The roton-triggered charge density wave (CDW) is widely studied in fractional quantum Hall (FQH) and fractional Chern insulator (FCI) systems, and there also exist field theoretical and numerical realizations of continuous transition from FCI to superfluid (SF). However, the theory and numerical explorations of the transition between FCI and supersolid (SS) featuring coexistence of CDW and SF orders, are still lacking. In this work, we study the topological flat-band lattice models with $\nu =1/2$ hard-core bosons, where previous studies have discovered the existence of FCI states and possible direct FCI-SS transitions [Wang et al., Phys. Rev. Lett. 107, 146803 (2011), Luo et al., Phys. Rev. B 102, 155120 (2020)]. While the FCI is robust, we find the direct FCI-SS transition is absent, and there exist more intriguing scenarios. In the case of checkerboard lattice, we find an intermediate gapless CDW state without SF, sandwiched between FCI and SS. This novel state is triggered by the roton instability in FCI and it further continuously brings about the intertwined finite-momentum SF fluctuation when the CDW order is strong enough, eventually transiting into an unconventional finite-momentum SS state that is similar to pair-density-wave superconductors. The intermediate gapless CDW state is a vestige from the SS state, since the increasing quantum fluctuation melts only the Larkin-Ovchinnikov-type SF order in SS but its (secondary) product—the CDW order—survives. On honeycomb lattice, we find no evidence of SS, but discover an interesting sequence of FCI-Solid I-Solid II transitions, with both solids incompressible. Moreover, in contrast to previous single-roton condensation, this sequence of FCI-Solid I-Solid II transitions is triggered by the softening of multiroton modes in FCI. The minimal roton mode in FCI gives rise to Solid I, and when this CDW is strong enough, a higher-energy mode in FCI goes soft and renders the doubled translation period of Solid II. Considering the intertwined wave vectors of the CDW orders, Solid I is also a vestige of Solid II. Our work provides new horizons not only for the quantum phase transitions in FCI but also for the intertwined orders and gapless states in bosonic systems, which will inspire future theoretical and experimental studies.

The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall states and their lattice analogs—fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations and, for spinful systems, are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group simulations, we demonstrate the emergence of a spin-polarized $1/3$-Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at $\nu =1$ and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around $\nu =1$, whereas we do not find such textures around $\nu =1/3$. The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.

Multiorbital Hubbard models with Hund coupling and crystal-field splitting exhibit an instability toward spin-triplet excitonic order in the parameter regime characterized by strong local spin fluctuations. Upon chemical doping, two distinct types of excitonic ferromagnetism have been reported. Using steady-state nonequilibrium dynamical mean-field theory, we demonstrate that photodoped half-filled systems can host nonthermal counterparts of these excitonic phases and exhibit a rich phase diagram in the space of photodoping and crystal-field splitting. Photodoping a spin-triplet excitonic insulator provides a route towards nonequilibrium control of magnetic order.

Antidamping-like (ADL) spin-orbit torques (SOTs) exhibit the efficiency of magnetization switching in recent experiments, especially in topological insulator/ferromagnet (TI/FM) heterostructures where a giant SOT has been reported even at room temperature. While most experiments have confirmed that the giant ADL torque arises from TI surface states via the well-known Edelstein effect, theoretical understanding of the physical origin of ADL SOT is challenging because the ADL SOT from the Edelstein effect is quite weak in linear-response theory. In this paper, in sharp contrast to the existing linear-response theory, we develop a nonlinear Edelstein effect theory as the mechanism of generating a large ADL torque in the nonlinear response regime. We unveil that mixed quantum metrics, defined in the extended parameter space spanned by momentum and magnetization, can contribute an intrinsic ADL SOT via interband coherence mechanisms (injection, shift, and anomalous), and the resulting SOT can exceed the linear one by several orders of magnitude around the Dirac points. This nonlinear ADL SOT provides an alternative explanation of the observed giant SOT in recent experiments, and also offers us a new route to probe quantum metrics.

We provide theoretical evidence of the emergent topology in a twisted bilayer system, despite the corresponding monolayer hosting topologically trivial properties. To this end, we investigate an interesting interplay of destructive interference due to lattice geometry and band folding due to enlargement of the unit cell in generating and subsequently modifying the band topology in a twisted bilayer $\alpha -T_3$ system. The large degeneracy of the emergent flat band in the dice limit of the $\alpha -T_3$ lattice is removed by aligning with h-BN layers, resulting in the formation of sub-bands with varied topological characteristics. Remarkably, while the sub-band near charge neutrality exhibits a trivial behavior, a topologically nondegenerate singular sub-band emerges away from it. The topological band remains isolated from the rest of the bands for a substantial area in the $\alpha -\theta$ plane (where $\alpha$ and $\theta$ correspond to the hopping ratio and twist angle, respectively) while exhibiting multiple phase transitions as a function of the aforementioned parameters via hybridization with its nearest bands. Finally, we study the evolution of the hybrid Wannier charge center and the Chern number to characterize the different emergent topological phases and corroborate our findings.

We present density-functional theory (DFT) calculations, which provide a microscopic picture of the recombination-enhanced migration of interstitial Mg in gallium nitride (GaN). We determine stable structures and migration pathways with accurate Heyd-Scuseria-Ernzerhof (HSE) approximation to the exchange-correlation energy, and also compute recombination rates using the obtained energy spectrum and wavefunctions. It is found that the migration between the most stable octahedral sites (${\mathrm{Mg}}_{\mathrm{O}}$) via our found interstitial complex structure shows the low migration energy in which one or two electrons are captured during the migration, that the most stable charge state of $2+$ changes to $1+$ or neutral, and that by this recombination of carriers the migration barrier is significantly reduced. Starting from ${\mathrm{Mg}}_{\mathrm{O}}^{2+}$, Mg captures an electron becoming the $1+$ charge state and overcomes the barrier of $1.65\mathrm{eV}$, much reduced from $2.23\mathrm{eV}$ in case of the migration with the $2+$ charge state kept. Moreover, further electron capture is realized accompanied by substantial structural relaxation, with Mg thus becoming neutral. Detailed HSE calculations for this second capture show that the migration barrier is $1.55\mathrm{eV}$, thus clarifying the important role of the carrier recombination for Mg migration in GaN. These findings are corroborated by the present quantitative calculations of recombination rates based on electronic Hamiltonian constructed from our DFT-obtained energy spectrum. The timescale of the recombination is clarified to be in or under the timescale of the migration with typical electron density and the enhancement is expected to be significant.

The Goos-Hänchen shift of a normally incident optical beam to a metagrating consisting of magneto-optical material is studied. The metagrating consists of a compound grating of magneto-optical rods atop a dielectric slab, which features staggered lateral shifts of the rods. The compound grating induces zone-folding quasibound states in the continuum at the $\mathrm{\Gamma }$ point with nonzero group velocity, whose $Q$ factor is inversely proportional to the lateral shift. By applying stationary-phase theory, the Goos-Hänchen shift of a normally incident quasiplane wave are found to be enhanced at the reflection peak. The maximum magnitude of the Goos-Hänchen shift within the reflection peak is proportional to the $Q$ factor of the zone-folding quasibound states in the continuum. Simulations of a normally incident Gaussian beam with a finite beamwidth show that the Goos-Hänchen shift is dependent on the beamwidth.

Contrary to canonical expectations, we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomenon by studying a spinless-fermion model on a square lattice with nearest-neighbor repulsion. We find an array of flux patterns, as a function of interaction strength and filling factor, that break time-reversal symmetry but may or may not preserve translational symmetry. A key finding is that the pattern of flux ordering does not uniquely determine the electronic properties. As such, another class of phases of matter is introduced that expands the set of candidate ground states in interacting many-body systems.

Discovering and classifying nontrivial mixed states are the most important current issues in condensed matter and quantum information. In this study, we characterize some nontrivial mixed states by numerically observing the second Rényi conditional mutual information (CMI). The CMI can measure mixed state gap, estimated by the exponential decay rate of the second Rényi CMI under a tripartition of system, which provides the second Rényi version of the Markov length. We introduce an efficient numerical scheme for the calculation of the second Rényi CMI based on the doubled Hilbert space formalism. In this work, we show that the second Rényi CMI is a powerful measure to characterize and detect nontrivial mixed gapped quantum matters. Concretely, we study two typical systems: (i) the cluster model under odd-site local $Z$ decoherence and (ii) transverse field Ising model under decoherence of $ZZ+X$ type. There, we numerically observe how the second Rényi CMI and its Markov length behave along the change of mixed states. In addition, in the present study, we provide numerical evidence that the second Rényi CMI changes across the crossover between the strong and weak spontaneous symmetry-breaking mixed regimes.

Anti-Heusler alloys, being a new addition to the Heusler alloys family, exhibit atomic disorders, and almost all of them are reported as a re-entrant spin-glass system. Although such spin-glass feature is generally attributed to the inherent atomic disorder, a comprehensive and extensive investigation on the individual roles of different types of disorders in magnetic interactions remains lacking for any of the reported anti-Heusler systems. As an illustrative case, we have carried out an in-depth experimental as well as theoretical investigation of structural, magnetic, and transport properties of a polycrystalline anti-Heusler alloy, ${\mathrm{Al}}_2\mathrm{MnFe}$. While the major atomic disorder is found to be among Fe and Mn atoms, which are randomly distributed among the two octahedral sites, $4a$ and $4b$ (B2-type disorder), a relatively small fraction ($\sim 12\%$) of Mn atoms also replace Al atoms at the tetrahedral $8c$ site. Magnetically, the system undergoes two transitions: a paramagnetic to a ferromagnetic transition at $T_{\mathrm{C}}\sim 113\mathrm{K}$, followed by a spin-glass phase transition below $T_{\mathrm{f}}\sim 20\mathrm{K}$. Here, the magnetic moment is primarily confined to Mn atoms. Very interestingly, our theoretical analysis reveals that the ferromagnetic spin arrangement remains rather robust in spite of the $50\%$ disorder of moment-carrying Mn atoms between the two octahedral sites, but a much smaller ($\sim 12\%$) cross-distribution of Mn atoms between octahedral and tetrahedral sites are sufficient to impose a reentrant spin-glass state at low temperature. Our analysis brings forth the importance of understanding the role of individual types of swap disorder on magnetic properties in the anti-Heusler family of materials.

Recent observations of time-reversal breaking superconductivity at twisted cuprate interfaces motivate the development of new approaches to better characterize this emergent phenomenon. Here we study the dynamical properties of the order parameters at the twisted unconventional superconductor interfaces. We reveal the emergence of a soft collective mode (Josephson plasmon) at the time-reversal breaking transition, which can be tuned by temperature, twist angle, or magnetic field. Furthermore, nonlinear dynamical responses contain direct signatures of both the transition and the broken symmetry itself. In particular, we show that the generation of a second harmonic voltage under alternating current driving is a necessary and sufficient signature of time-reversal symmetry breaking. Finally, we demonstrate that strong nonlinear driving induces dynamical phase transitions between phases with and without spontaneous symmetry breaking, introducing a tool for their out-of-equilibrium control. We discuss the signatures of our predictions in ac current-driven experiments on twisted ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$interfaces.

The outstanding physical properties of hyperuniform condensed matter systems hold significant promise for technological applications and studying effects that may disrupt this hidden order is therefore very important. Vortex matter in superconductors is a model system to study this problem since imaging experiments have revealed that correlated disorder in the host media and finite-size effects disrupt the hyperuniformity of the in-plane arrangement of vortices. Here we report simulations of layered interacting elastic lines as a model for the vortex lattice in three-dimensional superconductors, following a cooling protocol that closely mimics the experimental conditions. We show that finite-thickness effects limiting the hyperuniformity range arise both in equilibrium and out of equilibrium. Our results provide a theoretical framework to draw a realistic road-map on synthesizing hyperuniform materials when cooling structures on finite host media with disorder.

We address the fate of many-body localization (MBL) of mid-spectrum eigenstates of a matter-free $\mathrm{U}\left(1\right)$ quantum-link gauge theory Hamiltonian with random couplings on ladder geometries. Apart from level spacing distribution indicators like disorder-averaged mean level spacing, we also consider an intensive estimator $\mathcal{D}\in [0,1/4]$, which acts as a measure of elementary plaquettes on the lattice that are active or inert in mid-spectrum eigenstates as well as the concentration of these eigenstates in Fock space, with $\mathcal{D}$ equal to its maximum value of $1/4$ for Fock states in the electric flux basis. We calculate its distribution, $p\left(\mathcal{D}\right)$, for $L_x\times L_y$ lattices, with $L_y=2$ and 4, as a function of (a dimensionless) disorder strength $\alpha$ ($\alpha =0$ implies zero disorder) using exact diagonalization in many disorder realizations. Although finite-size estimators based on level spacings do not give a reliable critical disorder strength, ${\alpha }_c\left(L_y\right)$, beyond which MBL prevails as $L_x\to \infty$; a different estimator based on the skewness of $p\left(\mathcal{D}\right)$ gives ${\alpha }_c(L_y=2)=31.04\pm 0.54$ using data for $L_x\le 14$ due to faster convergence. $p\left(\mathcal{D}\right)$ for wider ladders with $L_y=4$ show a lower tendency to localize, suggesting a lack of MBL in two dimensions. A remarkable observation is the resolution of the (monotonic) infinite-temperature autocorrelation function of single plaquette diagonal operators in typical high-energy Fock states into a plethora of emergent timescales of increasing spatio-temporal heterogeneity as the disorder is increased. At intermediate $\alpha$ as well as for $\alpha$ slightly below ${\alpha }_c\left(L_y\right)$, a fraction of randomly selected initial Fock states display striking oscillatory temporal behavior of such plaquette operators in spatial regions formed out of connected plaquettes.

Li-based materials have garnered significant attention due to their diverse configurations, engaging electronic structures, and promising applications. Based on first-principles predictions, we identified several unusual stoichiometric lithium-gallium metallic phases under pressure, e.g., $\mathrm{LiG}{\mathrm{a}}_3$ and $\mathrm{L}{\mathrm{i}}_6\mathrm{Ga}$. Strikingly, the $\mathrm{LiG}{\mathrm{a}}_3$ with cubic symmetry and ${\mathrm{Ga}}_6$ octahedron is estimated to hold a superconducting critical temperature ($T_c$) of 6.5 K at atmospheric pressure, exceeding the representative superconductor mercury and the boiling point of liquid helium, deriving from the coupled interaction of Ga $4p$ electrons at the Fermi level with the low-frequency Ga atomic vibrations. Remarkably, the $\mathrm{L}{\mathrm{i}}_6\mathrm{Ga}$ exhibits pressure-driven structural transitions accompanied by the evolution of interstitial anionic electrons (IAEs) topologies: the zero-dimensional IAEs in ambient-pressure $R$-3 phase is converted into the one-dimensional (1D) IAEs in the compressed $C2/m$ and $R-3m$ phases, and the 1D IAEs and the valence electrons of Ga constitute a conducting network. Unexpectedly, the coexistence of electride and superconductivity states is uncovered in $\mathrm{L}{\mathrm{i}}_6\mathrm{Ga}$, and $R-3m \mathrm{L}{\mathrm{i}}_6\mathrm{Ga}$ has the highest $T_c$ (15.2 K at 240 GPa) among Li-Ga superconductors, originating from the coupling between the Li $2p$ and Ga $4p$ states and the Li-dominated softened phonon modes at low frequencies. These findings provide design guidance for future exploration of emerging superconductor materials.

The two-dimensional molecular conductor $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[{\mathrm{N}\left(\mathrm{CN}\right)}_2\right]}_3$ has been studied because of the intriguing magnetic coupling of the molecular $\pi$ electrons to the ${\mathrm{Mn}}^{2+}$ ions. Utilizing X-band electron spin resonance spectroscopy we have performed comprehensive investigations of the magnetic properties, in particular on the temperature and angular dependences of the spin susceptibility, the $g$ factor, and the linewidth. Due to the $\pi -d$ coupling, a rearrangement of the $\pi$ spins occurs: At low temperatures the $g$ factor shifts enormously with a pronounced in-plane anisotropy that flips as the temperature decreases, the lines broaden significantly, and the spin susceptibility increases upon cooling with a kink at the phase transition. By carefully analyzing the angular dependence of $g\left(\theta \right)$ and $\mathrm{\Delta }H\left(\theta \right)$ we reveal the influence of anisotropic Zeeman interaction in addition to spin-phonon coupling. We conclude the presence of two magnetically distinct BETS chains and discuss the possibility of altermagnetic order.

This work aims to elucidate the microscopic origins of various photoluminescence emissions in copper- and silver-based halide compounds by means of first-principles calculations. Our density functional theory based analysis reveals that Cu pair and Ag pair self-trapped excitons (STEs) exhibit distinct structural configurations and excited-state behaviors, with Ag pair STEs showing pronounced electrophilicity. Defect states, including interstitial iodine and halogen vacancies, play decisive roles in quenching or enabling emission. Cation substitution not only modifies STE configurations but can also enable the coexistence of multiple STE types within a single lattice, offering a route to tunable photoluminescence. These findings clarify the contrasting roles of Cu and Ag pairs and provide guidance for tailoring halide emitters through targeted cation substitution and defect engineering.

In this work we present an extended Drude model based on a memory function formalism to describe the optical conductivity and permittivity of disordered conductors, spanning non-Fermi liquids to materials featuring complex ion dynamics. The general form of our memory function ensures Kramers-Kronig consistency, and includes transverse optical-longitudinal optical terms that capture diffusive relaxation processes in the material. We validate our extended Drude model by measuring the optical properties of liquid mercury over a wide spectral range spanning the visible to long-wave infrared (wavelengths between 430 nm and $30\mu \text{m}$) via spectroscopic ellipsometry. We then demonstrate the versatility of the model for covering diverse regimes of disorder by replicating reported experimental data for the ionic liquid PeMeIm-$\mathrm{T}{\mathrm{f}}_2\mathrm{N}$, the high-$T_c$ superconductor $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.95}$, and thin-film indium tin oxide.

Braiding and fusion of Majorana zero modes are key elements of any future topological Majorana-based quantum computer. Here, we investigate the fusion dynamics of Majorana zero modes in the spinless Kitaev model, as well as in a spinful model describing magnet-superconductor hybrid structures. We consider various scenarios allowing us to reproduce the fusion rules of the Ising anyon model. Particular emphasis is given to the charge of the fermion obtained after fusing two Majorana zero modes: as long as it remains on the superconductor, charge quantization is absent. When moving the fermion to a nonsuperconducting region, such as a quantum dot, nearly quantized charge can be measured. Our findings confirm for both platforms that fusion dynamics of Majorana zero modes can indeed be used for the readout of Majorana qubits.

Pentagonal transition-metal dichalcogenides $\mathrm{Pd}{X}_2 (X=\mathrm{S},\mathrm{Se},\mathrm{Te})$, characterized by corrugated pentagonal lattices, have attracted considerable attention owing to their unconventional physical properties. In this work, we systematically investigate the anharmonic lattice dynamics and thermal transport properties of monolayer $\mathrm{Pd}{X}_2$ using first-principles calculations combined with harmonic approximation (HA), self-consistent phonon (SCP) theory and Boltzmann transport equation. Our results demonstrate that accurate evaluation of the lattice thermal conductivity (${\kappa }_{\mathrm{L}}$) for pentagonal $\mathrm{Pd}{X}_2$ monolayers requires effective-thickness correction, without which the predicted values markedly deviate from experimental measurements. In addition, cubic and quartic anharmonic phonon renormalization and strong four-phonon (4ph) scattering play decisive roles in determining ${\kappa }_{\mathrm{L}}$ in pentagonal $\mathrm{Pd}{X}_2$. Specifically, the SCP dispersions reveal temperature-driven hardening of acoustic and low-frequency optical modes, indicating strong temperature dependence of phonon transport and enhancing group velocities. When 4ph scattering is included, ${\kappa }_{\mathrm{L}}$ suppressed significantly. For example, ${\kappa }_{\mathrm{L}}$ of $\mathrm{Pd}{\mathrm{S}}_2$ along the $b$ axis decreases by 25.93% (300 K) and 43.65% (900 K) under HA+3,4ph relative to HA+3ph, and by 31.96% (300 K) and 47.38% (900 K) under SCP+3,4ph relative to SCP+3ph. For both crystallographic directions and theoretical levels, ${\kappa }_{\mathrm{L}}$ follows the order: $\mathrm{Pd}{\mathrm{S}}_2>\mathrm{PdS}{\mathrm{e}}_2>\mathrm{PdT}{\mathrm{e}}_2$. Owing to the larger atomic mass of Te, $\mathrm{PdT}{\mathrm{e}}_2$ exhibits strongly corrugated structure, enhanced anharmonicity and pronounced rattling modes, together with stronger phonon localization, smaller specific heat capacity, and lower phonon group velocities. These features significantly suppress phonon thermal transport and contribute to lower ${\kappa }_{\mathrm{L}}$. Moreover, $\mathrm{Pd}{X}_2$ display strongly softened acoustic modes and lower ${\kappa }_{\mathrm{L}}$ along the $a$ axis than those along the $b$ axis, reflecting the strong in-plane anisotropy. The pronounced anisotropy originates from the corrugated and flat $\left[\mathrm{Pd}{X}_4\right]$ units along the $a$ and $b$ axis, respectively. Our research highlights the importance of effective-thickness correction on ${\kappa }_{\mathrm{L}}$ for 2D materials and reveal the crucial role of strong anisotropy, lattice anharmonicity, and 4ph scattering in the phonon thermal transport of pentagonal $\mathrm{Pd}{X}_2$.