We explore the interplay between topology and eigenmodes by changing the stabilizing mechanism of skyrmion lattices (skX). We focus on two prototypical ultrathin films hosting a hexagonal [Pd/Fe/Ir(111)] and a square [Fe/Ir(111)] skyrmion lattice, which can both be described by an extended Heisenberg Hamiltonian. We first examine whether the Dzyaloshinkskii-Moriya, or the exchange interaction as the leading energy term affects the modes of the hexagonal skX of Pd/Fe/Ir(111). In all cases, we find that the lowest-frequency modes correspond to internal degrees of freedom of individual skyrmions, and suggest a classification based on azimuthal and radial numbers $(l,p)$, with up to $l=6$ and $p=2$. We also show that the gyration behavior induced by an in-plane field corresponds to the excitation of $l=1$ deformation modes with varying radial numbers. Second, we examine the square lattice of skyrmions of Fe/Ir(111). Its stabilization mechanism is dominated by the four-spin interaction. After relaxation, the unit cell does not carry a topological charge, and the eigenmodes do not correspond to internal skyrmion deformations. By reducing the four-spin interaction, the integer topological charge is recovered, but the charge carriers do not possess internal degrees of freedom, nor are they separated by energy barriers. We conclude that a four-spin dominated Hamiltonian does not yield skyrmion lattice solutions and that, therefore, a nontrivial topology does not imply the existence of skyrmions.

We present the effect of uniaxial stress on the magnetic stripes in the cuprate system ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ with $x=0.115$, previously found to have a stress-induced enhancement in the superconducting transition temperature. By means of neutron scattering, we confirm that the static stripes are suppressed by stress, pointing towards a trade-off between superconductivity and static magnetism, in direct agreement with previously reported muon spin rotation measurements. Additionally, we show that some of the reduced weight in the elastic channel appears to have moved to the inelastic channel, while we can exclude the opening of a spin gap down to an energy of 1 meV. Moreover, a stress-induced momentum shift of the fluctuations towards the typical 1/8 value of commensurability is observed, while no change in periodicity is seen in the static stripe signal. These results impose a strong constraint on the theoretical interpretation of stress-enhanced superconductivity in cuprate systems.

We investigated polyhedral π-conjugated molecules with threefold rotation symmetry, which can be suitable building blocks for both Dirac cones and a topological flat-band system. The two dimensional network structures of such molecules can be characterized by intra- and intermolecular interactions. We constructed tight binding models of these structures by systematically changing the intra- $\left(t_0\right)$ and intermolecular $\left(t_1\right)$ transfer integrals as independent parameters. The degree of freedom for the interactions provides a topological flat band and a massless or massive Dirac cone. We analyzed the topological features and origins of the flat band and Dirac cone of a molecule-based triangular lattice.

The interplay between the Kondo screening of quantum impurities (by the electronic channels to which they couple) and the interimpurity RKKY interactions (mediated by the same channels) has been extensively studied. However, the effect of unidirectional channels (e.g., chiral or helical edge modes of 2D topological materials) which greatly restrict the mediated interimpurity interactions, has only more recently come under scrutiny, and it can drastically alter the physics. Here we take Wilson's numerical renormalization group (NRG), the most established numerical method for treating quantum impurity models, and extend it to systems consisting of two impurities coupled at different locations to unidirectional channel(s). This is challenging due to the incompatibility of unidirectionality with one of the main ingredients in NRG—the mapping of the channel(s) to a Wilson chain—a tight-binding chain with the impurity at one end and hopping amplitudes which decay exponentially with the distance. We bridge this gap by introducing a “Wilson ladder” consisting of two coupled Wilson chains, and demonstrate that this construction successfully captures the unidirectionality of the channel(s), as well as the distance between the two impurities. We use this mapping in order to study two Kondo impurities coupled to a single chiral channel, showing that all local properties and thermodynamic quantities are indifferent to the interimpurity distance, and correspond to two separate single-impurity models. Extensions to more impurities and/or helical channels are possible.

The kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs})$ have attracted enormous interest as they exhibit an intertwined charge density wave (CDW) and superconductivity (SC). We report optical studies of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ across the whole family. With increasing alkali-metal atom radius from K to Cs, the CDW gap ${\mathrm{\Delta }}_{\text{CDW}}$ increases monotonically, whereas $T_{\text{CDW}}$ first rises and then drops, failing to establish a scaling relation with ${\mathrm{\Delta }}_{\text{CDW}}$. While the Fermi surface gapped by the CDW grows, $T_c$ is elevated in $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$, indicating that the interplay between the CDW and SC is not simply a competition for the density of states near $E_{\text{F}}$. More importantly, we observe an enhancement of electronic correlations in $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$, which suppresses the CDW but enhances SC, accounting for all the above peculiar observations. Our results suggest electronic correlations as an important factor in manipulating the CDW and its entanglement with SC in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$.

This paper presents a simple formalism for calculating x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) that has as input orbital-resolved density of states from a single-particle or many-body ab initio calculation and is designed to capture itinerant like features. We use this formalism to calculate both the XAS and RIXS with input from density functional theory (DFT) and $\mathrm{DFT}+\mathrm{DMFT}$ for the recently studied reduced valence nickelates $R_4{\mathrm{Ni}}_3{\mathrm{O}}_8$ and $R{\mathrm{NiO}}_2$ ($R=\text{rare earth}$), and these results are then contrasted with those for the cuprate ${\mathrm{CaCuO}}_2$ and the unreduced nickelate $R_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. In contrast to the unreduced $R_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$, the reduced valence nickelates as well as the cuprate show strong orbital polarization due to the dominance of $x^2-y^2$ orbitals for the unoccupied $3d$ states. We also reproduce two key aspects of a recent RIXS experiment for $R_4{\mathrm{Ni}}_3{\mathrm{O}}_8$: (i) a charge-transfer feature between $3d$ and oxygen $2p$ states whose energy we find to decrease as one goes from $R{\mathrm{NiO}}_2$ to $R_4{\mathrm{Ni}}_3{\mathrm{O}}_8$ to the cuprate, and (ii) an energy-dependent polarization reversal of the fluorescence line that arises from hybridization of the unoccupied $3z^2-r^2$ states with $R 5d$ states. We end with some implications of our results for the nature of the $3d$ electrons in reduced valence nickelates.

There is growing interest in using multiterminal Josephson junctions (MTJJs) as a platform to artificially emulate topological phases and to investigate superconducting mechanisms such as multiplet Cooper pairings. Current experimental signatures in MTJJs have led to conflicting interpretations of the salient features. In this work, we report a collaborative experimental and theoretical investigation of graphene-based four-terminal Josephson junctions. We observe resonant features in the differential resistance maps that resemble those ascribed to multiplet Cooper pairings. To understand these features, we model our junctions using a circuit network of resistively and capacitively shunted junctions (RCSJs). We find that the RCSJ model successfully reproduces the observed multiplet features. Therefore, our study suggests that differential resistance measurements alone are insufficient to conclusively distinguish resonant Andreev reflection processes from semiclassical circuit-network effects.

Terahertz nonlinear optics is a viable method to interrogate collective phenomena in quantum materials spanning ferroelectrics, charge-density waves, and superconductivity. In superconductors this includes the Higgs amplitude and Josephson phase modes. We have investigated the nonlinear $c$-axis response of optimally doped ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$ using high-field THz time domain spectroscopy at field strengths up to $\sim 80$ kV/cm. With increasing field, we observe a distinct redshift of the Josephson plasma edge and enhanced reflectivity (above the plasma edge) arising from third harmonic generation. The nonmonotonic temperature-dependent response is consistent with nonlinear drive of the Josephson plasma mode (JPM) as verified with comparison to theoretical expectations. Our results add to the understanding that, using THz light, the JPM (in addition to the Higgs mode) provides a route to interrogate and control superconducting properties.

We study quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasiparticle spreading under a field chosen randomly from binary values $\pm h$ at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasiparticle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with $\pm h$.

$\mathrm{Ba}R\mathrm{Fe}{\mathrm{O}}_4$ compounds containing magnetic rare-earth ions ($R=\mathrm{Yb}$, Tm) were prepared by a conventional solid-state method in air. We present detailed measurements of magnetic properties (specific heat, magnetic susceptibility) to demonstrate the presence of three successive magnetic phase transitions (at $T_{\mathrm{N}1}$, $T_{\mathrm{N}2}$, and $T_3$) in both compounds and employed neutron diffraction to determine the magnetic structures. Both compounds are isostructural (orthorhombic space group $Pnma$) and magnetic ions form rings and chains along the $b$ direction. All magnetic structures are incommensurate with a propagation vector $\mathbf{k}=\left(0,0,k_z\right)$. Magnetic ordering of ${\mathrm{Fe}}^{3+}$ ions occurs at $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$, where two different irreducible representations (irreps) order. Below $T_{\mathrm{N}1}$, there is a collinear spin-density wave with ordered ${\mathrm{Fe}}^{3+}$ moments along the chain direction ($b$ axis). Below $T_{\mathrm{N}2}$, this component remains stable and an additional component inside the $ac$ plane appears. Each Fe chain adopts a collinear antiferromagnetic structure with a constant magnetic phase. The two Fe rings in the unit cell have a different chirality and a noncollinear coupling. The mixing of two irreps leads to a cycloidal spiral magnetic structure that allows spin-induced ferroelectric polarization at $T_{\mathrm{N}2}$. With the presence of modulated components both perpendicular and along the propagation vector $\mathbf{k}$, the magnetic structure can be viewed as a sum of a helix and a cycloid structure. For ${\mathrm{BaTmFeO}}_4$, the magnetic structure has a larger cycloidal contribution and the dielectric constant ε exhibits a small peak at $T_{\mathrm{N}2}$. ${\mathrm{Yb}}^{3+}$ moments order at $T_3$ with each Yb chain having a constant magnetic phase and a collinear antiferromagnetic structure stabilized by $4f-4f$ electron-exchange interactions. In contrast, no constant magnetic phase is observed at the Tm chains. Below $T_3$, magnetic order of Tm2 ions is induced by $3d-4f$ electron-exchange interactions and Tm1 ions remain disordered down to the lowest measured temperature $T=1.6\mathrm{K}$ due to frustration of magnetic exchange interactions. The obtained magnetic structures are compared with those of ${\mathrm{BaYFeO}}_4$.

The recently synthesized ${\mathrm{SrH}}_{22}$, with a rich amount of ${\mathrm{H}}_2$ units, is predicted with low superconductivity, since two hydrogen (H) atoms in ${\mathrm{H}}_2$ units are inclined to stay together by forming a well-known sigma bond, where H electrons tend to occupy the low-lying energy level far below the Fermi energy, resulting in a less H populated Fermi surface. Of particular interest, for ${\mathrm{SrH}}_{22}$ or other similar ${\mathrm{H}}_2$-rich hydrides, is to optimize the H electron density of states in the search for high superconductivity. Here, via the strategy of bringing an additional metal element into the binary hydride, in combination with our developed global structure-searching method, we predict a ternary hydride of ${\mathrm{YSrH}}_{22}$. Compared with the parent hydride of ${\mathrm{SrH}}_{22}$, the H electron density of states at the Fermi level of ${\mathrm{YSrH}}_{22}$ is significantly enhanced, due to the favorable charge transfer from metal elements, such as Y, to the antibonding state of the sigma bond of ${\mathrm{H}}_2$, where such a bond is broken and H electrons come back to the Fermi surface. Our in-depth analysis indicates that this hydride could be viewed as a substitutional alloy superhydride of $(\mathrm{Y},\mathrm{Sr}){\mathrm{H}}_{11}$ with an estimated superconducting critical temperature $T_c$ of 240 K at 175 GPa, which is much higher than that of ${\mathrm{SrH}}_{22}$ ($T_c=21\mathrm{K})$ and ${\mathrm{LaH}}_{11}$ ($T_c=13\mathrm{K}$) both at 200 GPa. Our current findings not only offer a platform to tune the superconductivity of binary superhydrides ${\mathrm{SrH}}_{22}$ and ${\mathrm{LaH}}_{11}$, via the strategy of metal element doping, but also provide a roadmap in the search for high superconductivity, even toward room-temperature superconductivity, in the family of ternary alloy superhydrides.

The lattice dynamics of oxygen-doped ${\mathrm{Nd}}_2\mathrm{Ni}{\mathrm{O}}_{4+\delta }$ is explored by a combination of single-crystal neutron spectroscopy, ab initio molecular dynamics (AIMD), and harmonic phonon calculations using density functional theory. The inelastic response computed from AIMD finds better correspondence with the experimental inelastic neutron spectra than the harmonic phonon calculations. The comparison of experimental and simulated data indicates that the presence of extra oxygen in interstitial sites leads to marked differences in the dynamics of the system compared to the stoichiometric parent compound. In particular, a nondispersive scattering signal was detected below 15 meV in all the experimental spectra in the $\left(ab\right)$ plane. Its origin has been rationalized as an important incoherent scattering from Nd atoms, which emerges from in-plane atomic self-motions in the ${\mathrm{Nd}}_2{\mathrm{O}}_{2+\delta }$ rock-salt layers. The presence of additional interstitial oxygen atoms both dampens the long-range lattice dynamics as well as enhances oxygen and neodymium anharmonic displacements. The experimental observation of coherent and incoherent responses allows assessing the effect of interstitials on the vibrations of the whole crystal as well as on the dynamics of each atom independently.

The nature of the superconducting order parameter in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ has generated intense interest in recent years. Since the superconducting gap is very small, high-resolution methods such as scanning tunneling spectroscopy might be the best chance to directly resolve the gap symmetry. Recently, a Bogoliubov quasiparticle interference imaging (BQPI) experiment has suggested that the $d_{x^2-y^2}$ gap symmetry is appropriate for ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. In this work, we use a material-specific theoretical approach based on Wannier functions of the surface of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ to calculate the continuum density of states as detected in scanning tunneling microscopy experiments. We examine several different proposed gap order parameters and calculate the expected BQPI pattern for each case. Comparing to the available experimental data, our results suggest that a $s^{\prime }+i{d}_{xy}$ gap order parameter is the most probable state, but the measured BQPI patterns still display features unaccounted for by the theory for any of the states currently under discussion.

We theoretically investigate, within Schwinger-boson mean-field theory, the transition from a gapped ${\mathbb{Z}}_2$ quantum spin liquid, in a $J_1\text{−}{J}_2$ Heisenberg spin-$\frac{1}{2}$ system in a honeycomb lattice, to a chiral ${\mathbb{Z}}_2$ spin-liquid phase under the presence of time-reversal symmetry-breaking scalar chiral interaction (with amplitude $J_{\chi }$). We numerically obtain a phase diagram of this $J_1\text{−}{J}_2\text{−}{J}_{\chi }$ system, where different ground states are distinguished based on the gap and the nature of excitation spectrum, topological invariant of the excitations, the nature of spin-spin correlation, and the symmetries of the mean-field parameters. The chiral ${\mathbb{Z}}_2$ state is characterized by the nontrivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to a large thermal Hall coefficient.

Recent advances in fabrication of two-dimensional materials and their moiré heterostructures have opened up new avenues for realization of ground-state excitonic insulators, where the structure spontaneously develops a finite interlayer electronic polarization. We propose and analyze a scheme where an optically generated intralayer exciton is screened by excitations out of the excitonic insulator to form interlayer polarons. Using quantum Monte Carlo calculations we first determine the binding energy of the biexciton state composed of inter- and intralayer excitons, which plays a central role in understanding polaron formation. We describe the excitations out of the ground-state condensate using BCS theory and use a single interacting-quasiparticle-pair excitation Ansatz to describe dynamical screening of optical excitations. Our predictions carry the hallmarks of the excitonic insulator excitation spectrum and show how changing the interlayer exciton binding energy by increasing the layer separation modifies the optical spectra.

We study plasmonic excitations in the Kane-Mele model, a two-dimensional ${\mathbb{Z}}_2$ topological insulator on the honeycomb lattice, using the random phase approximation (RPA). In the topologically nontrivial phase, the model has conducting edge states that traverse the bulk energy gap and display spin-momentum locking. Such a state of matter is called the quantum spin hall (QSH) phase, which is robust against time-reversal (TR) invariant perturbations. We find that in the QSH phase, gapless spin-polarized plasmons can be excited on the edges of the system. The propagation of these plasmons is chiral for each individual spin component and shows spin-momentum locking for both spin components on the same edge. Moreover, we study the effect of external magnetic fields on the gapless edge plasmons. Specifically, out-of-plane magnetic fields delocalize edge plasmons propagating in one direction without affecting the other one, while an in-plane magnetic field can be applied to selectively excite a specific spin-plasmon branch with proper doping or gating to the system. Our findings may have potential applications in novel plasmonic and spintronic devices. We also investigate plasmons in the Kane-Mele model on a finite-sized diamond-shaped nanoflake and observe low-energy plasmons circulating the boundary of the material.

The topological nature of solids is related to the symmetries present in the material, for example, a quantum spin Hall effect can be observed in topological insulators with time-reversal symmetry, while broken time-reversal symmetry may give rise to the presence of an anomalous quantum Hall effect (AHE). Here, we consider the effects of broken rotational symmetry on the Dirac cone of an AHE material by adding trigonal warping terms to the Dirac Hamiltonian. We calculate the linear optical conductivity semianalytically to show how by breaking the rotational symmetry we can obtain a topologically distinct phase. The addition of trigonal warping terms causes the emergence of additional Dirac cones, which when combined has a total Chern number of $\mp 1$ instead of $\pm 1/2$. This results in drastic changes in the anomalous Hall and longitudinal conductivity. The trigonal warping terms also activate the higher-order Hall responses which do not exist in a $\mathcal{R}$-symmetric conventional Dirac material. We found the presence of a nonzero second-order Hall current even in the absence of a Berry curvature dipole. This shift current is also unaffected by the chirality of the Dirac cone, which should lead to a nonzero Hall current in time-reversal symmetric systems.

Nonequilibrium states driven by both electric bias voltages $V$ and temperature differences $\mathrm{\Delta }T$ (or thermal voltages $e{V}_T\equiv k_B\mathrm{\Delta }T$) are unique probes of various systems. Whereas average currents $I(V,V_T)$ are traditionally measured in majority of experiments, an essential part of nonequilibrium dynamics, stored particularly in fluctuations, remains largely unexplored. Here we focus on Majorana quantum dot devices, specifically on their differential shot noise $\partial S^{>}(V,V_T)/\partial V$, and demonstrate that in contrast to the differential electric or thermoelectric conductance, $\partial I(V,V_T)/\partial V$ or $\partial I(V,V_T)/\partial V_T$, it reveals a crossover from thermoelectric to pure thermal nonequilibrium behavior. It is shown that this Majorana crossover in $\partial S^{>}(V,V_T)/\partial V$ is induced by an interplay of the electric and thermal driving, occurs at an energy scale determined by the Majorana tunneling amplitude, and exhibits a number of universal characteristics which may be accessed in solely noise experiments or in combination with measurements of average currents.

We compute numerically the second- and third-order nonlinear magnetic susceptibilities of an Ising ladder model in the context of two-dimensional coherent spectroscopy by using the infinite time-evolving block decimation method. The Ising ladder model couples a quantum Ising chain to a bath of polarized spins, thereby effecting the decay of spinon excitations. We show that its third-order susceptibility contains a robust spinon echo signal in the weak-coupling regime, which appears in the two-dimensional coherent spectrum as a highly anisotropic peak on the frequency plane. The spinon echo peak reveals the dynamical properties of the spinons. In particular, the spectral peak corresponding to the high-energy spinons, which couple to the bath, is suppressed with increasing coupling, whereas those corresponding to low-energy spinons do not show any significant changes.