The magnetic exchange interaction is one of the key factors governing the basic characteristics of magnetic systems. In contrast to the symmetric nature of the Heisenberg exchange interaction, the interfacial Dzyaloshinskii-Moriya interaction (DMI) generates an antisymmetric exchange interaction, which offers challenging opportunities in spintronics with intriguing antisymmetric phenomena. The role of the DMI, however, is still under debate, because largely distinct strengths of the DMI have been measured for different magnetic objects, particularly chiral magnetic domain walls (DWs) and nonreciprocal spin waves (SWs). In this paper, by carefully examining the measurement principles, we demonstrate that both the DWs and SWs experience the same strength of the DMI. The key factor in this demonstration is to identify the appropriate experimental conditions by excluding all possible artifacts that causes additional undesired symmetric and antisymmetric contributions in chiral DW dynamics. The present demonstration, therefore, verifies the universality of the DMI between different magnetic dynamics as an intrinsic exchange interaction and also, guarantees the compatibility of several DMI-measurement schemes recently proposed.

Exciting new work on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) shows the presence of nontrivial spin-orbit coupling effects as seen in spin-resolved angle-resolved photoemission spectroscopy data [K. Gotlieb et al., Science 362, 1271 (2018)]. Motivated by these observations we consider how the picture of spin-orbit coupling through local inversion symmetry breaking might be observed in cuprate superconductors. Furthermore, we examine two spin-orbit driven effects, the spin-Hall effect and the Edelstein effect, focusing on the details of their realizations within both the normal and superconducting states.

Wölfle and Balatsky [Phys. Rev. B 98, 104505 (2018)] have proposed a microscopic pairing mechanism for doped ${\mathrm{SrTiO}}_3$ (STO) based on the gradient coupling of electronic density to the soft transverse optical (TO) phonon mode. Since this coupling to TO phonons is usually weak, this conclusion is surprising, especially for a low-density superconductor such as STO, where the density of states is small. A crucial step in the argument made by Wölfle and Balatsky is that the displacement vector of the TO mode is not strictly perpendicular to the momentum vector, making a deformation coupling possible. We show that they have made a mistake in computing the eigenvector and have grossly overestimated this lack of orthogonality. When corrected, the coupling is negligible. We also use transport data to put upper bounds on the coupling constant which are much smaller than the estimate by Wölfle and Balatsky. Finally, we also object to their use of the Eliashberg equation when the phonon frequency is larger than the Fermi energy.

In our paper [Wölfle and Balatsky, Phys. Rev. B 98, 104505 (2018)] we presented a microscopic theory of superconductivity for doped ${\mathrm{SrTiO}}_3$ by proposing two pairing mechanisms acting simultaneously with relative strength depending on the closeness to the ferroelectric quantum critical point. The first mechanism rests on the dynamically screened Coulomb interaction, and the second assumed a coupling to the soft transverse optical phonon. In their Comment Ruhman and Lee point out an error in our estimate of the deformation potential coupling to the soft mode. We agree that this type of coupling cannot explain the gigantic isotope effect observed experimentally, so that a different coupling mechanism needs to be found. As for the first pairing mechanism, Ruhman and Lee maintain the view expressed in their paper [Ruhman and Lee, Phys. Rev. B 94, 224515 (2016).] that the energy range over which the usual longitudinal optical-phonon mediated interaction operates is limited by the Fermi energy. We object to this view and in this Reply present evidence that the cutoff energy is much larger. In a weak-coupling system such as ${\mathrm{SrTiO}}_3$ the cutoff is given by the energy beyond which quasiparticles cease to be well defined.

A planar Josephson junction with a normal metal attached on its top surface will form a hollow nanowire structure due to its three-dimensional nature. In such hollow nanowire structure, a magnetic flux induced by a small magnetic field (about 0.01T) will tune the system into topologically nontrivial phase. Therefore two Majorana zero modes will form at the ends of the nanowire. Through tuning the chemical potential of the normal metal, the topologically nontrivial phase can be obtained for almost all the energy within the band. Furthermore, the system can be conveniently tuned between the topologically trivial and nontrivial phases via the phase difference between the two superconductor bulks. Such device, manipulable through flux, can be conveniently fabricated into desired 2D networks. Finally, we also propose a cross-shaped junction realizing the braiding of Majorana zero modes through manipulating the phase differences.

We report the temperature-dependent optical conductivity and angle-resolved photoemission spectroscopy (ARPES) studies of the multiband iron-based superconductor ${\mathrm{Sr}}_{0.67}{\mathrm{Na}}_{0.33}{\mathrm{Fe}}_2{\mathrm{As}}_2$. Measurements were made in the high-temperature tetragonal paramagnetic phase, below the structural and magnetic transitions at $T_{\mathrm{N}}\simeq 125$ K in the orthorhombic spin-density-wave (SDW)-like phase and $T_r\simeq 42$ K in the reentrant tetragonal double-$\mathbf{Q}$ magnetic phase where both charge and SDW order exist, and below the superconducting transition at $T_c\simeq 10$ K. The free-carrier component in the optical conductivity is described by two Drude contributions: one strong and broad and the other weak and narrow. The broad Drude component decreases dramatically below $T_{\mathrm{N}}$ and $T_r$, with much of its strength being transferred to a bound excitation in the midinfrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone folding below $T_r$. Below $T_c$ the dramatic decrease in the low-frequency optical conductivity signals the formation of a superconducting energy gap. ARPES reveals holelike bands at the center of the Brillouin zone (BZ), with both electron- and holelike bands at the corners. Below $T_{\mathrm{N}}$, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; however, below $T_r$ the electronlike bands shift and split, giving rise to a low-energy excitation in the optical conductivity at $\simeq 20$ meV. The $C_2$ and $C_4$ magnetic states, with resulting spin-density-wave and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets but appears to have relatively little impact on the superconductivity in this material.

Recently, considerable attention has been paid to tune the emission using hybrid systems composed of layered transition-metal dichalcogenides and metal nanoparticles (NPs) since metal NPs have the ability to enhance and localize the incident electromagnetic field. Furthermore, these hybrid systems show great interest from the standpoint of fundamental science as it constitutes an atomic scale prototype of charge-transfer complexes. Here, we realized ${\mathrm{WS}}_2$–gold (Au) NPs hybrids by chemically growing Au NPs at the edges of the mechanically exfoliated bilayer ${\mathrm{WS}}_2$. The Au NPs significantly increase the light-matter interaction which has been studied through Raman and photoluminescence (PL) spectroscopy. A substantial enhancement of the PL intensity in the ${\mathrm{WS}}_2$–Au composite concerning the pristine ${\mathrm{WS}}_2$ has been observed, and it increases as the number and size of the Au NPs on ${\mathrm{WS}}_2$ is increased. Geometry-dependent modification of plasmon resonance energy of Au NP alters the coupling strength between the emission pathways of ${\mathrm{WS}}_2$ and the plasmon which is manifested by a change in relative intensity between trion $\left(X^{-}\right)$ and exciton $\left(X\right)$ emissions. We probe the mechanism of the PL intensity modulation through polarization-dependent measurements and simulation. We have demonstrated that, in ${\mathrm{WS}}_2$, the internal quantum efficiency increases and activation energy decreases due to coupling with Au NPs. Compared to pristine ${\mathrm{WS}}_2$, a faster change in optical band gap with temperature in ${\mathrm{WS}}_2$–Au may be due to enhancing electron-phonon interaction and lattice expansion in the latter. Our paper indicates the possibility to develop high performance transition-metal dichalcogenide-based photonic devices.

We assess several recently developed dispersion-corrected exchange-correlation functionals $[\mathrm{PBE}+\mathrm{VV}10\mathrm{L}$ of H. Peng and J. P. Perdew, Phys. Rev. B 95, 081105 (2017); $\mathrm{SG}4+\mathrm{VV}10\mathrm{m}$ of A. V. Terentjev et al., Computation 6, 7 (2018); and $\text{PBEsol}+\text{VV}10\text{s}$ of A. V. Terentjev et al., Phys. Rev. B 98, 214108 (2018)] for the adsorption of a noble-gas atom/monolayer as well as a graphene on the Cu(111), Pt(111), Pd(111), and Ag(111) close-packed surfaces. Most of these systems are characterized by weak interactions between the surface and the atom/monolayer, where the van der Waals interaction dominates. Here we investigate the above mentioned dispersion-corrected exchange-correlation functionals using atomic orbitals instead of plane waves applied in earlier works. We find that $\text{PBEsol}+\text{VV}10\text{s}$ is an optimal functional for such hybrid interfaces, being accurate for both the equilibrium distance and the adsorption energy and providing realistic potential-energy curves. Moreover, we also show that $\text{PBEsol}+\text{VV}10\text{s}$ and $\mathrm{SG}4+\text{VV}10\text{m}$ are both very accurate for the investigation of surface formation energies of all transition metals under consideration.

We use density functional theory to explore the possibility of making the semiconducting transition-metal dichalcogenide ${\mathrm{MoS}}_2$ ferromagnetic by introducing holes into the narrow Mo $d$ band that forms the top of the valence band. In the single impurity limit, the repulsive Coulomb potential of an acceptor atom and intervalley scattering lead to a twofold orbitally degenerate effective-mass-like $e^{\prime }$ state being formed from Mo $d_{x^2-y^2}$ and $d_{xy}$ states, bound to the $K$ and $K^{\prime }$ valence band maxima. It also leads to a singly degenerate $a_1^{\prime }$ state with Mo $d_{3z^2-r^2}$ character bound to the slightly lower lying valence band maximum at $\mathrm{\Gamma }$. Within the accuracy of our calculations, these $e^{\prime }$ and $a_1^{\prime }$ states are degenerate for ${\mathrm{MoS}}_2$ and accommodate the hole that polarizes fully in the local spin density approximation in the impurity limit. With spin-orbit coupling included, we find a single ion magnetic anisotropy of $\sim 5$ meV favoring out-of-plane orientation of the magnetic moment. Pairs of such hole states introduced by V, Nb, or Ta doping are found to couple ferromagnetically unless the dopant atoms are too close in which case the magnetic moments are quenched by the formation of spin singlets. Combining these exchange interactions with Monte Carlo calculations allows us to estimate ordering temperatures as a function of the dopant concentration $x$. For $x\sim 9\%$, Curie temperatures as high as 100 K for Nb and Ta and in excess of 160 K for V doping are predicted. Factors limiting the ordering temperature are identified and suggestions made to circumvent these limitations.

Quantum Hall stripe phases near half-integer filling factors $\nu \ge 9/2$ were predicted by Hartree-Fock (HF) theory and confirmed by discoveries of giant resistance anisotropies in high-mobility two-dimensional electron gases. A theory of such anisotropy was proposed by MacDonald and Fisher, although they used parameters whose dependencies on the filling factor, electron density, and mobility remained unspecified. Here, we fill this void by calculating the hard-to-easy resistivity ratio as a function of these three variables. Quantitative comparison with experiment yields very good agreement, which we view as evidence for the “plain vanilla” smectic stripe HF phases.

Electric multipole moments are the most fundamental properties of insulating materials. However, the general formulation of bulk multipoles has been a long-standing problem. The solution for the electric dipole moment was provided decades ago by King-Smith, Vanderbilt, and Resta. Recently, there have been attempts at generalizing Resta's formula to higher-order multipoles. We point out several issues in the recent proposals.

We propose many-body order parameters for bulk multipoles in crystalline systems, whenever the bulk multipole moments can be defined in terms of the nontrivial topology of the nested Wilson loop. The many-body order parameters are designed to measure multipolar charge distribution in a crystalline unit cell, and they match the localized corner charge originating from the multipoles when the symmetries quantizing the multipoles are protected. Our many-body order parameters provide a complementary view to the nested Wilson loop approaches and even go beyond, as our many-body order parameters are readily applicable to interacting quantum many-body systems. Furthermore, even when the symmetries quantizing multipoles are lost so that the nested Wilson loop spectrum does not exactly reproduce the physical multipole moments, our many-body order parameters faithfully measure the physical multipole moments, which is confirmed numerically during Thouless pumping processes. We provide analytic arguments and numerical demonstration of the order parameters for various higher-order insulators having bulk multipole moments. Finally, we discuss the applicability of our many-body order parameters in the cases where the Wannier gap is absent so that the bulk multiple moments cannot be defined in terms of the nested Wilson loop.

The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta [Phys. Rev. Lett. 80, 1800 (1998)], who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher multipole moments, e.g., quadrupole and octupole. We define $n\mathrm{th}$-order multipole operators whose expectation values can be used to calculate the $n\mathrm{th}$ multipole moment when all of the lower moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of $n-1\mathrm{st}$ multipole currents, and encode the adiabatic evolution of the system in the presence of an $n-1\mathrm{st}$ gradient of the electric field. Finally, we test our operators on a set of tight-binding models to show that they correctly determine the phase diagrams of topological quadrupole and octupole models, capture an adiabatic quadrupole pump, and distinguish a bulk quadrupole moment from other mechanisms that generate corner charges.

We report a first-principles study of Bi-based $3d\text{−}5d$ ordered double-perovskite oxides $\left({\mathrm{A}}_2{\mathrm{BB}}^{\prime }\mathrm{O}6\right)$ with a $3d$ atom (Fe) at the B site and $5d$ atoms (Re, Ir) at the ${\mathrm{B}}^{\prime }$ site while keeping highly polarizable ions $\left({\mathrm{Bi}}^{3+}\right)$ at the A site. We find that, under coherent heteroepitaxy, ${\mathrm{Bi}}_2{\mathrm{FeReO}}_6$ exhibits a strain-driven antiferromagnetic insulator to ferrimagnetic semimetal transition, while ${\mathrm{Bi}}_2{\mathrm{FeIrO}}_6$ shows a correlation driven ferromagnetic insulator to ferrimagnetic half-metal transition with calculated magnetic moments of 5 and $3{\mu }_B/\mathrm{f}.\mathrm{u}.$, respectively. These properties along with the low band gaps in the insulating phases make the compounds appealing for spintronics applications. Furthermore, in ${\mathrm{Bi}}_2{\mathrm{FeIrO}}_6$, the conduction and valence states are localized on different transition metal sublattices implying more efficient electron-hole separation upon photoexcitation, a desirable feature for photovoltaic applications.

Anatase ${\mathrm{TiO}}_2$ (a-${\mathrm{TiO}}_2)$ exhibits a strong x-ray absorption linear dichroism in the pre-edge, the XANES and the EXAFS at the titanium $K$ edge. In the pre-edge region, the behavior of the A1–A3 and B peaks originating from the $1s-3d$ transitions is due to the strong $p$-orbital polarization and strong $p-d$ orbital mixing. An unambiguous assignment of the pre-edge peak transitions is made in the monoelectronic approximation with the support of ab initio finite difference method calculations and spherical tensor analysis in quantitative agreement with the experiment. Our results suggest that several previous studies relying on octahedral crystal field splitting assignments are in accurate due to the significant p-d orbital hybridization induced by the broken inversion symmetry in a-${\mathrm{TiO}}_2$. It is found that A1 is mostly an on-site $3d-4p$ hybridized transition, while peaks A3 and B are nonlocal transitions, with A3 being mostly dipolar and influenced by the $3d-4p$ intersite hybridization, while B is due to interactions at longer range. Peak A2, which was previously assigned to a transition involving pentacoordinated titanium atoms, is shown to exhibit a quadrupolar angular evolution with incidence angle, which implies that its origin is primarily related to a transition to bulk energy levels of a-${\mathrm{TiO}}_2$ and not to defects, in agreement with theoretical predictions [Vorwerk et al., Phys. Rev. B 95, 155121 (2017)]. Finally, ab initio calculations show that the occurence of an enhanced absorption at peak A2 in defect-rich a-${\mathrm{TiO}}_2$ materials originates from defect-related $p$ density of states due to the formation of doubly ionized oxygen vacancies. The formation of peak A2 at almost the same energy for single crystals and nanomaterials is a coincidence while the origin is different. These results pave the way to the use of the pre-edge peaks at the Ti $K$ edge of a-${\mathrm{TiO}}_2$ to characterize the electronic structure of related materials and in the field of ultrafast x-ray absorption spectroscopy where the linear dichroism can be used to compare the photophysics along different axes.

We demonstrate a self-induced topological transition and the formation of topologically protected edge states in a two-dimensional array of coupled resonant cavities placed on a Kagome lattice with saturable nonlinearity introduced in the interconnecting bonds. The dynamic response of the structure is shown to be governed by an intensity-dependent band topology. Our findings uncover prospects for generating and controlling topologically nontrivial edge modes in nonlinear metasurfaces, and delineate a roadmap towards self-reconfigurable robust signal transport in various dynamic systems, ranging from acoustics to electronics and optics.

Although equilibrium spin currents (ESCs) may exist in materials with spin-orbit coupling, they are not transport currents and cannot lead to spin accumulation in the presence of time-reversal symmetry. It is for this reason that the detection of ESCs has remained elusive. Here we show that in a nanowire with spin-orbit coupling, breaking the time-reversal symmetry by a Zeeman field leads to a bulk equilibrium spin current which manifests itself in a sizable edge spin polarization, transverse to the Zeeman field. The net accumulated spin does not depend on specific properties of the wire ends, being fully determined by the bulk spin current. This bulk-boundary correspondence is a universal property that occurs in both the normal and superconducting states independently of the degree of disorder. The transverse edge spin polarization is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the induced superconducting gap. This leads to a hitherto unknown transverse magnetic susceptibility that can be much larger than the longitudinal, and it drastically changes the paramagnetic response of the nanowire.

We report high-resolution resonant inelastic x-ray scattering (RIXS) measurements of the collective spin fluctuations in three compositions of the superconducting cuprate system ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$. We have mapped out the excitations throughout much of the two-dimensional $(h,k)$ Brillouin zone. The spin fluctuations in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ are found to be fairly well described by a damped harmonic oscillator model, thus our data allows us to determine the full wave vector dependence of the damping parameter. This parameter increases with doping and is largest along the $(h,h$) line, where it is peaked near $(0.2,0.2)$. We have used a new procedure to determine the absolute wave vector dependent susceptibility for the doped compositions ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4(x=0.12,0.16)$ by normalizing our data to ${\mathrm{La}}_2{\mathrm{CuO}}_4$ measurements made with inelastic neutron scattering (INS). We find that the evolution with doping of the intensity of high-energy excitations measured by RIXS and INS is consistent. For the doped compositions, the wave vector dependent susceptibility is much larger at $(\frac{1}{4},\frac{1}{4})$ than at $(\frac{1}{2},0)$. It increases rapidly along the $(h,h)$ line towards the antiferromagnetic wave vector of the parent compound $(\frac{1}{2},\frac{1}{2})$. Thus, the strongest magnetic excitations, and those predicted to favor superconductive pairing, occur towards the $(\frac{1}{2},\frac{1}{2})$ position as observed by INS.