Cavity electrodynamics is emerging as a promising tool to control chemical processes and quantum material properties. In this work we develop a formalism to describe the cavity mediated energy exchange between a material and its electromagnetic environment. We show that coplanar cavities can significantly affect the heat load on the sample if the cavity resonance lies within the frequency region where free-space radiative heat dominates, typically the mid-IR at ambient temperature, while spectral filtering is necessary for having an effect with lower frequency cavities.

Probing the homogeneous ice nucleation process from scratch at the molecular level is of great value but still experimentally unachievable. Previous theoretical simulations have found that ice originates from the low-mobile region with increasing abundance and persistence of tetrahedrally coordinated water molecules. However, a detailed microscopic picture of how the disordered hydrogen-bond network rearranges itself into an ordered network is still unclear. In this work, we use a deep neural network (DNN) model to “learn” the interatomic potential energy from quantum-mechanical data, thereby allowing for large-scale and long molecular dynamics simulations with ab initio accuracy. Using the forward flux sampling, a $36\text{−}\mu \mathrm{s}$-long simulation is performed to achieve complete homogeneous ice nucleation trajectories from scratch. We demonstrate that the nucleation mechanism and dynamics at the molecular resolution are deeply affected by the structural and dynamical heterogeneities in supercooled water. In distinct contrast to previous understanding, we find that ice formation occurs in coexisting high-mobile and low-mobile regions of supercooled water, with low-mobile, highly ordered regions first transforming into high-mobile regions before they crystallize into ice. Specifically, imperfectly coordinated (IC) water molecules with high mobility pave the way for the hydrogen-bond network rearrangement through the mechanisms of IC status transfer, annihilation, and generation, leading to the growth or shrinkage of the ice nucleus; the hydrogen-bond network formed by perfectly coordinated (PC) molecules stabilizes the nucleus, thus preventing it from vanishing and growing. Ice is born through competition and cooperation between IC and PC molecules. In the end, the nucleation rate at supercooling 46 K is calculated in a direct manner, and the result agrees well with experiments.

The bulk $\mathrm{LaMn}{\mathrm{O}}_3$ (LMO) is antiferromagnetic (AFM) at low temperature, whereas its thin films growing on $\mathrm{SrTi}{\mathrm{O}}_3$ (STO) substrates are ferromagnetic (FM) in experiments. The underlying mechanism driving this AFM→FM transition remains elusive and has attracted significant research interest. In bulk LMO, the $\mathrm{Mn}{\mathrm{O}}_6$ octahedra exhibit substantial crystal-field distortion. Our study reveals that the lattice mismatch between LMO films and STO substrates induces this magnetic phase transition in the ultrathin regime. The epitaxial strain effectively suppresses the octahedral distortion in LMO, leading to near degeneracy of the two Mn $e_g$ orbitals. This alteration in orbital energy splitting modifies the exchange interactions, thereby changing the magnetic ordering. Test calculations with varying octahedral symmetry by strains reproduced the AFM←FM transition in LMO films, demonstrating a close correlation between the energy splitting between the two Mn $e_g$ orbitals and magnetic order in LMO. Based on these findings, we propose a superexchange mechanism driven by orbital degeneracy, offering a straightforward explanation for the magnetic transition in LMO films.

Spin-1 chain models have been extensively studied in condensed matter physics, significantly advancing our understanding of quantum magnetism and low-dimensional systems, which exhibit unique properties compared to their spin-$1/2$ counterparts. Despite substantial progress in this area, a rigorous proof of nonintegrability for the bilinear-biquadratic chain model has been lacking. While integrable solutions are known for specific parameter values, a comprehensive understanding of the model's general integrability has remained elusive. In this paper, we present a rigorous proof of nonintegrability for general spin-1 bilinear-biquadratic chain models, by extending the proofs of nonintegrability on spin-$1/2$ models. Our proof not only confirms the nonintegrability of widely studied models but also provides offer deeper insights into several areas. These include the identification of the absence of local conserved quantities in quantum many-body scar systems with perfect fidelity revivals, such as the AKLT model. This paper marks a significant step toward understanding the complex dynamics of spin-1 systems.

We design a three-dimensional kagome-like boron allotrope, referred to as 3D kagome boron, with boron tetrahedron as the building block. By means of density-functional first-principles calculations, we find that 3D kagome boron is dynamically stable and shows metallic behavior within a near-ambient pressure ranging from 7 to 13 GPa. The electronic structure of 3D kagome boron is insensitive to pressure, while acoustic phonons become stiffened with increasing pressure. Based on the Wannier interpolation technique, we investigate the electron-phonon coupling (EPC) superconductivity in 3D kagome boron. The EPC constant $\lambda$ is calculated to be 0.91 and 0.74 under 7 and 13 GPa, respectively. By solving anisotropic Eliashberg equations, the superconducting transition temperature ($T_c$) is determined to be $\sim 35\mathrm{K}$ under 7 GPa. With increasing pressure, we find that the EPC matrix element weakens and acoustic phonons stiffen, which causes a lower superconducting $T_c\sim 30\mathrm{K}$ under 13 GPa. We also find that 3D kagome boron possesses a wide superconducting region ranging from 7 to 50 GPa, as well as showing a robust high $T_c$ which is higher than 15 K throughout. The 3D kagome boron predicted here exhibits a high superconducting $T_c\sim 35\mathrm{K}$ under 7 GPa, which is the elemental superconductor with the highest superconducting $T_c$ within a pressure of 20 GPa and almost comparable to the highest superconducting $T_c$ of 36 K of elemental Sc under 260 GPa.

We use the Bogoliubov-de Gennes (BDG) formalism to undertake a microscopic investigation of a vortex lattice in a strongly correlated, type-II, d-wave superconductor (SC) treating strong correlation within Gutzwiller formalism. We demonstrate that in the underdoped region, the presence of subdominant charge and bond modulation introduces low-energy core states in the local density of states (LDOS) at the vortex core instead of U-shaped (i.e., with a hard gap) Mott core in a strongly correlated d-wave superconductor. Intriguingly, the LDOS at the vortex core is distinct from a metallic core with a Caroli–de Gennes–Matricon (CdGM) peak in the case of weakly coupled superconductors. We have investigated that such subdominant order changes the structure and spectrum of the d-wave vortex in the underdoped region. We have demonstrated the formation of charge and bond modulation at the vortex center by decreasing the doping and reaching an underdoped zone.

Superconductors exhibit a nonlinear interaction with an applied light, which can resonantly excite the collective amplitude (Higgs) mode. Here we study light-induced dynamics of layered superconductors, where each layer is coupled to adjacent layers via the Josephson coupling and the first few layers near the surface are driven by an in-plane-polarized light. We study the system under the assumption that the interlayer Coulomb interactions are sufficiently screened out and that the phase-difference mode becomes available in the low-energy regime. We find that interlayer transport is induced via excitations of the collective amplitude and phase-difference modes, even when the applied electric field is parallel to the planes. We provide analytic calculations as well as numerical simulations of the real-time dynamics and investigate the influence on the light-induced interlayer Josephson current and intralayer third-harmonic generation.

The surface of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ has been observed in scanning tunneling microscopy (STM) experiments to host a checkerboard charge order and locally broken fourfold rotational symmetry around impurity sites. Interestingly, this electronic ordering can be tuned by rotating an in-plane external magnetic field. It has been argued that the charge anisotropy is caused by an underlying surface ferromagnetic order that forms in the presence of spin-orbit coupling and enhanced oxygen octahedral rotation on the surface of bilayer strontium ruthenate. In this work, we consider a realistic model for the surface of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and self-consistently calculate the charge order, magnetic order, and local density of states to get further insight into this observed order. We find agreement with the hypothesis that the surface anisotropy is dependent on the presence of an in-plane ferromagnetic moment whose direction modulates the magnitude and phase of the electronic checkerboard pattern. We further find that the anisotropy in electronic and magnetic properties depends nonmonotonically on the degree of rotation of oxygen octahedra and on the magnitude of an external magnetic field. We then show that the sublattice anisotropy exists in the local density of states only at low energies but significantly weakens near the Van Hove singularity. Finally, assuming that the bulk material is paramagnetic but close to a Stoner instability and associated with a weaker oxygen octahedral rotation, we explore the nature of local impurity-induced magnetism in the bulk material.

The structural stability and phonon properties of SnSe/SnS superlattices at finite temperatures have been studied using machine learning force field molecular dynamics and the anharmonic phonon approach. The vertical SnSe/SnS superlattice undergoes a phase transition from the $Pnma$ phase to a $P4/nmm$ phase at finite temperatures, which is different from the high-temperature $Cmcm$ phase of the SnSe and SnS systems. The stability of $P4/nmm$ phase is determined by molecular dynamics trajectories and anharmonic phonon dispersion relations. The TO modes at the $q=\mathrm{\Gamma }(0,0,0)$ and $q=M(1/2,1/2,0)$ points in the $P4/nmm$ phase exhibit imaginary frequencies in the harmonic approximation but stabilize at elevated temperatures. An analysis of phonon power spectra upon temperature also confirms the dynamic stabilization. The $P4/nmm$ phase has higher symmetry than the $Pnma$ phase, and the phase transition between them is accompanied by competition between the Jahn-Teller effect and phonon anharmonicity. Unlike the anisotropic distribution of Sn-Se/S bonds in the $Pnma$ phase, the $P4/nmm$ phase forms chemical bonds with similar bond lengths both in plane and interlayer, and their resonance effect can significantly enhance phonon scattering. The calculated phonon density of states and lifetime are strongly temperature dependent, demonstrating the heavy anharmonicity in the SnSe/SnS system. The $P4/nmm$ phase has an extremely low lattice thermal conductivity, close to the experimental values of SnSe and SnS. Moreover, with the reduction of band gap and the enhancement of band degeneracy near the Fermi level, the $P4/nmm$ phase exhibits superior electronic transport properties and significantly enhanced response to infrared and visible light. This makes it show great potential in thermoelectric and photovoltaic applications.

This paper studies the topological and magnetic properties of a noncollinear spin state on a honeycomb lattice that evolves from coplanar to ferromagnetic with a magnetic field applied along the $z$ axis. The coplanar state is stabilized by nearest-neighbor ferromagnetic interactions, single-ion anisotropy along $z$, and Dzyaloshinskii-Moriya interactions between next-nearest-neighbor sites. Below the critical field $H_c$ that aligns the spins, the magnetic unit cell contains six sites and the spin dynamics contains six magnon modes. Although the classical energy is degenerate with respect to the twist angle $\varphi$ between nearest-neighbor spins, the dependence of the free energy on $\varphi$ at low temperatures is dominated by the magnon zero-point energy, which contains extremum at $\varphi =\pi l/3$ for integer $l$. The only unique ground states $\mathrm{GS}\left(\varphi \right)$ have $l=0$ or 1. For $H<H_c^{\prime }$, the zero-point energy has minima at even $l$ and the ground state is GS(0); for $H_c^{\prime }<H<H_c$, the zero-point energy has minima at odd $l$ and the ground state is $\mathrm{GS}(\pi /3$). In GS(0), the magnon density of states exhibits five distinct topological phases with increasing field associated with the opening and closing of energy gaps between two or three magnonic bands. While the Berry curvature vanishes for the coplanar $\varphi =0$ phase in zero field, the Berry curvature and Chern numbers exhibit signatures of the five topological phases below $H_c^{\prime }$. Whereas the Berry curvature and Chern number are sensitive to changes in the magnon density of states within $\mathrm{GS}(\pi /3$), the inelastic spectrum $S(\mathbf{k},\omega )$ is sensitive to changes in the intensity of the magnon modes in the different magnetic phases GS(0) and $\mathrm{GS}(\pi /3$) rather than the five topological phases within $\mathrm{GS}(\pi /3$).

The anomalous temperature dependence of uniaxial magnetocrystalline anisotropy constant $K_{\mathrm{u}1}\left(T\right)$ recently discovered in van der Waals (vdW) ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, which is favorable for spintronic application, provides a case of Carr-type $K_{\mathrm{u}1}\left(T\right)$. Here, we report that by varying the content of Fe deficiency $x$, the Carr-type $K_{\mathrm{u}1}\left(T\right)$ in vdW ferromagnet ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ can be effectively tuned. Although the scale of $K_{\mathrm{u}1}\left(T\right)$ is overall reduced with increasing $x$ as expected, the increment in $K_{\mathrm{u}1}$ relative to the ground-state one distinctly increases and the maximum point shifts to higher temperature. Strikingly, a giant relative increment in $K_{\mathrm{u}1}$ up to 180% is observed at elevated temperature of about $0.4T_{\mathrm{C}}$ in an Fe-poor sample with $x=0.21$. The considerably enhanced localized nature and altered lattice symmetry in an Fe-poor sample suggested by further analyses are proposed to be responsible for our experimental observations. Our findings provide an effective way and insight for optimizing the promising Carr-type $K_{\mathrm{u}1}\left(T\right)$ for advancing spintronic application.

Observing the “Higgs” or amplitude mode in superconductors has been a central challenge in condensed matter physics. Moreover, arriving at a theoretical understanding of this mode and how it is accessible in, say, conductivity experiments presents an additional challenge as here one needs to satisfy gauge invariance in the presence of disorder. In this paper, we characterize the Higgs contribution within a fully gauge-invariant treatment of the linear optical conductivity, $\sigma \left(\omega \right)$, for a disordered superconductor carrying a uniform supercurrent. As a consequence of gauge invariance, there are two distinct charge conservation laws underlying the linear electromagnetic response with two associated sets of $f$-sum rules. An interesting finding from the Higgs-related sum rule is that the imaginary part of $\sigma \left(\omega \right)$ yields an anisotropic, negative $1/\omega$ contribution in the terahertz regime. This is relevant to device applications and appears to be consistent with recent experiments. The paper presented here emphasizes how difficult it is to disentangle the neutral amplitude mode contributions from those of the charged quasiparticles and we demonstrate why this is the case.

Almost four decades of intense research have been invested to study the physics of high-$T_c$ cuprate superconductors. The recent discovery of high-$T_c$ superconductivity in pressurized bilayer nickelates and its potential similarities with cuprate superconductors may open a new window to understand this long-standing problem. We have studied the proposed bilayer $t\text{−}{J}_{\parallel }\text{−}{J}_{\perp }$ model [where $J_{\parallel }$ ($J_{\perp }$) is the in-plane (out-of-plane) magnetic exchange] in a large-$N$ approach on the basis of the path integral representation for Hubbard operators, which allows to obtain results at mean-field and beyond mean-field level. We find that $J_{\perp }$ is a candidate for triggering high superconducting $T_c$ values at quarter filling (hole doping $\delta =0.5$) of the $d_{x^2-y^2}$ orbitals. Beyond mean-field level, we find a new phase, an out-of-plane bond-order phase (z-BOP), triggered also by $J_{\perp }$. z-BOP develops below a critical temperature which decreases with increasing doping and vanishes at a quantum critical point below quarter filling. The occurrence of this phase and its competition with superconductivity leads to a superconducting dome-shaped behavior as a function of doping and as a function of $J_{\perp }$. Qualitative comparisons with the physics of cuprates and the recent literature on the new pressurized nickelates are given along the paper.

We report results of magnetic susceptibility, specific heat, and muon spin relaxation measurements on the polycrystalline titanate ${\mathrm{Ba}}_6{\mathrm{Nd}}_2{\mathrm{Ti}}_4{\mathrm{O}}_{17}$, an essentially disorder-free triangular-lattice antiferromagnet. The absence of long-range magnetic order or spin freezing is confirmed down to 30 mK, well below the Curie-Weiss temperature −1.8 K. Magnetism and specific heat measurements reveal Ising-like effective-spin-1/2 behavior. Persistent spin dynamics are observed down to 37 mK. Our study has discovered a remarkable example of Ising spins on the triangular lattice, which remains magnetically disordered at low temperatures and potentially hosts a quantum spin liquid ground state.

We study the phase diagram of a disordered Kitaev chain with long-range pairing when connected to two metallic leads exchanging particles with external Lindblad baths. We (i) monitor the subgap modes at increasing disorder, (ii) compute the current flowing across the system at a finite voltage bias between the baths, and (iii) study the normal single particle lead correlations across the chain. Throughout our derivation, we evidence the interplay between disorder and topology. In particular, we evidence the reentrant behavior of the massive, topological phase at limited values of the disorder strength, similar to what happens in the short-range pairing Kitaev model. Our results suggest the possibility of a disorder-induced direct transition between the massive and the short-range topological phase of the long-range pairing Kitaev model.

We apply the tensor cross interpolation (TCI) algorithm to solve equilibrium quantum impurity problems with high precision based on the weak-coupling expansion. The TCI algorithm, a kind of active learning method, factorizes high-dimensional integrals that appear in the perturbative expansion into a product of low-dimensional ones, enabling us to evaluate higher-order terms efficiently. This method is free from the sign problem which quantum Monte Carlo methods sometimes suffer from, and allows one to directly calculate the free energy. We benchmark the TCI impurity solver on an exactly solvable impurity model and find good agreement with the exact solutions. We also incorporate the TCI impurity solver into the dynamical mean-field theory to solve the Hubbard model and show that the metal-to-Mott insulator transition is correctly described with comparable accuracy to the Monte Carlo methods. Behind the effectiveness of the TCI approach for quantum impurity problems lies the fact that the integrands in the weak-coupling expansion naturally have a low-rank structure in the tensor-train representation.

The $F$ function, the three-dimensional counterpart of the central charge in the two-dimensional (2D) conformal field theory, measures the effective number of degrees of freedom in three-dimensional (3D) quantum field theory, and it is monotonically decreasing under the renormalization group flow. However, unlike the 2D central charge, the $F$ function is a nonlocal quantity and cannot be computed using correlators of local operators. Utilizing the recently proposed fuzzy sphere regularization, we have performed the first nonperturbative computation of the $F$ function for the paradigmatic 3D Ising conformal field theory through entanglement entropy. Our computation yields $F_{\text{Ising}}=0.0612\left(5\right)$, slightly smaller than the $F$ function of a real free scalar, $F_{\text{free}}=\frac{log2}{8}-\frac{3\zeta \left(3\right)}{16{\pi }^2}\approx 0.0638$, consistent with the $F$ theorem, and close to the $4-\epsilon$ expansion estimates of $F_{\text{Ising}}\approx 0.061\sim 0.062$.

It has been recently established that transport measurements in the nonlinear regime can give direct access to the quantum metric (QM): the real part of the quantum geometric tensor characterizing the geometry of the electronic wave functions in a solid. In topological materials, the QM has been so far revealed in thin films of the topological antiferromagnet ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ where it provides a direct contribution to longitudinal currents quadratic in the driving electric field. Here, we show that the Dirac surface states of strong three-dimensional topological insulators have a QM that can be accessed from the nonlinear transport characteristics in the presence of an externally applied planar magnetic field. A previously unknown intrinsic part of the longitudinal magnetoconductivity carries the signature of the QM while coexisting with the extrinsic part responsible for the so-called bilinear magnetoelectric resistance. We prove that the QM-induced nonlinear magnetotransport carries specific signatures of single Dirac cones. This allows its use as an efficient diagnostic tool of the bulk topology of three-dimensional nonmagnetic insulators.