Magnetic materials hosting stable topological spin textures have demonstrated energy efficiency and potential as information carriers in logic and memory devices, offering an alternative to magnetic tunnel junction technology. While these structures are well understood in two dimensions (2D), in 3D their stability, interactions, and topological transitions require further exploration. Here we present two thermodynamically stable topological states, termed the “hourglass” and “dome,” in centrosymmetric magnetic films of varying thickness. Crucially, we observe thickness-dependent transitions between the two states, with regions of metastability where both configurations coexist. We construct a phase diagram detailing the parameter space for their existence and transitions, provide an effective description of the interactions that mediate the transition, and discuss the implications of this type of state switching.

The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of the high Chern number QAH effect in pentalayer and tetralayer rhombohedral graphene highlight the intriguing interplay between strong interactions and spin-orbit coupling (SOC). Here, we propose a minimal interacting model for spin-orbit-coupled rhombohedral graphene and use Hartree-Fock analysis to explore the phase diagram at charge neutrality. We find that, with Ising SOC on one outmost graphene layer, in-plane layer-antiferromagnetic (LAF) order is the insulating ground state without a displacement field. Upon increasing the gate displacement field, we find that the QAH state with the Chern number being equal to the layer number emerges between the LAF and layer-polarized states, which is consistent with experimental observations. Remarkably, we study the phase diagram for different thicknesses and find the pentalayer is optimal for the QAH effect. Finally, we propose that the QAH state is enlarged by engineering opposite Ising SOCs on the opposite outmost layers of rhombohedral graphene. These results will facilitate the realization of QAH states in rhombohedral graphene with different thicknesses. This paper serves as a foundation for further exploration of correlated physics of the insulating state in rhombohedral graphene.

Kagome materials with flat bands exhibit wildly different physical properties depending on symmetry group and electron number. We analyze the case of the kagome 166 material ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ in symmetry group 191, with the Fermi level away from the flat bands. Experimentally, an $\sim 95$ K charge density wave (CDW) at vector $\overline{K}=(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ exists, with no nesting or peaks in the electron susceptibility at $\overline{K}$. We show that ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ has a collapsed phonon mode at $H=(\frac{1}{3},\frac{1}{3},\frac{1}{2})$ and an imaginary flat phonon band in the $H$ vicinity. The soft phonon is supported on the triangular Sn (${\mathrm{Sn}}^T$) $z$-directed mirror-even vibration, which is faithfully described by a three-degree-of-freedom simple force constant model. We show that the phonon softening comes from the electron-phonon coupling between mirror-even electron orbitals at ${\mathrm{Sn}}^T$ and the mirror-even vibration of ${\mathrm{Sn}}^T$ atoms. We model it using a (Gaussian) approximation of the hopping parameter Yu et al., Nat. Phys. 20, 1262 (2024) and show that the resulting field-theoretical renormalization of the phonon frequency reproduces the collapse of the $H$ phonon and induces small in-plane dispersion away from $H$. To explain the appearance of the $\overline{K}$ CDW we build an effective model of two order parameters (OPs): one at the collapsed phonon $H$ and one at the CDW $\overline{K}$. Comparing our results with experimental data [Korshunov et al., Nat. Commun. 14, 6646 (2023)], we show that the $H$ OP undergoes a second-order phase transition; however, its flatness around $H$ induces large fluctuations and stabilizes a $\overline{K}$ CDW via a first-order transition. We construct CDW OPs in the electron and phonon fields that match the ab initio calculations. Our results not only explain the CDW in ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ but also show an unprecedented level of modeling of complex electronic systems that open different collaboration between ab initio calculations and analytics.

The structures and equations of states of dysprosium have been studied up to 337 GPa without a pressure transmitting medium using synchrotron x-ray diffraction. Beyond the previously reported transition sequences, namely hP2 → hR9 → hP4 → hR24 → oF16, we herein disclose an isosymmetric structural transition that occurs above 195.5 GPa, wherein the structure transforms from orthorhombic face-centered oF16 to oF8. The oF8 phase comprises eight atoms per unit cell and belongs to the space group Fddd, being isostructural with lanthanides Nd-VI, Sm-VI, and actinides Am-III, Cf-III, and Cm-IV. During the phase transition, the reduction in lattice volume occurs continuously and is concomitant with the expansion along the $b$ axis, manifesting negative linear compressibility and an increasing degree of anisotropy. Our finding further corroborates the intimate structural correlation between lanthanides and actinides.

We report on the induction of magnetization in Rydberg systems by means of the inverse Faraday effect and propose the appearance of the effect in two such systems: Rydberg atoms proper and shallow dopants in semiconductors. Rydberg atoms are characterized by a large orbital radius. This large radius gives such excited states a large angular moment, which when driven with circularly polarized light translates to a large effective magnetic field ${\mathcal{B}}_{\text{eff}}$. We calculate this effect to generate effective magnetic fields of $O\left(1\mu \text{T}\right)\times {\left(\frac{\omega }{1\text{THz}}\right)}^{-1}\left(\frac{\mathcal{I}}{10\text{W}{\text{cm}}^{-2}}\right)n^4$ in the Rydberg states of atoms such as Rb and Cs for off-resonant photon beams with frequency $\omega$ and intensity $\mathcal{I}$ expressed in units of the denominators and $n$ the principal quantum number. Additionally, terahertz spectroscopy of phosphorus-doped silicon reveals a large cross section for excitation of shallow dopants to Rydberg-like states, which even for small $n$ have the potential to be driven similarly with circularly polarized light to produce an even larger magnetization. Our theoretical calculations estimate ${\mathcal{B}}_{\text{eff}}$ as $O\left({10}^2\text{T}\right)$ for Si:P with a beam intensity of ${10}^8\text{W}{\text{cm}}^{-2}$.

Strong field terahertz pulses are increasingly used to excite and control quantum materials at the ultrafast timescale. They have found widespread application by enabling direct addressing of the superconducting gap or Josephson resonances and are essential in Higgs spectroscopy. Large non-linear optical signals can be induced by the strong coupling of the THz and superconducting degrees of freedom. However, far less attention has been paid to the strong bidirectional coupling between field and material this implies. Here, we use the framework of the time-dependent Ginzburg-Landau equations to study the full field and material evolution of a superconductor driven by strong field terahertz pulses. We find that at high field strengths, the backreaction of the superconductor induces large changes to the driving pulse, which in turn leads to a runaway melting of the superconducting condensate. This results in a surprisingly large sensitivity to the initial driving pulse chirp, enabling these purely dynamical changes to produce order of magnitude differences in the level of melting. We also find large-scale spectral shifting of the driving pulse to occur in just a few hundred nanometers of propagation through a superconductor. We attribute these effects to an inverse plasma redshift, in which the driving field breaks Cooper pairs and decreases the free-electron mobility, analogous to reducing the density of a plasma.

The symmetry-topology interplay dictates how to define order parameters and classify material ordered phases. However, current understanding of this interplay has been predominately approached from a one-sided perspective, with topological states being classified within the constraints imposed by specific fixed symmetries. Here we complete this full circle by demonstrating spontaneous symmetry breaking that results from a periodic alteration of topological phases induced by light in a centrosymmetric Dirac material ${\mathrm{ZrTe}}_5$. The distinguishing feature is the observation of robust correlation and striking anomalies in the fluence and temperature dependence of key transport parameters. First, both shift current $J_s$ and displacement current $J_d$, arising from interband transition and infrared phonon driving, respectively, along with charge carrier pumping, exhibit similar behaviors. Second, they all peak at similar low pump fluence, followed by a subsequent reduction as the fluence further increases. This behavior cannot be explained by conventional energetically allowed, direct excitations. Third, all the three observables exhibit anomalies when they approach the topological phase transition temperature. These results highlight the unique low-energy pumping behaviors in ${\mathrm{ZrTe}}_5$, characterized by reversible fluence dependence and a “hinge-like” interaction that connects various electronic and lattice observables, including phonons, charge carriers, and currents. Our findings, supported by model analysis, provide key insights into the fragility of crystalline (inversion) and time-reversal symmetries during the dynamics of topological phase transitions. This fragility drives spontaneous symmetry breaking, evidenced by the synchronized emergence of off-resonant infrared phonons and broken-symmetry photocurrents.

Plutonium-based correlated electron materials host exotic physical phenomena ranging from unconventional heavy-fermion superconductivity to topological Kondo insulating states. Self-irradiation damage can influence many properties of such radioactive materials. Structural disorder effects due to α radiation have been frequently studied using techniques such as transport, thermodynamics, and x-ray diffraction. Here, we use ${}^{239}\mathrm{Pu}$ nuclear magnetic resonance (NMR) to study the long-term influence of self-damage on the lattice and local electronic structures in a single crystal of the candidate topological insulator plutonium tetraboride (${\mathrm{PuB}}_4$). We first characterize the anisotropy of the ${}^{239}\mathrm{Pu}$ resonance and confirm the local axial-site symmetry inferred from previous polycrystalline measurements. Aging effects are then evaluated over the time frame of six years. We find that, though the static ${}^{239}\mathrm{Pu}$ NMR spectra show a slight modulation in their shape, their field-rotation pattern reveals no change in ${}^{239}\mathrm{Pu}$ local site symmetry over time, suggesting that aging has a surprisingly small impact on the spatial distribution of the static hyperfine field. Further, ligand-site ${}^{11}\mathrm{B}$ NMR finds little time-dependent change in the size of electric field gradient around ${}^{11}\mathrm{B}$ sites. By contrast, aging has a prominent impact on the ${}^{239}\mathrm{Pu}$ NMR relaxation processes and signal intensity. Specifically, aging-induced damage manifests itself as an increase in the spin-lattice relaxation time $T_1$, an increased distribution of $T_1$, and a signal intensity that decreases linearly by 20% per year. An effective spin-spin relaxation time $T_{2,\mathrm{eff}}$ in the aged sample shortens drastically towards lower temperature, suggesting growth of slow fluctuations of the hyperfine field that are linked to radiation-damage-induced inhomogeneity. Our NMR study sheds light on the interplay of radiation damage and local magnetic interactions in correlated insulators.

The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of band complexes. By translating the symmetry conditions into a set of band balance equations, we show that all possible band structure solutions can be described by a positive affine monoid structure, which has a unique minimal set of generators, called Hilbert basis. We show that Hilbert basis completely determines whether a band complex is reducible and how it can be decomposed. The band complexes corresponding to Hilbert basis vectors, termed as Hilbert band complexes (HBCs), can be regarded as elementary building blocks of band structures. We develop algorithms to construct HBCs, analyze their graph features, and merge them into large complexes. We find some interesting examples, such as HBCs corresponding to complete bipartite graphs, and complexes that can grow without bound by successively merging a HBC.

The Aharonov-Bohm (AB) effect on the thermoelectric properties of three-terminal quantum devices is investigated. Thermodynamic relations among the linear-response coefficients of these devices are derived and interpreted. General expressions are derived using nonequilibrium Green's functions, and applied to calculate the thermoelectric response of a model quantum thermocouple. It is shown that the AB effect can generate a large thermoelectric response in a device with particle-hole symmetry, which nominally has zero Seebeck and Peltier coefficients. In addition to modifying the external electric and thermal currents of the device, the AB effect also induces persistent electric and thermal currents. One might expect that a persistent electric current in a quantum thermocouple, through the Peltier effect, could lead to persistent Peltier cooling, violating the first and second laws of thermodynamics. However, this apparent paradox is resolved by elucidating the distinction between persistent and dissipative currents in quantum thermoelectrics.

We study characterized single crystals of CrTe using photoemission spectroscopy (PES), x-ray absorption spectroscopy (XAS), and x-ray magnetic circular dichroism (XMCD) combined with density functional theory–based electronic structure calculations. X-ray diffraction confirms the hexagonal structure of CrTe ($P63/mmc$ space group) and $T$-dependent magnetization $M\left(T\right)$ shows a Curie temperature $T_C=340\mathrm{K}$, with a three-dimensional Ising-type critical behavior. A quantitative analysis of $\mathrm{Cr}3p$ and $\mathrm{Te}4d$ core levels using hard x-ray PES (HAXPES; $h\nu =6.5\mathrm{keV}$) and low-energy PES $(h\nu =100\mathrm{eV})$ indicates a nearly stoichiometric composition of ${\mathrm{Cr}}_{0.99\pm 0.01}\mathrm{Te}$. HAXPES of $\mathrm{Te}3p$ and $3d$ core levels show clean asymmetric single peaks with plasmon satellites. The $\mathrm{Cr}2p$ spectrum lies close to the $\mathrm{Te}3d$ spectrum but could be separated out and shows weak charge-transfer satellites. The Cr $L$-edge XAS-XMCD and $\mathrm{Cr}2p$ PES spectra could be simulated using charge transfer multiplet cluster-model calculations for a ${\mathrm{Cr}}^{2+}$ configuration with on-site Coulomb energy $U_{dd}=3.5\mathrm{eV}$ and a negative charge-transfer energy $\mathrm{\Delta }=-1\mathrm{eV}$. A sum-rule analysis of XAS-XMCD spectra indicates a very small orbital magnetic moment $m_o=0.01\pm 0.01{\mu }_B$ and a spin magnetic moment $m_s=2.49\pm 0.2{\mu }_B$ at $T=25\mathrm{K}$, consistent with magnetization measurements and cluster-model calculations. Comparison of the calculated density of states (DOS) with the HAXPES valence band spectrum shows that the $\mathrm{Te}5p$ states dominates the spectrum due to the large photoionization cross section of Te $5p$ states with hard x rays. The Cr $3d$ partial DOS are spread between the Fermi level $(E_F$) to $\sim 5\text{−}\mathrm{eV}$ binding energy (BE), while the $\mathrm{Te}5p$ partial DOS are spread between the $E_F$ and $\sim 7\text{−}\mathrm{eV}$ BE. The obtained electronic parameters suggest that CrTe is a $p$-type metal in the Zaanen-Sawatzky-Allen phase diagram, with $p\to p$-type lowest-energy excitations.

Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting weight, Drude weight, and optical responses. Motivated by the recent advances in flat-band interacting systems, we investigate the role of interaction effects on the quantum metric. By using the fermionic Creutz ladder as a representative system, we show that the repulsive Hubbard interaction monotonically suppresses the quantum metric. While the eigenstates and their overlap quantifying the quantum metric can be obtained exactly in the presence of interactions through exact diagonalization, this method is limited to small system sizes. Alternatively, two theoretical proposals, the generalized quantum metric and the dressed quantum metric, suggest using renormalized Green's functions to define the interacting quantum metric. By comparing these analytical approaches with results from exact diagonalization, we show that the dressed quantum metric provides a better fit to the exact diagonalization results. Our conclusion holds for both flat-band and dispersive systems.

Quantum magic, or nonstabilizerness, provides a crucial characterization of quantum systems, regarding the classical simulability with stabilizer states. In this work, we propose an alternative and efficient algorithm for computing stabilizer Rényi entropy, one of the measures for quantum magic, in spin systems with sign-problem free Hamiltonians. This algorithm is based on the quantum Monte Carlo simulation of the path integral of the work between two partition function ensembles and it applies to all spatial dimensions and temperatures. We demonstrate this algorithm on the one- and two-dimensional transverse field Ising model at both finite and zero temperatures and show the quantitative agreements with tensor-network based algorithms. We analyze the computational cost and provide analytical and numerical evidences for it to be polynomial in system size. This work also suggests a unifying framework for calculating various types of entropy quantities including entanglement Rényi entropy and entanglement Rényi negativity.

We elaborate that many nonexcitonic dielectric and optical properties of semiconductors and insulators caused by interband absorption are originated from quantum geometry, including charge susceptibility, relative dielectric constant, optical conductivity, dielectric function, refractive index, absorption coefficient, reflectance, and transmittance. The key to this recognition is the complex optical conductivity, which contains the quantum metric in the optical transition matrix element, and the fact that all these dielectric and optical properties can be expressed in terms of the real and imaginary parts of optical conductivity. Our formalism allows to map all these properties to real-space lattice sites as local markers, which can help to explain the spatial inhomogeneity of optical properties detected by near-field scanning optical microscopy, as demonstrated by a minimal model of three-dimensional topological insulators. In addition, the dielectric function marker can be used to detect a recently proposed fidelity marker or, equivalently, the spread of valence band Wannier functions generalized to disordered insulators.

Quantum spin Hall insulators with a pair of helical edge states and proximity-induced superconductivity have been shown to support second-order topological superconductors with Majorana corner modes. As the Majorana corner modes originate from the helical edge states of the quantum spin Hall insulators, the question of whether quantum spin Hall insulators with multiple pairs of helical edge states and proximity-induced superconductivity can give rise to second-order topological superconductors with multifold Majorana corner modes is an interesting one to address. In this work, we consider a quantum spin Hall insulator with two pairs of helical edge states. We find that robust twofold Majorana corner modes can be achieved when the helical edge states are gapped by a combined action of a magnetic exchange field and an $s$-wave pairing or an $s+p$ mixed-parity pairing. The stability of two Majorana zero modes per corner under the action of magnetic exchange fields is attributed to the protection from the chiral symmetry. Our study reveals that heterostructures composed of superconductors and quantum spin Hall insulators with multiple pairs of helical edge states could serve as a platform to pursue multifold Majorana corner modes.

Interacting impurity spins adsorbed on surfaces have been suggested as basic components for applications in quantum computation and spintronics. Such spins usually prefer a parallel or antiparallel configuration, but weakly noncollinear alignments are possible due to the Dzyaloshinskii-Moriya interaction (DMI) that arises in the presence of relativistic spin-orbit coupling. Here, we show that an effective Dzyaloshinskii-Moriya-type interaction (DMTI) can emerge purely from superconducting correlations without any spin-orbit interaction. We give an analytical proof and provide a numerical study which shows that DMTI arises in mixed-parity superconductors solely from the superconducting pairing. Moreover, we show that the same effect can be realized in Josephson junctions between $s$-wave and $p$-wave superconductors, where a phase bias toggles the DMTI entirely on and off. These results enable a way to engineer spin textures using superconducting order.

The quasiparticle relaxation dynamics of the iron-based superconductor ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ ($T_c\sim 29$ K) were investigated using ultrafast optical spectroscopy. A pseudogap (${\mathrm{\Delta }}_{\text{PG}}=3.3\pm 0.3$ meV) was observed to open below $T^{*}\approx 60$ K, prior to the emergence of a superconducting gap [$\mathrm{\Delta }\left(0\right)=6.6\pm 0.4$ meV]. At high excitation fluence, a coherent $A_{1g}$ phonon mode at 5.49 THz was identified, exhibiting deviations from anharmonic behavior below $T_c$. The electron-phonon coupling constant for this mode was estimated to be ${\lambda }_{A_{1g}}\approx 0.23$. These results provide insights into the interplay between the electron-phonon interactions, pseudogap, and the superconducting pairing mechanism in ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$.