entangled photon pairs. However, it was demonstrated recently that the two-photon excitation scheme employed in state-of-the-art experiments limits the achievable degree of entanglement by introducing which-path information. In this work, the combined impact of two-photon excitation and longitudinal acoustic phonons on photon pairs emitted by strongly-confining quantum dots is investigated. It is found that phonons further reduce the achievable degree of entanglement even in the limit of vanishing temperature due to phonon-induced pure dephasing and phonon-assisted one-photon processes, which increase the reexcitation probability. In addition, the degree of entanglement, as measured by the concurrence, decreases with rising temperature and/or pulse duration, even if the excitonic fine-structure splitting is absent and when higher electronic states are out of reach. Furthermore, in the case of finite fine-structure splittings, phonons enlarge the discrepancy in concurrence for different laser polarizations.

Out-of-time-ordered correlators (OTOCs) help characterize the scrambling of quantum information and are usually studied in the context of nonintegrable systems. In this work, we compare the relaxation dynamics of OTOCs in interacting integrable and nonintegrable spin-$\frac{1}{2}$ XYZ chains in regimes without a classical counterpart. In both kinds of chains, using the presence of symmetries such as $U\left(1\right)$ and supersymmetry, we consider regimes in which the OTOC operators overlap or not with the Hamiltonian. We show that the relaxation of the OTOCs is slow (fast) when there is (there is not) an overlap, independently of whether the chain is integrable or nonintegrable. When slow, we show that the OTOC dynamics follows closely that of the two-point correlators. We study the dynamics of OTOCs using numerical calculations, and gain analytical insights from the properties of the diagonal and of the off-diagonal matrix elements of the corresponding local operators in the energy eigenbasis.

Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase, which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a “Landau-forbidden” continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

We study the effects of measurements, performed with a finite density in space, on the ground state of the one-dimensional transverse-field Ising model at criticality. Local degrees of freedom in critical states exhibit long-range entanglement, and as a result, local measurements can have highly nonlocal effects. Our analytical investigation of correlations and entanglement in the ensemble of measured states is based on properties of the Ising conformal field theory (CFT), where measurements appear as $(1+0)$-dimensional defects in the $(1+1)$-dimensional Euclidean spacetime. So that we can verify our predictions using large-scale free-fermion numerics, we restrict ourselves to parity-symmetric measurements. To describe their averaged effects analytically we use a replica approach, and we show that the defect arising in the replica theory is an irrelevant perturbation to the Ising CFT. Strikingly, the asymptotic scalings of averaged correlations and entanglement entropy are therefore unchanged relative to the ground state. In contrast, the defect generated by postselecting on the most likely measurement outcomes is exactly marginal. We then find that the exponent governing postmeasurement order parameter correlations, as well as the “effective central charge” governing the scaling of entanglement entropy, vary continuously with the density of measurements in space. Our work establishes connections between the effects of measurements on many-body quantum states and of physical defects on low-energy equilibrium properties.