Multiple-$Q$ states are expressed as a superposition of spin density waves at multiple ordering wave vectors, which results in unconventional complicated spin textures, such as skyrmions, hedgehogs, and vortexes. We investigate the multiple-$Q$ instability by focusing on the low-symmetry ordering wave vectors in momentum space. By systematically performing the simulated annealing for effective spin models with various ordering wave vectors on a two-dimensional square lattice, we classify the magnetic phase diagram into four types according to the position of the ordering wave vectors. Three out of four cases lead to a plethora of isotropic multiple-$Q$ instabilities yielding collinear, coplanar, and noncoplanar double-$Q$ and quadruple-$Q$ magnetic phases, while the remaining case leads to an anisotropic double-$Q$ instability when the multiple-spin interaction is introduced. Our results indicate that exotic multiple-$Q$ phases distinct from the skyrmion crystal phase are expected when the ordering wave vectors lie on the low-symmetry positions in the Brillouin zone.

By employing the first-principles calculations, the influence mechanism of external pressure and charge doping on the electron-phonon coupling (EPC) and superconductivity (SC) of bulk ${\mathrm{VSe}}_2$ is investigated. Our calculations reveal that with increasing pressure the charge density wave (CDW) of $1\mathrm{T}\text{−}{\mathrm{VSe}}_2$ is gradually suppressed, and a SC state subsequently emerges which is accompanied by a structural phase transition from the trigonal phase to a monoclinic phase at $15.5\mathrm{GPa}$. Increasing pressure from 15.5 to $35\mathrm{GPa}$, the SC transition temperature $T_c$ of ${\mathrm{VSe}}_2$ slightly increases from 4.2 to $5.2\mathrm{K}$ and no SC dome is found, which are in good agreement with the previous experimental results [S. Sahoo et al., Phys. Rev. B 101, 014514 (2020)]. Through electron- or hole-doping (denoted by $n_e$ and $n_h$), the CDW order of the trigonal phase can be suppressed and SC states with $T_c$ greater than 10.5 and $9.0\mathrm{K}$, respectively, emerge. The highest $T_c$ under charge doping can be up to about $12\mathrm{K}$, and a weak double-dome like dependence of $T_c$ on $n_e$ and $n_h$ is found. Combining systematical analysis of effects of pressure and charge doping, we demonstrate that the Kohn anomalies of phonons at certain $Q$ points associated with the in-plane vibrations of V atoms play key roles in strengthening the EPC, which brings about the intriguing SC in ${\mathrm{VSe}}_2$. However, due to the weak pressure-induced modifications of phonon spectrum as well as Fermi surface (FS), the changes of EPC and $T_c$ caused by pressure are not significant. Interestingly, charge doping will produce a local flat band along $\mathrm{\Gamma }\mathrm{A}$ direction near the FS, which is mainly contributed by V $3d$-orbitals, and result in large values of electronic density of states at Fermi level. Therefore, the effects caused by charge doping to the electronic structures, phonon anomalies, EPC, and $T_c$ are evident. Our findings may provide a promising understanding to the pressure and doping-dependent SC of ${\mathrm{VSe}}_2$, and may be valuable for designing new materials with enhanced SC through the strategic manipulation of electronic and phononic properties.

The accurate description of the structural and thermodynamic properties of ferroelectrics has been one of the most remarkable achievements of density functional theory (DFT). However, running large simulation cells with DFT is computationally demanding, while simulations of small cells are often plagued with nonphysical effects that are a consequence of the system's finite size. To avoid these finite-size effects one is thus often forced to use empirical models that describe the physics of the material in terms of effective interaction terms, that are fitted using the results from DFT. In this study we use a machine-learning (ML) potential trained on DFT, in combination with accelerated sampling techniques, to converge the thermodynamic properties of barium titanate (BTO) with first-principles accuracy and a full atomistic description. Our results indicate that the predicted Curie temperature depends strongly on the choice of DFT functional and system size, because of emergent long-range directional correlations in the local dipole fluctuations. Our findings demonstrate how the combination of ML models and traditional bottom-up modeling allow one to investigate emergent phenomena with the accuracy of first-principles calculations over the large size and time scales afforded by empirical models.

The random tiling hypothesis, first proposed by Elser and Henley in the 1980s, states that quasicrystals are entropy-stabilized and, hence, are high-temperature phases. We confirm the hypothesis for a two-dimensional Tübingen triangle tiling, which arises in molecular dynamics simulations with a Lennard-Jones-Gauß potential, by investigating the temperature dependence of its two phason elastic constants ${\lambda }_6$ and ${\lambda }_8$. These are the second derivatives of the free energy $F({\chi }_6,{\chi }_8,T)$ with respect to symmetrized phason strain modes ${\chi }_6$ and ${\chi }_8$. At $T=0, F$ has a saddle point by descending along the ${\chi }_8$ direction. Therefore ${\lambda }_8<0$ characterizes the quasicrystal's initial instability. The configurational entropy due to phason flips turns $F$ upwards at higher temperatures, reverses the sign of ${\lambda }_8$, and leads to a stable quasicrystal. We obtain this result by applying geometric methods in the form of the polar calculus, where the projection window $\mathcal{W}$ is divided into atomic domains ${\mathcal{C}}_i$ for each vertex environment. We extend the calculus to a dynamic one by separating the window into areas ${\mathcal{P}}_k$ that characterize the different kinds of phason flips. By phasonic deformation of the window, we can determine the types of flips and their frequency of occurrence in dependence on phason strain, perform energy relaxations by flips, and compute the configurational free energy. Previously, flips therein had been dealt with as uncorrelated and described as Ising spins. We consider nearest neighbor correlations between flips by extending the Ising to a Potts model and find that they constitute an important mechanism supporting the quasicrystal stability.

4-4′dichlorobiphenyl sulfone (BCPS) presents a phase transition from a high-symmetry monoclinic phase $I2/a$ to an incommensurate phase $I2/a$ (0β0) at $T_{\mathrm{i}}=150$ K without any lock-in phase transition observed down to the lowest temperatures at atmospheric pressure. Such examples which remain incommensurate close to 0 K are quite rare and are prototype materials for the study of the competitive terms between internal energy and residual entropic contributions defining their stable phases. The present study reports an experimental determination of the temperature versus pressure phase diagram for BCPS. A Raman study of the amplitudon mode in the incommensurate phase reveals that the transition temperature diminishes under pressure and vanishes at about 320 MPa for the hydrogenated compound. It also sheds light on the properties of the low-frequency phonons and their assignments by a hydrogen isotopes comparison. In particular, it shows that the chlorophenyl torsion modes have frequencies in the 100 $\mathrm{c}{\mathrm{m}}^{-1}$ range and cannot be a primary order parameter. A neutron-diffraction experiment reveals that there is no tendency for a lock-in phase transition at any pressure, with the critical wave vector remaining always far away from any simple rational value. Inelastic neutron-scattering experiments on the deuterated compound versus pressure at 50 K report, as expected, much lower damping of the critical excitations around $T_{\mathrm{i}}$ compared to the ones at atmospheric pressure ($T_{\mathrm{i}}=150$ K). It reveals the complexity of the spectral function when both soft mode and central peak are present and allows the observation of both the phason and the amplitudon modes at lower pressure within the incommensurate phase. High-resolution neutron diffraction carried out at the same temperature reveals very different pressure responses of the crystallographic parameters inducing deviatoric strains.

Using the inelastic x-ray scattering (IXS) technique, we investigate the lattice dynamics of inorganic–organic hybrid iodide perovskites ${\mathrm{FAPbI}}_3$ and ${\mathrm{FASnI}}_3$ (FA $\equiv \mathrm{CH}{\left({\mathrm{NH}}_2\right)}_2$, formamidinium) in their cubic $\alpha$ phase and tetragonal $\beta$ phase. We find that the IXS spectra of ${\mathrm{FASnI}}_3$ are highly broad at all momentum points, as has been widely observed in the Pb-based halide perovskites. The speeds of sound (phonon group velocities) and absolute values of elastic constants of ${\mathrm{FASnI}}_3$ are smaller than those of ${\mathrm{FAPbI}}_3$ in both phases. In addition, no significant difference in the phonon lifetimes of ${\mathrm{FAPbI}}_3$ and ${\mathrm{FASnI}}_3$ is observed. These results correlate better with the reported tendency that the lattice thermal conductivity of ${\mathrm{ASnX}}_3$ is lower than that of ${\mathrm{APbX}}_3$. We discuss that our results also favor the up-conversion mechanism by acoustic phonons in the phonon bottleneck effect for the long lifetime of hot carriers.

Recently, researchers have shown that nanostructured interfaces can manipulate the thermal boundary conductance at the interface, but their conclusions are contradictory, and mechanisms are unclear. In this paper, we investigate the impact of nanostructured interfaces on thermal boundary conductance by considering roughness dependence. To achieve this goal, first, an interface model accounting for spectral specularity and spectral specular and spectral diffuse scatterings is deduced. Next, the Monte Carlo framework of interface treatment for spectral specularity and spectral specular and spectral diffuse scatterings at heterogeneous interfaces is constructed. Then they are validated through comparisons with the discrete-ordinates method and experiments. Finally, the roughness dependence for thermal transport through planar and nanostructured interfaces is studied. Results give a nonmonotonic relationship between thermal boundary conductance and roughness for planar interface, and the manipulation of thermal boundary conductance by nanostructured interfaces depends on the system and interface geometries and the interface roughness. The effect of interface roughness is found to be the dominant impact factor in films with a thickness of tens of nanometers. Further investigations for these small-scale films show that the roughness of their horizontal and vertical interfaces impact thermal boundary conductance differently. Thus, the nonuniform roughness for horizontal and vertical interfaces is proposed to successfully expand the manipulation of thermal boundary conductance in films with small size.

In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this paper, we develop a process of finding a Slater determinant representation of free-fermion wave functions that accurately characterizes localized particles, a procedure we dub “unscrambling.” The central idea is to minimize the overlap between envelopes of single-particle wave functions or, equivalently, to maximize the inverse participation ratio of each orbital. This numerically efficient methodology can differentiate between distinct types of wave functions: exponentially localized, power-law localized, and conformal critical, also revealing the underlying physics of these states. The method is readily extendable to systems in higher dimensions. Furthermore, we apply this approach to a more challenging problem involving disordered monitored free fermions in one dimension, where the unscrambling process unveils the presence of a conformal critical phase and a localized area-law quantum Zeno phase. Importantly, our method can also be extended to free fermion systems without particle number conservation, which we demonstrate by estimating the phase diagram of ${\mathbb{Z}}_2$-symmetric disordered monitored free fermions. Our results unlock the potential of utilizing single-particle wave functions to gain valuable insights into the localization transition properties in systems such as monitored free fermions and disordered models.

Twisting has been demonstrated as a technique for creating strongly correlated effects in two-dimensional bilayered materials and can tunably generate nontrivial topological properties, magnetism, and superconductivity. Magnetism is particularly significant, as it can both compete with superconductivity and lead to the emergence of nontrivial topological states. Due to the technique challenges in theoretical methods without input parameters, theorical studies on twisted materials beyond twisted bilayer graphene are rarely reported. Thus, first-principles studies on a wide range of materials are expected in both fields of fundamental physics and materials science. By using self-developed large-scale density functional theory calculations uniquely capable of simulating twisted systems, we found the ferromagnetism arising due to spin splitting in different twisted bilayer systems across various two-dimensional materials, such as twisted bilayer $h$-BN, $2H-\mathrm{MoT}{\mathrm{e}}_2$, PbS, and $2H-\mathrm{NbS}{\mathrm{e}}_2$. The spin splitting itself is induced by the enhanced ratio of the exchange interaction to band dispersion near the Fermi level. An important discovery in this paper is that, in some nonmagnetic metallic bilayers, e.g., $2H-\mathrm{NbS}{\mathrm{e}}_2$ and $1T-\mathrm{Mo}{\mathrm{S}}_2$, twisting transforms a nonmagnetic state into a collective ferromagnetic state even without any doping.

Topological excitations in periodic magnetic crystals have received significant recent attention. However, their fate once the lattice periodicity is broken is an open question. In this paper, we theoretically study the topological properties embedded in the collective dynamics of magnetic texture array arranged into a Sierpiński carpet structure with effective Hausdorff dimensionality $d_f=1.893$. By evaluating the quantized real-space quadrupole moment, we obtain the phase diagram supporting peculiar corner states that are absent in conventional square lattices. We identify three different higher-order topological states, i.e., outer corner state and type-I and II inner corner states. We further show that all these corner states are topologically protected and are robust against moderate disorder. Full micromagnetic simulations are performed to verify theoretical predictions with good agreement. Our results pave the way to investigating topological phases of magnetic texture based fractals and bridging the gap between magnetic topology and fractality.

We identify a superconducting order featuring spatial pair modulations on the kagome lattice subject to on-site Hubbard $U$ and nearest-neighbor $V$ interactions. Within our functional renormalization group analysis, this state appears with a concomitant $d$-wave superconducting (SC) instability at zero lattice momentum, where it distinguishes itself through intra-unit-cell modulations of the pairing function thus breaking the discrete space group symmetry. The relative weight of the sublattice modulated superconductor (SMS) and $d$-wave SC is influenced by the absolute interaction strength and coupling ratio $V/U$. Parametrically adjacent to this domain at weak coupling, we find an intra-unit-cell modulated vestigial charge density wave and an $s$-wave SC instability. Our study provides a microscopic setting and thorough description of this novel SMS arising within a translation symmetry broken background.

We apply hydrodynamic effective field theory techniques to an ersatz Fermi liquid (FL). Our effective theory, which captures the correlation functions of density operators at each angle on the Fermi surface, can only deviate from conventional FL behavior if the effective theory is nonlocal. Neglecting nonlocal effects, the effective action of the ersatz FL is the Legendre transform of the effective action for FLs, based on the coadjoint orbit method, up to irrelevant corrections.

Recent experiments have uncovered a distinctive magnetic metal in lightly doped multilayer graphene, coined the quarter metal. This quarter metal consolidates all the doped carriers, originally distributed evenly across the 4 (or 12) Fermi surfaces of the paramagnetic state, into one expansive Fermi surface by breaking time-reversal and/or inversion symmetry. In this work, we map out a comprehensive mean-field phase diagram of the quarter metal in rhombohedral trilayer graphene within the four-dimensional parameter space spanned by the density $n_e$, interlayer electric potential $U$, external magnetic field parallel to the two-dimensional material plane $B_{\parallel }$, and Kane-Mele spin-orbit coupling $\lambda$. We found an annular Lifshitz phase transition and an Ising-XY phase transition and located these phase boundaries on the experimental phase diagram. The movement of the Ising-XY phase boundary offers insights into $\lambda$. Our analysis reveals that it moves along the line $\partial n_e/\partial B_{\parallel }\sim -0.5\times {10}^{11}{\text{cm}}^{-2}{\text{T}}^{-1}$ within the $n_e\text{−}{B}_{\parallel }$ parameter space when $\lambda =30\mu \mathrm{eV}$. Additionally, we estimated the in-plane spin susceptibility of the valley-Ising quarter metal ${\chi }_{{}_{\parallel }}\sim 8\mu \text{eV}{\text{T}}^{-2}$. Beyond these quantitative findings, two general principles emerge from our study: (1) The valley-XY quarter metal's dominance in the $n_e\text{−}U$ parameter space grows with an increasing number of layers due to the reduced valley-polarization variations within the Fermi sea. (2) Layer polarization near the band edge plays an important role in aiding the reentrance of the paramagnetic state at low density. The insights derived from the quarter-metal physics may shed light on the complex behaviors observed in other regions of the phase diagram.

Magnetic and multipolar ordering in $f$ electron systems takes place at low temperatures of order 1–10 Kelvin. Combinations of first-principles with many-body calculations for such low-energy properties of correlated materials are challenging problems. We address multipolar ordering in $f$ electron systems based on the dynamical mean-field theory (DMFT) combined with density functional theory. We derive the momentum-dependent multipolar susceptibilities and interactions in two ways: by solving the Bethe-Salpeter (BS) equation of the two-particle Green's function and by using a recently developed approximate strong-coupling formula. We apply the formalism to the prototypical example of multipolar ordering in ${\mathrm{CeB}}_6$ using the Hubbard-I solver, and demonstrate that the experimental quadrupole transition is correctly reproduced. The results by the approximate formula show good agreement with those by the BS equation. This first-principles formalism for multipolar ordering based on DMFT has applications which are beyond the reach of the traditional RKKY formula. In particular, more itinerant electron systems including $5f$, $4d$, and $5d$ electrons can be addressed.

Phonon-induced anomalous Hall or thermal Hall effects have been observed in various systems in recent experiments. However, the theoretical studies on this subject are still incomplete and not unified, and the current works mainly focus on the semiclassical Boltzmann equation approach. In this work, we present a systematic and fundamental quantum field theory study on the phonon-induced anomalous Hall effect, including both the side jump and skew scattering contributions, in a two-dimensional massive Dirac metal, which is considered as the minimum anomalous Hall system. We reveal a significant difference from the anomalous Hall effect induced by the widely studied Gaussian disorder which is known to be insensitive to temperature. While the anomalous Hall effect induced by phonons (deformation potential) approaches that by Gaussian disorder at high temperature, it behaves very differently at low temperature. Our work provides a microscopic and quantitative description of the crossover from the low to high temperature regime of the phonon-induced anomalous Hall conductivity, which may be observed in two-dimensional Dirac metals with broken time-reversal symmetry.

Symmetries play a paramount role in many aspects of topological physics. A particularly illuminating example is the Su-Schrieffer-Heeger (SSH) chain, whose reflection and chiral symmetry endow the quantization of the Zak phase and winding number, subsequently guaranteeing the existence of topological edge states. Here, we harness recent graph-theoretical results to construct families of setups whose unit cells feature neither of these symmetries, but instead a so-called latent or hidden reflection symmetry. This causes the isospectral reduction—akin to an effective Hamiltonian—of the resulting lattice to resemble an SSH model. These latent SSH models exhibit features such as multiple topological transitions, edge states, a quantized Zak phase, and, counterintuitively, immunity to orientational disorder. We confirm our findings through electric circuit experiments, where the topological edge states can be directly observed. Serving as a first proof of principle, our paper demonstrates the wealth and generality of a stroboscopic point of view, taking advantage of hidden properties such as symmetries.

Weyl semimetals are predicted to host signature magneto-optical properties sourced by their peculiar Landau-level structure, including the chiral level. Analytical studies are often leaving out the Hall component of the conductivity due to its complicated nature, and even though the chiral anomaly requires Weyl nodes to come in charge-conjugate pairs, toy models hosting only one node are considered almost exclusively; numerical studies including several Weyl nodes are, on the other hand, often limited to high-field quantum limits or dc studies. Here, we present a twofold purpose study, where we (a) analytically derive a closed-form expression also for the Hall conductivity of a generic Weyl semimetal using linear response theory and (b) apply this general framework to evaluate the transverse conductivity components for Weyl systems with two nodes. We study how various model parameters, including the tilt, momentum separation, and energy location of the nodes, as well as the chemical potential, affect the magneto-optical conductivity, and complement these studies by deriving an analytical expression for the dc Hall conductivity, which is also evaluated in various systems. Including a chiral pair of nodes results in two important differences compared to earlier studies: the contribution from the chiral level is equal in size but opposite at the two nodes, making the net contribution disappear, and the energy scales at which intraband transitions occur is smeared out and approaches that of interband transitions, strengthening the hypothesis that intraband transitions mask signature optical features in materials. This general formalism can be applied to a large family of generic Weyl semimetals, and comprise an important piece towards unravelling the source of the mismatch between theoretical predictions and experimental observations in candidate materials.

The fractional quantum Hall (FQH) effect gives rise to abundant topological phases, presenting an ultimate platform for studying the transport of edge states. Generic FQH edge contains multiple edge modes, commonly including the counterpropagating ones. A question of the influence of Anderson localization on transport through such edges arises. Recent experimental advances in engineering novel devices with interfaces of different FQH states enable transport measurements of FQH edges and edge junctions also featuring counterpropagating modes. These developments provide an additional strong motivation for the theoretical study of the effects of localization on generic edge states. We develop a general framework for analyzing transport in various regimes that also naturally includes localization. Using a reduced field theory of the edge after localization, we derive a general formula for the conductance. We apply this framework to analyze various experimentally relevant geometries of FQH edges and edge junctions.

Electronic states play a crucial role in many quantum systems of moiré superlattices, quasicrystals, and fractals. As recently reported for Sierpiński lattices [Yao et al., Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy-level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the Sierpiński carpet, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by the “seed lattice” of the generator and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are made multifractal by scaling the $q\mathrm{th}$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the gene pattern, an average state-based multifractal dimension of second order would increase as its Hausdorff dimension increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals.