The density functional theory plus Hubbard $U$ ($\mathrm{DFT}+U$) technique is one of the most widely used tools by condensed matter physicists and solid-state chemists for the simulation of transition-metal and lanthanide-bearing crystals, and increasingly of much more diverse chemistries. Although often synonymous with the corrective functionals of Dudarev et al. [Phys. Rev. B 57, 1505 (1998)] and Liechtenstein et al. [Phys. Rev. B 52, R5467 (1995)], there exists a wide variety of $\mathrm{DFT}+U$-type functionals ready to be utilized, and no doubt yet to be developed. Since the earliest days, the gap in the $\mathrm{DFT}+U$ single-particle eigenspectrum has been associated with the fundamental band gap, and the method has typically found more success for spectra than for total-energy derived properties. There has been some doubt, however, as to the conceptual validity of this association. Here, extending findings from recent years regarding local, semilocal, and hybrid functionals within the generalized Kohn-Sham framework, we prove and numerically demonstrate that the $\mathrm{DFT}+U$ eigenspectrum gap is conceptually valid, in the specific sense that it matches its own fundamental gap calculated using total-energy differences. We emphasize that this does not imply its agreement with experimental values, and indeed our argument is independent of the Hubbard $U$ parameter. The result holds for pristine periodic systems with converged $k$-point sampling but not, however, for defective ones, isolated systems, or systems in which added charges exhibit spontaneous localization. We show that band-gap validity for pristine solids holds in the presence of pseudopotentials and PAW potentials, when using hybrid functionals, and in DFT+$U(+J)$ irrespective of the level of subspace projection onto the band-edge states. We survey every collinear-spin $\mathrm{DFT}+U$-type functional known to have been published to date, within a unified notation. We verify analytically under which conditions the eigenvalue gap equals its fundamental gap, for each functional. Returning to the related but different question of band-gap correction efficiency, we offer fresh analysis of $\mathrm{DFT}+U$ band-gap projection dependence, and each functional's effect on energies and gaps for the hydrogen lattice in the Mott-Hubbard limit.

Excitons, bound states of electrons and holes, are affected by the properties of the underlying band structure of a material. Defects in lattice systems may trap electronic defect states, to which an electron can be excited to form defect-bound excitons. Here, we examine the effect of band topology on excitons in systems with a single-site defect. We show that in the topological phase, when robust, in-gap, ring-shaped electronic states appear around defects, the excitons' binding energies are lowered as a result of the wide spatial profile of the defect state. In addition, the excitonic wave functions have distinct shapes that change in order with small changes in the model due to the mixed orbital character of the topological bands. Our study therefore sheds light on the dominant mechanisms that govern the behavior of defect-bound excitons in topological materials.

Electrons in transition metal dichalcogenides (TMDs) possess valley and spin degrees of freedom, which leads to rich exciton and exciton-polariton physics with nontrivial scattering dynamics and enhanced nonlinearities, presenting a key mechanism for photonic devices. Yet, existing descriptions of bosonization and polariton interactions in TMD-based systems overlook the valley degree of freedom as well as the various particles' spins combinations. In this work, we derive a nonequilibrium field-theory approach in the path integral formalism that allows one to track all the polariton nonlinearities in the strong-coupling regime. We demonstrate that, when all the bright- and dark-exciton species are considered, the TMD monolayer-based polariton systems feature 16 different nonlinear contributions due to interactions and even more saturation-related terms. Strikingly, while the interactions of excitons within one valley are overall dominant, we show that the interaction constant corresponding to the scattering of spin-dark and bright excitons is much larger than that for bright excitons alone, indicating a possibly much higher contribution to the blueshift from spin-dark excitons than from bright intravalley excitons.

We develop a computationally efficient finite-temperature continuum approach for exciton renormalization and optical absorption in doped monolayer transition-metal dichalcogenides. The model combines a massive-Dirac electronic structure, the nonlocal Rytova-Keldysh interaction, finite-temperature carrier screening, Hartree-Fock (HF) and random phase approximation (RPA) quasiparticle self-energy corrections, and a momentum-space Bethe-Salpeter equation (BSE). This approach enables the quasiparticle gap, exciton transition energies, and exciton binding energies to be followed systematically as functions of carrier density, temperature, dielectric environment, material parameters, and excitonic state. We find that quasiparticle BGR and binding-energy reduction can substantially compensate, producing comparatively weak shifts of the lowest exciton resonance, while excited states show a stronger response to screening. The RPA calculations further reveal a nonmonotonic temperature dependence of the excitonic energies at low carrier densities, reflecting the competition between quasiparticle and excitonic renormalizations. The calculated optical spectra also exhibit pronounced material-dependent density and temperature trends. These results substantially advance the compensation picture, providing a unified finite-temperature framework for excitonic many-body renormalization in monolayer TMDCs.

The discovery of high-$T_c$ superconductivity in pressurized bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ presents a new arena for exploring unconventional pairing mechanisms. A pivotal yet unresolved issue is the specific role of the $3d_{z^2}$ orbital of Ni. While its interlayer superexchange antiferromagnetic coupling is widely considered crucial for superconductivity, the role of its itinerancy remains undetermined. Early studies showed that the superconductivity is accompanied by the emergence of a small Fermi pocket of $3d_{z^2}$ orbitals. However, recent experiments show controversial results on the role of the $3d_{z^2}$ Fermi pocket on superconductivity. Motivated by these experimental results, we investigate an effective bilayer two-orbital model for ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ using density-matrix renormalization group on a minimal one-dimensional geometry. By systematically varying the $3d_{z^2}$ orbital filling from $1/12$ doping to half filling, we observe a pronounced suppression of superconducting correlations near half filling. Our results demonstrate the itinerancy of the $3d_{z^2}$ orbital is favorable for pairing in the bilayer two-orbital model for ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Moreover, we observe that the pairing correlation is enhanced in regions where charge fluctuations are large, suggesting a competition between charge order and superconductivity in the model.

The interplay between long-range structural distortions and orbital order, and local short-range phenomena such as polarons, are key for understanding the properties of the manganites. In this work we examine the role of local and long-range physics in relation to orbital ordering in the single-layered manganite ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{1.5}{\mathrm{MnO}}_4$ with a combination of optical reflection anisotropy and ultrafast broadband pump-probe spectroscopy. We find that the reflection anisotropy, measured in equilibrium, is strongly sensitive to charge and orbital-ordering transition only. However, the ultrafast response, measuring the nonequilibrium state, is sensitive to a range of phenomena in the material, including delocalized (long wavelength) phonons as well as localized polarons. In particular, we find that a strong sensitivity to electronic and structural changes gives rise to apparent nonlinearities when probed at specific wavelengths, despite the key degrees of freedom remaining linear. These observations point to the important role of orbital-lattice couplings and polarons dressing the electronic states across the ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{1.5}{\mathrm{MnO}}_4$ phase diagram.

In gyrotropic crystals, an oscillating magnetic field induces a charge response known as the gyrotropic magnetic current. While its conventional origin is attributed to magnetic-field-modified band energy and shifts in the Fermi surface, a recent study identified an additional spin-driven magnetic displacement contribution. Here, we complete the picture by identifying the orbital counterpart of the magnetic displacement current. Using a density matrix formulation that incorporates both minimal coupling and spin-Zeeman interactions, we derive the electronic equations of motion in the presence of an oscillating magnetic field and uncover an orbital contribution to the wave-packet velocity. Physically, this contribution arises from the time variation of the magnetic-field-induced charge polarization. In the low-frequency transport regime, this mechanism becomes purely intrinsic. We illustrate this intrinsic gyrotropic current of orbital origin in the $\mathcal{P}\mathcal{T}$-symmetric antiferromagnet CuMnAs. We show that the intrinsic gyrotropic magnetic current reverses sign upon Néel vector reversal, establishing it as a direct probe of antiferromagnetic order in CuMnAs and other $\mathcal{PT}$-symmetric antiferromagnets.

Peculiar features of the Josephson effect in graphene were described theoretically by Titov and Beenakker [Phys. Rev. B 74, 041401(R) (2006)], who solved the Dirac-Bogoliubov-de Gennes equation for a superconductor-graphene-superconductor junction with rectangular geometry. Here, we adopt the analysis for graphene Corbino disks, finding out that—for the outer to inner radii ratio $r_2/r_1\gtrsim 5$—such systems may demonstrate, when varying the electrochemical potential and the spatial profile of the electrostatic barrier, crossover from standard Josephson tunneling (SJT), via graphene-specific multimode Dirac-Josephson tunneling (MDJT), toward the ballistic Josephson effect (BJE). Signatures of SJT appear only near the Dirac point when the barrier shape is close to rectangular, MDJT appears in the tripolar range and is very robust against varying the barrier shape, and BJE is restored in the unipolar range when smoothing the barrier shape. A comparison with the results of a numerical simulation of quantum transport on the honeycomb lattice is also given.

We consider the renormalization of transport in a quantum contact by the external electromagnetic environment and show that weak quantum fluctuations from a symmetric environment can lead to a quantized transconductance in five-terminal contacts. This mechanism does not work for fewer terminals. We present an implementation of the environment and investigate several example quantum contacts where the quantization takes place.

Pressure provides a clean and continuous route for tuning electronic structure and magnetic interactions in itinerant ferromagnets without introducing chemical disorder. Here, we report high-pressure structural, transport, and electronic structure studies of hexagonal ferromagnetic ${\mathrm{SmCrGe}}_3$, a rare-earth chromium germanide that exhibits giant uniaxial magnetocrystalline anisotropy and strong coupling between localized Sm $4f$ and itinerant Cr $3d$ electrons. Synchrotron high-pressure x-ray diffraction measurements reveal that the hexagonal $P{6}_3/mmc$ structure remains stable up to 10 GPa without a crystallographic phase transition, indicating that the pressure-driven evolution is primarily electronic rather than structural in origin. High-pressure electrical resistance measurements show a nonmonotonic pressure dependence of the Curie temperature ($T_{\mathrm{C}}$) inferred from the resistance anomaly, where $T_{\mathrm{C}}$ initially decreases with pressure, followed by a slight recovery before the magnetic order is suppressed above 6.4 GPa. Concomitantly, a low-temperature resistance minimum emerges above 4.3 GPa, consistent with enhanced Kondo-like scattering associated with Sm $4f$ electrons. Density functional theory calculations on ${\mathrm{SmCrGe}}_3$ reveal a highly pressure-sensitive Cr-derived flat band near the Fermi level. Systematic lattice-parameter tuning calculations further show that anisotropic lattice compression, particularly along the crystallographic $c$, strongly modifies the flat-band position relative to the Fermi level. These results identify ${\mathrm{SmCrGe}}_3$ as a promising platform for studying the coupled evolution of fragile itinerant ferromagnetism, pressure-sensitive flat-band electronic structure, and emergent $4f$-derived correlated scattering under pressure.

Altermagnets ($\text{AMs}$) are spin-compensated materials in which opposite-spin sublattices are connected by a symmetry that causes a spin splitting in their elementary excitations. As there is a strong effect of altermagnetism on domain wall properties, it is quite natural to also expect an enrichment of the physics of magnetic excitations at $\text{AM}$ domain walls. Here, we consider the propagation of spin eigenexcitations along domain walls in easy-axial $d$-wave $\text{AMs}$. Investigating the presence of bound states localized on a domain wall, we find that the effect of the $\text{AM}$ on the bound states strongly depends on the orientation of the domain wall relative to the crystallographic directions. If the domain wall is oriented along a nodal direction [100] or [010], $\text{AM}$ does not change the number of bound states; however, it leads to a nonlinear dispersion and a tilt of the wavefront. The effect of $\text{AM}$ is strongest when the domain wall is oriented along the directions [110] or $\left[\overline{1}10\right]$, i.e., along the directions of the strongest $\text{AM}$ splitting in the magnon spectrum. In this case, (i) the additional gapped bound states appear, (ii) degeneracy of the eigenstates with respect to their polarization (right-hand or left-hand precession of the Néel vector) is removed, and (iii) the localization area of the bound states strongly depends on the eigenfrequency. The latter may lead to strong localization of the bound state at the domain wall. We further consider the influence of a static magnetic field that is applied along the easy axis and find that the magnetic field induces an asymmetry between the localization regions on opposite sides of the domain wall and sets an upper limit on the absolute value of the propagating eigenstate's wave vector.

The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's original paradigm. Here, we develop an algebraic framework for systematically deriving the fusion rules of topological defects in higher-dimensional lattice systems with noninvertible generalized symmetries, and focus on a $(2+1)$-dimensional quantum Ising plaquette model as a concrete illustration. We show that bond-algebraic automorphisms, when combined with the so-called half-gauging procedure, reveal the structure of the noninvertible duality symmetry operators, which can be explicitly represented as a sequential quantum circuit. The resulting duality defects are constrained by the model's rigid higher symmetries (lower-dimensional subsystem symmetries), leading to restricted mobility. We establish the fusion algebra of these defects. Finally, in constructing the noninvertible duality transformation, we explicitly verify that it acts as partial isometry on the physical Hilbert space, thereby satisfying a recent generalization of Wigner's theorem applicable to noninvertible symmetries.

Few-layer ${\mathrm{CrI}}_3$ exhibits thickness-dependent interlayer antiferromagnetic coupling and magnetic-field-induced spin-flip transitions. Although bilayer ${\mathrm{CrI}}_3$ has been extensively studied, the spin dynamics of thicker multilayer structures remain less well understood. In this work, we present systematic simulations and analytical modeling of magnetization reversal and antiferromagnetic resonance modes in bilayer (2L), trilayer (3L), and tetralayer (4L) monoclinic ${\mathrm{CrI}}_3$. By solving coupled Landau-Lifshitz equations using parameters benchmarked against bilayer experimental results, we identify thickness-dependent resonance maps, mode frequencies, and critical fields under both out-of-plane and in-plane magnetic fields. The analytical mode frequencies obtained from linearized equations show good agreement with numerical results. We further demonstrate that antiferromagnetic resonances can be tuned by tens of gigahertz through rotation of the magnetic-field angle. These findings reveal thickness-controlled spin dynamics in van der Waals antiferromagnets and highlight their potential for multistate memory and high-frequency spintronic applications.

As a high-thermal-conductivity material, graphite is not only important in thermal management applications, but also serves as a fundamental platform for exploring phonon hydrodynamics at elevated temperatures. However, the modeling and understanding of the spatiotemporal dynamics of heat pulse propagation in finite-size graphite are not yet established. In this work, we target this challenge by directly solving the transient phonon Boltzmann transport equation in real and reciprocal spaces as well as in temporal domain with first-principles input. We investigate the dynamics of both ballistic heat waves and second sound, and uncover the impact of temperature and isotope concentration. In the ballistic regime, the present computational framework accurately captures the ballistic peaks of various phonon branches propagating at distinct speeds and reveals different “peak attenuation” effects induced by elevated temperatures and isotope scattering. In the hydrodynamic regime, we unveil the kinetic formation process of the second sound-wave packet and demonstrate an optimal temperature window around 100–120 K and the monotonic dissipative effect of isotope scattering. Therefore, this study provides not only a robust computational framework, but also deeper physical insights for transient dynamics of heat pulse propagation in graphitic materials.

We investigate a quantum dynamical phase transition induced by the competition between local unitary evolution and dissipation in a qubit chain with a strong, on-site ${\mathbb{Z}}_2$ symmetry. While the steady state of this evolution is always maximally mixed, we show that the dynamical behavior of certain nonlocal observables on the approach to this steady state is dictated by a quantum Ising model with a complex transverse field (cTFIM). A crucial feature of our mapping to the cTFIM is an extensive number of local, weak ${\mathbb{Z}}_2$ symmetries possessed by the dynamics, allowing us to investigate these observables analytically and uncover a dynamical phase transition as the relative rate of unitary evolution and dissipation is tuned. We show that the weak-dissipation limit corresponds to a cTFIM with a large magnitude of the imaginary transverse field, for which the many-body ground state (with smallest real eigenvalue) is gapless, exhibiting quasi-long-range correlations of the local magnetization with a continuously varying exponent. Correspondingly, the dynamics of the nonlocal observables show oscillatory behavior with an amplitude decaying exponentially in time. The strong-dissipation limit corresponds to a gapped ferromagnetic phase of the cTFIM, and nonlocal observables show exponential decay on the approach to equilibrium. This transition in ($1+1$) dimensions has a peculiar two-sided nature appearing as either first or second order depending on the phase from which the transition is approached, an analytic result which is corroborated by numerical studies. In higher dimensions, we present a field-theoretic understanding of the first-order nature of this transition, when approaching from the ferromagnetic phase of the cTFIM, though the nature of the phase with large imaginary transverse field remains to be understood.

Spin relaxation results in spin decoherence and a finite spin lifetime, which are detrimental to spintronic devices. To achieve a long spin lifetime desirable for spintronic devices, elucidating the spin relaxation mechanism and factors influencing the spin lifetime is of vital importance. Here, we investigate the spin relaxation in $X$-wave magnets ($X=p,d,f,g,i$) with Rashba spin-orbit coupling within the framework of the D'yakonov-Perel' mechanism. We calculate the tensor of the spin relaxation rate for an arbitrary Néel vector direction in the regime of a weak spin-orbit field. It is found that the spin relaxation rate matrices are anisotropic and can be dictated by magnetic point group symmetry. As an illustration, we study the spin relaxation for a Néel vector along the [001] direction. For the $p$-wave magnet, we derive analytical expressions for the temporal evolution of spins. Moreover, we show that the spin relaxation is highly controllable by the Néel vector and the spin relaxation rate is proportional to the momentum relaxation time, Rashba, and spin-split strengths. Our results shine more light on the fundamental understanding of the spin relaxation mechanism in unconventional $X$-wave magnets.

Multiferroic materials are of great importance for the development of next-generation multifunctional devices. Here, we predict a stable one-dimensional (1D) antiferromagnetic (AFM) semiconductor ${\mathrm{NbI}}_3$ chain, in which moderate electron doping induces site-centered charge order, ferrimagnetism (FIM), and ferroelectric polarization. The asymmetric Jahn-Teller distortion makes adjacent Nb sites inequivalent, and the resulting charge order, combined with bond dimerization, generates ferroelectricity. At 0.5 $e/\text{u.c.}$ doping (where u.c. denotes unit cell), the FIM chain is half metallic and has a calculated polarization-reversal barrier of about 13 meV/u.c. The optimized ferromagnetic configuration suppresses this asymmetric distortion and charge order, linking polarization to the magnetic configuration. Finally, considering the experimental feasibility of doping, we identify Li-intercalated bulk ${\mathrm{NbI}}_3$, i.e., ${\left({\mathrm{NbI}}_3\right)}_2\mathrm{Li}$, as a viable platform to realize the electron-doping effect in the ${\mathrm{NbI}}_3$ chain and the coexistence of magnetic and ferroelectric orders in this system further confirms its multiferroic nature. Our research paves a new way for the design of 1D multiferroic materials.

Anisotropic magnetoresistance (AMR) arises from symmetry lowering of the conductivity tensor induced by magnetic order. In simple ferromagnets, AMR is a relativistic effect, relying on spin-orbit interaction (SOC). Here, we demonstrate that a comparable symmetry lowering can also occur in a nonrelativistic limit. Using tight-binding models, density functional theory calculations, and Boltzmann transport theory, we investigate systems with multiple magnetic sublattices, including both collinear and noncollinear antiferromagnets, as well as ferrimagnetic configurations. We show that AMR and related anisotropies can emerge purely from magnetic order, without the need for SOC, and may reach significant magnitudes. The findings are supported by case studies on toy-model lattices and real materials such as MnN and ${\mathrm{Mn}}_3\mathrm{Sn}$ and are further interpreted using a symmetry analysis based on Neumann's principle. Material candidates that exhibit nonrelativistic anisotropic magnetoresistance are identified by symmetry analysis applied to entries in the MAGNDATA database.

In this paper, we investigate how a topologically ordered state changes to another one from a microscopic point of view. To this end, we focus on the behavior of topological entanglement and 1-form symmetry under decoherence, which induces a phase transition between these states. After a detailed numerical study of the color code as a first case study, we explain how the decoherence changes the topological properties of the state, observing topological entanglement negativity (TEN) and the disorder parameter of the 1-form symmetry. Our results suggest that the above quantities are closely connected with the first and 0th simplicial homology, respectively, and that the transition can be understood from the point of view of decoherence percolation. For a detailed microscopic investigation, we introduce the concept of quasilocal TEN (QLTEN) and show snapshots of the local topological property of the state, which is capable of clearly describing the decoherence percolation. To further investigate how QLTEN and the 1-form symmetry are related to the transition, we introduce the concept of explosive percolation (EP) to the present system, which has received a lot of attention in the last two decades. EP in the present context means that there exists some bias in the decoherence, reducing a large cluster of decohered regions. As a second case study, we consider a toric code on a triangular lattice under an external-field-type decoherence. Detailed numerical study reveals that QLTEN can faithfully describe the emergent Higgs region and the surviving logical qubits. We find that although topological entanglement negativity (TEN), clusters of QLTEN, and string operators strongly correlate with each other in both the color code and the toric code, the two systems react to patterns of EP quite differently. This fact indicates that obtaining a universal understanding of the topological phase transition is challenging even for strongly related systems.