Cobalt-doped ZnO nanoparticles (NPs) with different Co concentrations are investigated by means of $X$- and $Q$-band electron spin resonance (ESR) near liquid-helium temperature in both parallel and perpendicular modes. The high crystal quality of the NPs allows for the hyperfine-structure resolution within the single ${\mathrm{Co}}^{2+}$ ions' ESR powder spectra. Depending on cobalt concentration, common additional weak ESR lines are detected which are here demonstrated to arise from some ${\mathrm{Co}}^{2+}$ high-spin pairs with a distance of about 4–6 Å. ESR simulations show that these 3/2 spin pairs are weakly coupled by an isotropic Heisenberg Hamiltonian with either ferromagnetic or antiferromagnetic $J$ coupling constants, almost identical to those previously detected in bulk and microwire ZnO:Co. The presence of substantial (axial) single-ion anisotropy in ZnO:Co makes the different pairs' resonance positions strongly depending on the $J$ value. For resonance frequency $\nu$ in the microwave range, four cobalt pairs can satisfy the condition $\left|J\right|\sim h\nu /3$ to resonate at almost zero magnetic field. Such near-zero-field transitions notably resonate in the parallel ESR mode, which is the signature of the gapped nonlinear Zeeman effect, which is of particular interest for highly stable atomic-clock transitions.

We study a two-dimensional spin model obtained by “Higgsing” the rank-2 U(1) lattice gauge theory (LGT) with scalar or vector charges on the $L_x\times L_y$ square lattice under the periodic boundary condition (PBC). There are $p$ degrees of freedom per orbital and three orbitals per unit cell in the spin model. The resulting spin model is a stabilizer code consisting of three mutually commuting projectors that are, in turn, obtained by Higgsing the mutually commuting Gauss's law operators and the magnetic field operators in the underlying LGT. The spin model thus obtained is exactly solvable, with the ground state degeneracy (GSD) $D$ given by ${\text{log}}_{p}D=2+(1+{\delta }_{L_x\text{mod}p,0})(1+{\delta }_{L_y\text{mod}p,0})$ when $p$ is a prime number. Two types of dipole excitations, pristine and emergent, are identified. Both the monopoles and the dipoles are free to move, with restrictions on monopoles to hop only by $p$ lattice spacing along with certain directions. The monopole-monopole braiding phase depends on the separation of the $x$ or $y$ coordinates of the initial monopole positions, making it distinct from the ordinary anyon braiding statistics. The monopole-dipole braiding obeys the usual anyonic statistics. Despite the oddity, the monopole-monopole braiding phase can be understood as the Aharonov-Bohm phase of some emergent vector potentials.

Tungsten (W) is an important and versatile transition metal and has a firm place at the heart of many technologies. A popular experimental technique for the characterization of tungsten and tungsten-based compounds is x-ray photoelectron spectroscopy (XPS), which enables the assessment of chemical states and electronic structure through the collection of core level and valence band spectra. However, in the case of tungsten metal, open questions remain regarding the origin, nature, and position of satellite features that are prominent in the photoelectron spectrum. These satellites are a fingerprint of the electronic structure of the material and have not been thoroughly investigated, at times leading to their misinterpretation. The present work combines high-resolution soft and hard x-ray photoelectron spectroscopy (SXPS and HAXPES) with reflected electron energy loss spectroscopy (REELS) and a multitiered ab initio theoretical approach, including density functional theory (DFT) and many-body perturbation theory (G0W0 and $\mathrm{GW}+\mathrm{C}$), to disentangle the complex set of experimentally observed satellite features attributed to the generation of plasmons and interband transitions. This combined experiment-theory strategy is able to uncover previously undocumented satellite features, improving our understanding of their direct relationship to tungsten's electronic structure. Furthermore, it lays the groundwork for future studies into tungsten-based mixed-metal systems and holds promise for the reassessment of the photoelectron spectra of other transition and post-transition metals, where similar questions regarding satellite features remain.

The polarization dependence of the near edge x-ray absorption spectroscopy (XANES) is an element specific probe to the real-space distribution of the density of unoccupied states in solid-state materials. In this paper, we present Fe and As $K$-edge experiments of $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{M}_x\right)}_2{\mathrm{As}}_2$ ($M=\mathrm{Mn}$, Co, and $x=0.0$ and 0.08). The experiments reveal a strong polarization dependence of the probed XANES spectra, which concerns mainly an increase in the intensity of electronic transitions when the beam polarization is set out of the sample's $ab$ crystallographic plane. The results show that states with $p_z$-orbital character dominate the density of unoccupied states close to the Fermi level. Partial substitution of Fe by Co is shown to decrease the intensity anisotropy, suggesting that Co promotes electronic transfer preferentially to states with $p_z$-orbital character. On the other hand, Mn substitution causes the increase in the spectra $p_z$-orbital anisotropy, which is proposed to take place by means of an enhanced local $\mathrm{Fe}3d4p$ mixing, unveiling the role of $\mathrm{Fe}4p$ states in the localization of the $\mathrm{Fe}3d$ orbitals. Moreover, by comparing our results to previous experiments, we identify the relative mixing between Fe and pnictide $4p_{x,y,z}$ orbitals as a clear divide between the electronic properties of iron arsenides and selenides. Our conclusions are supported by multiple-scattering theory calculations of the XANES spectra and by quantum chemistry calculations of the Fe coordination electronic structure.

${\text{BaBiO}}_3$ compound is known as an archetype example of a three-dimensional Holstein model with the realization of the charge-density wave state at half filling and the superconducting state when doped. Although many works are devoted to the study the electron–phonon interaction in ${\text{BaBiO}}_3$, the influence of the electron–electron Hubbard interaction on the electronic structure in this system is still under investigation. In our work, we obtain analytical expression for the screened Coulomb potential, and along with the basis of ab initio-computed maximally localized Wannier orbitals, we quantitatively estimate the magnitude of the effective on-site Hubbard potential scrutinizing the effects of distortion of the crystal lattice. We show that a proper inclusion of the electron–electron interactions into the Holstein model significantly lowers the value of the underlying electron–phonon coupling. Finally, we find that the amplitudes of the repulsive electron–electron potential and its attractive counterpart mediated by the electron–phonon coupling are rather comparable. This may open a way for a realization of the intermediate phase of ${\text{BaBiO}}_3$ in terms of the Holstein-Hubbard model.

Quantum systems characterized by an interplay between several resonance scattering channels demonstrate very rich physics. To illustrate it we consider a multistage Kondo effect in nanodevices as a paradigmatic model for a multimode resonance scattering. We show that the channel crosstalk results in a destructive interference between the modes. This interplay can be controlled by manipulating the tunneling junctions in the multilevel and multiterminal geometry. We present a full-fledged theory of the multistage Kondo effect at the strong-coupling Fermi-liquid fixed point and discuss the influence of quantum interference effects to the quantum transport observables.

We have implemented the Bogoliubov–de Gennes equation in a screened Korringa-Kohn-Rostoker method for solving, self-consistently, the superconducting state for three-dimensional (3D) crystals including substitutional impurities. In this paper we extend this theoretical framework to allow for collinear magnetism and apply it to fcc Pb with 3D magnetic impurities. In the presence of magnetic impurities, there is a pair-breaking effect that results in in-gap Yu-Shiba-Rusinov (YSR) states which we decompose into contributions from the individual orbital character. We determine the spatial extent of these impurity states, showing how the different orbital character affects the details of the YSR states within the superconducting gap. Our work highlights the importance of a first-principles-based description which captures the quantitative details, making direct comparisons with experimental findings possible.

We present the low-temperature magnetic structures of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ combining neutron diffraction methods on polycrystalline and single-crystal samples containing the ${}^{160}\mathrm{Gd}$ isotope. In contrast to other members of the $\mathrm{Sr}L{n}_2{\mathrm{O}}_4$ family ($Ln=\text{lanthanide}$) this system reveals two long-range ordered magnetic phases, which our diffraction data unambiguously identify. Below $T_{\mathrm{N}1}=2.73$  K, a ${\mathbf{q}}_1=\left(000\right)$ magnetic structure is stabilized where ferromagnetic chains along the $c$ axis (space group $Pnam$) are coupled antiferromagnetically with neighboring chains. On cooling below $T_{\mathrm{N}2}=0.48$ K, an additional incommensurate component modulated by ${\mathbf{q}}_2=\left(000.42\right)$ evolves and is aligned along either of the perpendicular axes for the two different Gd sites, resulting in a fanlike magnetic structure. The identification of the particular Gd sites with the magnetic order observed with neutron diffraction is facilitated by a detailed analysis of the crystal fields acting on the sites. The observed ordering phenomena underline the complex multiaxial anisotropy in this system.

We study a class of non-Hermitian topological superconductors described by one-dimensional Aubry-André Harper and mosaic quasiperiodic models with $p$-wave superconducting pairing, where the non-Hermiticity is introduced by on-site complex quasiperiodic potentials. We generalize two topological invariants, one is based on the transfer matrix method and the other is the generalized Majorana polarization, to characterize the topological superconducting phases and verify the existence of Majorana zero modes in non-Hermitian quasiperiodic superconductors. By combing the Lyapunov exponent, the fractional dimension of wave functions, and topological invariants, we investigate the localization phenomena, topological superconductivity, and topological phase transitions. In the non-Hermitian Aubry-André Harper model with $p$-wave pairing, the system undergoes an extended-critical-localized phase transition with increasing the complex phase. The localization transition is consistent with the topological phase transition and unconventional real-complex transition of eigenenergy. In the non-Hermitian mosaic model, we provide an analytical expression of mobility edges and prove the intrinsic relation between the mobility edges and unconventional real-complex transitions. Our discoveries unveil the richness of topological and localization phenomena in non-Hermitian quasicrystals with $p$-wave pairing.

We present a unifying picture of the magnetic in-plane anisotropies of two-dimensional superconductors based on transition metal dichalcogenides. The symmetry considerations are first applied to constrain the form of the conductivity tensor. We hence conclude that the twofold periodicity of transport distinct from the planar Hall-related contributions requires a tensor perturbation. At the same time, the sixfold periodic variation of the critical field results from the Rashba spin-orbit coupling on a hexagonal lattice. We have considered the effect of a weak tensor perturbation on the critical field, gap function, and magnetoconductivity. The latter is studied using the time-dependent Ginzburg-Landau phenomenology. The common origin of the $\pi$ periodicity in transport and thermodynamics properties is identified. The scheme constructed here is applied to describe the existing theoretical scenarios from a unified point of view. This allows us to single out the differences and similarities between the suggested approaches.

The nontrivial topology in the layered ${\text{FeTe}}_{0.55}{\text{Se}}_{0.45}$ superconductor has been suggested by both theory and experiment to be strongly dependent on the Te concentration. Motivated by this together with the Te fluctuations expected from alloy disorder, we develop a simple layered model for a strong topological insulator that allows us to describe a scenario where topologically trivial domains permeate the sample. We refer to such a phase as topological domain disordered and study the local density (LDOS) of the topological surface states that can be measured using scanning tunneling spectroscopy (STS) in this phase. We find that topologically trivial domains on the surface, where one would expect the topological surface state to be absent, appear as regions of suppressed LDOS surrounded by domain walls with enhanced LDOS. Furthermore, we show that studying the energy dependence of the STS should allow us to distinguish the topologically trivial parts of the surface from other forms of disorder. Finally, we discuss implications of such local disappearance of the topological surface states for the observation of Majorana modes in vortices.

Halide perovskites are perceived to be a promising class of materials for optoelectronics, spin orbitronics, and topological electronics due to the presence of strong spin-orbit coupling and polarization field. Here, we develop a Hamiltonian using quasidegenerate perturbation theory to describe polarization field driven band structures and unique topological phases such as Dirac semimetallic rings for a universal class of halide perovskites including both inorganic and hybrid members. The spin textures obtained through this theoretical model captures minute effects of polarization and hence can be used as a modern tool to determine the polarization field directions which have a significant influence on spin orbitronics. The analysis brings out the concepts of hybrid spin textures intermixing the effects of valence and conduction bands under topological quantum phase transitions and spin texture binaries where alignment of the spins are reversed between domains in the momentum space with sharp boundaries. The results are validated through density-functional calculations.

The development of applications based on metallic nano-objects requires an extensive knowledge of their vibrational properties. Its size, shape, materials, or even crystallinity have a strong influence on the vibrational frequencies of a nano-object. It is also known that the coupling with environment has a strong effect on the lifetime of its resonating modes. However, the impact of the contact between a nano-object and its substrate still requires further investigation. Here we report on the vibrational response of gold disks for different contact area with a silicon substrate. The investigation of the quality factor of the first thickness mode of the disks highlights an important energy transfer from the disks to the substrate. The impact of the size of the contact area on the frequencies of the radial eigenmodes is also reported both experimentally and numerically. Finally, it is shown that such objects can be excited by acoustic waves propagating from the substrate. These findings display the possibility to use nanodisks to develop acoustic microscopy at the nanoscale.

The interplay of nontrivial band topology and magnetism gives rise to a series of exotic quantum phenomena, such as the emergent quantum anomalous Hall (QAH) effect and topological magnetoelectric effect. Many of these quantum phenomena have local manifestations when the global symmetry is broken. Here, we report local signatures of the thickness-dependent topology in intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ (MBT), using scanning tunneling microscopy and spectroscopy on molecular beam epitaxy grown MBT thin films. A thickness-dependent band gap is revealed, which we reproduce with theoretical calculations. Our theoretical results indicate a topological quantum phase transition beyond a film thickness of one monolayer, with alternating QAH and axion insulating states for odd and even layers, respectively. At step edges, we observe localized electronic states, in general agreement with axion insulator and QAH edge states, respectively, indicating topological phase transitions across the steps. The demonstration of thickness-dependent topological properties highlights the role of nanoscale control over novel quantum states, reinforcing the necessity of thin film technology in quantum information science applications.

The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to the competition between on-site Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of possessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multiband Hubbard model and performing SOC tunable density functional theory$+U$ calculations on prototypes ${\mathrm{SrIrO}}_3$ and ${\mathrm{CaIrO}}_3$ and extending the analysis to other isostructural and isovalent compounds, we present eight quantum phases that can be observed in the family of low-spin $d^5$ perovskites. In the cubic configuration, the $U$-SOC phase diagram shows stabilization of nonmagnetic metal phase in the weak $U$ regime irrespective of the strength of SOC with the doubly degenerate $t_{2\mathrm{g}}\text{−}{J}_{1/2}$ states occupying the Fermi surface. However, the system become ferromagnetic metal with increasing $U$ while the SOC is maintained low. As the SOC increases, the moderate and higher values of $U$ makes the transition to an antiferromagnetic metal and eventually to an antiferromagnetic insulating state. The ${\mathrm{GdFeO}}_3$-type orthorhombic distortion through tilting and rotation of the octahedra reform the $t_{2\mathrm{g}}$ states through orbital intermixing to introduce a noncollinear spin arrangement. In the weak correlation regime, the nonmagnetic metal phase transform to ferromagnetic metal phase for weak SOC and an invariant Dirac semimetal phase for the strong SOC. On increasing the correlation strength, the ferromagnetic metal phase becomes insulating while the Dirac semimetal phase becomes a canted antiferromagnetic metal and finally transform to the canted antiferromagnetic insulating phase. Interestingly, in the higher $U$ and higher SOC regimes the normal-spin $\left(S_z\right)$ component vanishes to form a pure coplanar spin arrangement. The presence of several soft phase boundaries makes the family of $d^5$ perovskites an ideal platform to study electronic and magnetic phase transitions under external stimuli.

${\mathrm{ReS}}_2$, a group VII transition metal dichalcogenide (TMD), bears immense prospect in optoelectronic, thermoelectric, catalytic, and energy storage applications. Its distorted structure and significant in-plane anisotropy introduce extra degree of freedom but, on the other hand, make it challenging to determine the absolute characteristics of the material. Here, through experimental and theoretical analysis, we present additional phonon modes in the Raman spectrum of layered ${\mathrm{ReS}}_2$ which, in literature, are regarded as ambiguous modes arising due to either double resonance or defects. However, we demonstrate that these additional phonon modes arise from the crystal symmetry. This report proves the most followed notion of a layer-independent monolayer (ML)-based unit cell of ${\mathrm{ReS}}_2$ to be misleading. We further demonstrate that the observed additional phonon modes are driven by unique layer-dependent variations in the crystal symmetry. Moreover, layer-parity-dependent splitting of $E_g^1$ mode and inversion symmetry breaking are discussed in detail. Such layer-dependent features have remained largely ignored in the literature. The results presented here may open new avenues for the application of this material and resolve several contradictions in its properties including the significance of stacking order, layer-dependent crystal symmetry, and shifting of Raman modes.

Based on first-principles calculations and symmetry analysis, we predict atomically thin ($1-N$ layers) $2H$ group-VIB transition metal dichalcogenides (TMDs) $M{X}_2$ ($M$ = Mo, W; $X$ = S, Se, Te) are large-gap higher-order topological crystalline insulators (HOTCIs) protected by $C_3$ rotation symmetry. We explicitly demonstrate the nontrivial topological indices and the existence of hallmark corner states with quantized fractional charge for these familiar TMDs with a large bulk optical band gap ($1.64\text{–}1.95\mathrm{eV}$ for the monolayers), which would facilitate the experimental verification and exploration of the HOTCI states. Furthermore, we find that the well-defined corner states exist in the triangular finite-size flakes with armchair edges of the atomically thin ($1-N$ layers) $2H$ group-VIB TMDs, and the corresponding quantized fractional charge is the number of layers $N$ modulo three. The fractional corner charge will double when spin degree of freedom is taken into account.

Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result allows one to obtain the finite-size and finite-temperature partition function and to show that there are no thermal phase transitions.

The quest for a Ni-based oxide analog to cuprate ${\mathrm{Cu}}^{2+}\left(d^9\right)$ superconductors was long known to require a reduced form of ${\mathrm{Ni}}^{1+}\left(d^9\right)$ as in $A^{3+}{\mathrm{Ni}}^{1+}{\mathrm{O}}_2$, being an extremely oxygen-poor form of the usual $A^{3+}{\mathrm{Ni}}^{3+}{\mathrm{O}}_3$ compound. Through $\mathrm{Ca}{\mathrm{H}}_2$ chemical reduction of a parent $R^{3+}{\mathrm{Ni}}^{3+}{\mathrm{O}}_3$ perovskite form, superconductivity was recently achieved in Sr-doped $\mathrm{NdNi}{\mathrm{O}}_2$ on a $\mathrm{SrTi}{\mathrm{O}}_3$ substrate. Using density functional theory (DFT) calculations, we find that stoichiometric $\mathrm{NdNi}{\mathrm{O}}_2$ is significantly unstable with respect to decomposition into $\frac{1}{2}\left[{\mathrm{Nd}}_2{\mathrm{O}}_3+\mathrm{NiO}+\mathrm{Ni}\right]$ with exothermic decomposition energy of +176 meV/atom, a considerably higher instability than that for common ternary oxides. This poses the question of whether the stoichiometric $\mathrm{NdNi}{\mathrm{O}}_2$ nickelate compound used extensively to model the electronic band structure of the Ni-based oxide analog to cuprates, and found to be metallic, is the right model for this purpose. To examine this, we study via DFT the role of the common H impurity expected to be present in the process of chemical reduction needed to obtain $\mathrm{NdNi}{\mathrm{O}}_2$. We find that H can be incorporated exothermically, i.e., spontaneously in $\mathrm{NdNi}{\mathrm{O}}_2$, even from ${\mathrm{H}}_2$ gas. In the concentrated limit, such impurities can result in the formation of a hydride compound, $\mathrm{NdNi}{\mathrm{O}}_2\mathrm{H}$, which has significantly reduced instability relative to hydrogen-free $\mathrm{NdNi}{\mathrm{O}}_2$ (decomposition energy of +80 meV/atom instead of +176 meV/atom). Interestingly, the hydrogenated form has lattice constants similar to those of the pure form (leading to comparable x-ray diffraction patterns), but unlike the metallic character of $\mathrm{NdNi}{\mathrm{O}}_2$, the hydrogenated form is predicted to be a wide gap insulator, thus requiring doping to create a metallic or superconducting state, just like cuprates, but unlike unhydrogenated nickelates. While it is possible that hydrogen would be eventually desorbed, the calculation suggests that pristine $\mathrm{NdNi}{\mathrm{O}}_2$ is hydrogen stabilized. One must exercise caution with theories predicting new physics in pristine stoichiometric $\mathrm{NdNi}{\mathrm{O}}_2$ as it might be an unrealizable compound. Experimental examination of the composition of real $\mathrm{NdNi}{\mathrm{O}}_2$ superconductors and the effect of hydrogen on the superconductivity is called for.