We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two classical magnetic impurities in one-dimensional lattice models with flat bands. As two representative examples, we pick the stub lattice and the diamond lattice at half filling. We first calculate the exact RKKY interaction numerically and then compare our data to results obtained via different analytical techniques. In both our examples, we find that the RKKY interaction exhibits peculiar features that can directly be traced back to the presence of a flat band in the energy spectrum. Importantly, these features are not captured by the conventional RKKY approximation based on nondegenerate perturbation theory. Instead, we find that degenerate perturbation theory correctly reproduces our exact results if there is an energy gap between the flat and the dispersive bands, while a nonperturbative approach becomes necessary in the absence of a gap.

Scale evolution of interactions between a Weyl fermion and a heavy magnetic impurity is calculated nonperturbatively using the functional renormalization group technique. Using an expansion around the vanishing pairing gap, we derive the flow equations for all possible quartic couplings in the system. We find that, contrary to conventional perturbation theory, the usual spin-spin isotropic interaction necessarily splits into two invariant parts during the scale evolution, which are fully allowed by the $SU\left(2\right)$ spin-rotation symmetry. We also find the existence of an infrared stable interacting fixed point, which can be responsible for intermediate-coupling screening effects. The calculation scheme presented here is rather general, and is expected to be easily applicable to various spin-spin-like interactions in fermionic systems.

Optical singularities of polarizations have received much interest owing to their extraordinary performances. Recently, it was reported that originating from high-order singularities, a variety of controllable developments of singularities could be achieved by reducing symmetries, providing a feasible way to produce and manipulate optical singularities in momentum space. However, there are rare investigations on evolutions of polarization singularities in the system with $C_2$ symmetry transiting into no in-plane rotation symmetry. In this work, we realized adjustable evolutions of singularities through breaking $C_2$ symmetry. The singularities including bound states in the continuum (BICs) and degenerate states occur in a $C_2$ symmetry photonic crystal slab. The evolutions of singularities were attained during the process of symmetry transition by introducing a symmetry breaking factor. A process of off-$\mathrm{\Gamma }C$ points spawned from off-$\mathrm{\Gamma }$ BICs and merged to be quasi-BICs eventually were observed by increasing the symmetry breaking factor. In addition, an at-$\mathrm{\Gamma }$ quasi-BIC accompanied by a pair of $C$ points and axis conversions of singularities were observed. Our observations could enrich the understanding of the evolution of optical singularities and supply a meaningful way to engineer optical singularities.

In parallel to the condensed-matter realization of quantum Hall (Chern insulators), quantum spin Hall (topological insulators), and fractional quantum Hall (fractional Chern insulators) effects, we propose that bilayer flat band (FB) lattices with one FB in each layer constitute solid-state analogs of bilayer quantum Hall (BQH) system, leading to anomalous BQH effect without a magnetic field. By exact diagonalization of a bilayer kagome lattice Hamiltonian, as a prototypical example, we demonstrate the stabilization of excitonic condensate Halperin's (1,1,1) state at the total filling $v_T=1$ of the two FBs. Furthermore, by tuning the interlayer tunneling and distance between the kagome layers at $v_T=2/3$, we show phase transitions among Halperin's (3,3,0), spin-singlet (1,1,2), and particle-hole conjugate of Laughlin's $1/3$ states, as previously observed in conventional BQH systems. Our work opens a new direction in the field of FB physics by demonstrating bilayer FB materials as an attractive avenue for realizing exotic anomalous BQH states including non-Abelian anyons.

Motivated by the thermal transport problem in the Kitaev spin liquids, we consider a nearest-neighbor tight-binding model on the honeycomb lattice in the presence of random uncorrelated $\pi$ fluxes. We employ different numerical methods to study its transport properties near half-filling. The zero-temperature dc conductivity away from the Dirac point is found to be quadratic in Fermi momentum and inversely proportional to the flux density. Localization due to the random $\pi$ fluxes is observed and the localization length is extracted. Our results imply that, for realistic system size, the thermal conductivity of a pure Kitaev spin liquid diverges as ${\kappa }_{\text{K}}\sim T^3{e}^{{\mathrm{\Delta }}_v/k_{B}T}$ when $k_{B}T\ll {\mathrm{\Delta }}_v$, and suggest the possible occurrence of strong Majorana localization ${\kappa }_{\text{K}}/T\ll k_B^2/2\pi \hslash$ when $k_{B}T\sim {\mathrm{\Delta }}_v$, where ${\mathrm{\Delta }}_v$ is the vison gap.

We study the crossed Andreev reflection and the nonlocal transport in the proximitized graphene/ superconductor/proximitized graphene junctions with the pseudospin staggered potential and the intrinsic spin-orbit coupling. The crossed Andreev reflection with the local Andreev reflection and the elastic cotunneling being completely eliminated can be realized for the electrons with the specific spin-valley index when the intrinsic spin-orbit couplings in the left graphene and the right graphene possess the opposite sign. The perfect crossed Andreev reflection with its probability equal to $100\%$ can be obtained in the space consisting of the incident angle and the energy of the electrons. The crossed conductance and its oscillation with the superconductor length are also investigated. The energy ranges for the crossed Andreev reflection without the local Andreev reflection and the elastic cotunneling are clarified for the different magnitudes of the pseudospin potential and the spin-orbit coupling. The spin-valley index of the electrons responsible for the perfect crossed Andreev reflection can be switched by changing the sign of the intrinsic spin-orbit coupling or exchanging the biases applied on the left graphene and the right graphene. Our results are helpful for designing the flexible and high-efficiency Cooper pair splitter based on the spin-valley degree of freedom.

The properties of $x{\mathrm{Na}}_2\mathrm{S}\text{−}\left(100\text{−}x\right){\mathrm{GeS}}_2$ glasses, which represent promising systems for all-solid-state batteries, are thoroughly investigated from a variety of experimental and theoretical techniques. The ionic conduction is measured as a function of composition. It reveals a powerlike behavior with a threshold composition found at low Na content. In contrast, temperature evolution suggests a typical Arrhenius behavior indicative of Na motions achieved by jumps between neighboring sites. Three particular compositions (0%, 33%, and 66% ${\mathrm{Na}}_2\mathrm{S}$) are characterized by a combination of x-ray diffraction and density functional based molecular dynamics. Different structural properties are measured and calculated, such as structure factors, pair distribution functions, angular distributions, coordination numbers, and neighbor distributions. The comparison with experiments reveals a rather good agreement in real and reciprocal space. The short-range order is found to consist of a base network made of ${\mathrm{GeS}}_{4/2}$ tetrahedra (with Ge and S coordination numbers being of about 4 and 2) that are progressively depolymerized upon Na addition that also leads to a breakdown of the ring structure. Na coordination numbers are loosely defined, especially at high Na content. Typical features of alkali-modified silicates are also found, such as the presence of channel-like dynamics, a bond-length distribution that is different between Ge and bridging or nonbridging sulfur, a distribution $Q^n$ of Ge tetrahedra having $n$ bonding sulfur, and a decoupling at low temperatures between network species (Ge, S) and Na dynamics. However, unlike such archetypal glasses, sodium thiogermanates contain homopolar Ge-Ge bonds that are specific to Ge chalcogenides and which lead to isolated ${\left({\mathrm{Ge}}_2{\mathrm{S}}_6\right)}^{6\ominus }$ anions at high Na content.

Despite a very good understanding of single-particle Anderson localization in one-dimensional (1D) disordered systems, many-body effects are still full of surprises; a famous example is the interaction-driven many-body localization (MBL) problem, about which much has been written, and perhaps the best is yet to come. Interestingly enough the noninteracting limit provides a natural playground to study nontrivial multiparticle physics, offering the possibility to test some general mechanisms with very large-scale exact diagonalization simulations. In this paper, we first revisit the 1D many-body Anderson insulator through the lens of extreme value theory, focusing on the extreme polarizations of the equivalent spin chain model in a random magnetic field. A many-body-induced chain breaking mechanism is explored numerically, and compared to an analytically solvable toy model. A unified description, from weak to large disorder strengths $W$ emerges, where the disorder-dependent average localization length $\xi \left(W\right)$ governs the extreme events leading to chain breaks. In particular, tails of the local magnetization distributions are controlled by $\xi \left(W\right)$. Remarkably, we also obtain a quantitative understanding of the full distribution of the extreme polarizations, which is given by a Fréchet-type law. In a second part, we explore finite interaction physics and the MBL question. For the available system sizes, we numerically quantify the difference in the extreme value distributions between the interacting problem and the noninteracting Anderson case. Strikingly, we observe a sharp “extreme-statistics transition” as $W$ changes, which may coincide with the MBL transition.

The world is full of fluids that flow. The fluid nature of flowing skyrmionic quasiparticles is of fundamental physical interest and plays an essential role in the transport of many skyrmions. Here, we report the laminar and transiently disordered dynamic behaviors of many magnetic skyrmions flowing in a pipe channel. The skyrmion flow driven by a uniform current may show a lattice structural transition. The skyrmion flow driven by a nonuniform current shows a dynamically varying lattice structure. A large uniform current could result in the compression of skyrmions toward the channel edge, leading to the transition of the skyrmion pipe flow into an open-channel flow with a free surface. Namely, the width of the skyrmion flow could be adjusted by the driving current. Skyrmions on the free surface may form a single shear layer adjacent to the main skyrmion flow. In addition, although we focus on the skyrmion flow dynamics in a clean pipe channel without any pinning or defect effect, we also show that variation of the magnetic anisotropy in the pipe channel could lead to more complicated skyrmion flow dynamics and path lines. Our results reveal the fluid nature of skyrmionic quasiparticles, which may motivate future research on the complex flow physics of magnetic textures.

In this study, we present a comprehensive theoretical analysis of magnetic Fibonacci quasicrystals, which could potentially be realized through the stacking of ferromagnetic van der Waals layers. We introduce a model that incorporates up to second-neighbor interlayer magnetic interactions and displays a complex interplay between geometric frustration and magnetic order. To explore the parameter space and identify distinct magnetic phases, we employ a machine learning approach. This methodology proves effective in elucidating the intricate magnetic behavior of the system. We offer a detailed magnetic phase diagram as a function of the model parameters and notably discover a unique ferromagnetic alternating helical phase among other collinear and noncollinear phases. In this noncollinear, quasiperiodic, and ferromagnetic configuration, the magnetization decreases logarithmically with the stack height.

Nontrivial topological materials are emerging as fascinating objects in condensed matter research due to their great potential in low-power and low-dissipation electronic applications. In this work, using first-principles calculations and a tight-binding method, we propose a promising candidate with novel topological states and high experimental feasibility. We prove that ${\mathrm{Sr}}_3\mathrm{PbO}$ exhibits a topological crystalline insulator (TCI) phase in its three-dimensional (3D) bulk lattice and a quantum spin Hall insulator (QSHI) phase in its two-dimensional (2D) thin film, presenting a picture of evolution from 3D TCI to 2D QSHI. Moreover, the topological phase transition between QSHI and trivial phases occurs as the thickness of the thin-film ${\mathrm{Sr}}_3\mathrm{PbO}$ varies. This intriguing behavior can also be confirmed using a low-energy effective model with infinite potential well boundary conditions. The high-quality bulk and thin-film ${\mathrm{Sr}}_3\mathrm{PbO}$ have been prepared in an experiment, implying high feasibility for experimental characterization.

We developed a theory describing elementary excitations in the Bose-Fermi system induced by circularly polarized light in a two-dimensional (2D) gas of charge carriers with different masses. In such a hybrid system, the Fermi subsystem is a degenerate Fermi gas, whereas the Bose subsystem is a condensate of the light-induced composite bosons consisting of two fermions (electrons or holes) with different effective masses. The interaction of the single-particle excitations and the collective excitations (plasmons) in the Fermi subsystem with the Bogoliubov collective modes (bogolons) in the Bose subsystem is analyzed. The renormalization and damping (lifetime) of the excitations are calculated, and the possibility of their experimental observation is discussed. The developed theory can be applied to describe 2D condensed-matter structures containing charge carriers with different effective masses, including transition metal dichalcogenide monolayers and semiconductor quantum wells.

Metal-insulator transition materials such as ${\mathrm{NbO}}_2$ have generated much excitement in recent years for their potential applications in computing and sensing. ${\mathrm{NbO}}_2$ has generated considerable debate over the nature of the phase transition and the values of the band gap and bandwidths in the insulating phase. We present a combined theoretical and experimental study of the band gap and electronic structure of the insulating phase of ${\mathrm{NbO}}_2$. We carry out ab initio density functional theory (DFT) plus $U$ calculations, directly determining the $U$ and $J$ parameters for both the Nb $4d$ and O $2p$ subspaces through the recently introduced minimum-tracking linear response method. We find a fundamental bulk band gap of 0.80 eV for the full $\mathrm{DFT}+U+J$ theory. We also perform calculations and measurements for a (100)-oriented thin film. Scanning tunneling spectroscopy measurements show that the surface band gap varies from 0.75 to 1.35 eV due to an excess of oxygen in and near the surface region of the film. Slab calculations indicate metallicity localized at the surface region caused by an energy level shift consistent with a reduction in Coulomb repulsion. We demonstrate that this effect in combination with the simple, low-cost $\mathrm{DFT}+U+J$ method can account for the bandwidths and $p\text{−}d$ gap observed in x-ray photoelectron spectroscopy experiments. Overall, our results indicate the possible presence of a two-dimensional anisotropic metallic layer at the (100) surface of ${\mathrm{NbO}}_2$.

Common proposals for realizing topological superconductivity and Majorana zero modes in semiconductor-superconductor hybrids require large magnetic fields, which paradoxically suppress the superconducting gap of the parent superconductor. Although two-channel schemes have been proposed as a way to eliminate magnetic fields, geometric constraints make their implementation challenging, since the channels should be immersed in nearly antiparallel electric fields. Here, we propose an experimentally favorable scheme for realizing field-free topological superconductivity, in two-channel InAs-Al nanowires, that overcomes such growth constraints. Crucially, we show that antiparallel fields are not required, if the channels are energetically detuned. We compute topological phase diagrams for realistically modeled nanowires, finding a broad range of parameters that could potentially harbor Majorana zero modes. This paper, therefore, solves a major technical challenge and opens the door to near-term experiments.

Infinite-layer nickelate superconductors ${R\mathrm{Ni}\mathrm{O}}_2$ $(R=\mathrm{La}, \mathrm{Nd}, \mathrm{Pr})$ are synthesized via chemical reduction using the ${\mathrm{CaH}}_2$ agent, and the unintentional introduction of H dopant during the reduction process may affect ${R\mathrm{Ni}\mathrm{O}}_2$ quality and ultimately determine their electronic properties. However, the ground-state configurations and electronic structures of ${R\mathrm{Ni}\mathrm{O}}_2$ under varying H concentrations (δ) remain unclear. In this work, we employ the cluster-expansion method and first-principles calculations to examine the intermediate ground-state structures, electronic structures, and magnetic properties of ${\mathrm{LaNiO}}_2{\mathrm{H}}_{\delta }$ $\left(0<\delta <1\right)$. Interestingly, our results show that H always occupies apical oxygen vacancies, forming ordered H-Ni-H chains along the out-of-plane direction but with different δ-dependent patterns along the in-plane direction. Notably, the interstitial $s$-like orbital in the ${\mathrm{LaNiO}}_2$ host is annihilated by H and the filling of the Ni $3d$ bands, especially the $3d_{x^2-y^2}$ and $3d_{z^2}$ orbitals, is greatly altered. With H doping, both enhanced magnetic stability of G-type antiferromagnetic states and simultaneous metal-to-insulator transition occur. Our study demonstrates the remarkable doping impact of H in ${\mathrm{LaNiO}}_2$, allowing us to gain deeper insight into the structure and superconductivity of infinite-layer nickelates.

Zirconium pentatelluride $\left({\mathrm{ZrTe}}_5\right)$, a system with a Dirac linear band across the Fermi level and anomalous transport features, has attracted considerable research interest for it is predicted to be located at the boundary between strong and weak topological insulators separated by a topological semimetal phase. However, the experimental verification of the topological phase transition and the topological ground state in ${\mathrm{ZrTe}}_5$ is full of controversies, mostly due to the difficulty of precisely capturing the small gap evolution with single-particle band structure measurements. Alternatively, the collective excitations of electric charges, known as plasmons, in Dirac systems exhibiting unique behavior can well reflect the topological nature of the band structure. Here, using reflective high-resolution electron energy loss spectroscopy (HREELS), we investigate the temperature-dependent collective excitations of ${\mathrm{ZrTe}}_5$, and discover that the plasmon energy in ${\mathrm{ZrTe}}_5$ is proportional to the $1/3$ power of the carrier density $n$, which is a unique feature of plasmons in three-dimensional Dirac systems or hyperbolic topological insulators. Based on this conclusion, the origin of the resistivity anomaly of ${\mathrm{ZrTe}}_5$ can be attributed to the temperature-dependent chemical potential shift in extrinsic Dirac semimetals.

We study phase-controlled planar Josephson junctions comprising a two-dimensional electron gas with strong spin-orbit coupling and $d$-wave superconductors, which have an advantage of a high critical temperature. We show that a region between the two superconductors can be tuned into a topological state by the in-plane Zeeman field, and can host Majorana bound states. The phase diagram as a function of the Zeeman field, chemical potential, and the phase difference between superconductors exhibits the appearance of Majorana bound states for a wide range of parameters. We further investigate the behavior of the topological gap and its dependence on the type of $d$-wave pairing, i.e., $d, d+is$, or $d+i{d}^{\prime }$, and note the difficulties that can arise due to the presence of gapless excitations in pure $d$-wave superconductors. On the other hand, the planar Josephson junctions based on superconductors with $d+is$ and $d+i{d}^{\prime }$ pairings can potentially lead to realizations of Majorana bound states. Our proposal can be realized in cuprate superconductors, e.g., in a twisted bilayer, combined with the layered semiconductor ${\mathrm{Bi}}_2{\mathrm{O}}_2\mathrm{Se}$.

Second-order topological insulators (SOTIs) support topological states beyond the usual bulk-boundary correspondence and provide important connections between quantum chemistry and topology. A hallmark of the two-dimensional (2D) SOTIs is the emergence of corner states, which usually arise from the topologically nontrivial obstructed states in the bulk. In contrast, we reveal a very different scenario where even trivial obstructed bulk states can induce corner states due to their open boundaries. Remarkably, we show that these two types of corner states can coexist in a single system and predict, from first-principles calculations, that the monolayer ${\text{C}}_2\text{N}$ is a promising candidate for their observation. To overcome the limitation in manipulating corner states, we demonstrate it can be accomplished using a magnetic exchange field, where the corner states can be fully spin polarized and moved into the bulk states. Focusing on the example of the ${\text{C}}_2\text{N}/\text{Cr}{\text{I}}_3$ van der Waals heterostructure, we put forth a class of proximitized materials which enable the versatile control of corner states through strain-controlled magnetic proximity effects. Our work reveals another type of topological state, and provides a universal proposal for topological corner state modulations and applications.