We investigate the effects of single, multiple, and extended defects in the form of nonmagnetic impurities and vacancies in twisted bilayer graphene (TBG) at and away from the magic angle, using a fully atomistic model and focusing on the behavior of the flat low-energy moiré bands. For strong impurities and vacancies in the $AA$ region, we find a complete removal of one of the four moiré bands, resulting in a significant depletion of the charge density in the $AA$ regions even at extremely low defect concentrations. We find similar results for other defect locations, with the exception of the least coordinated sites in the $AB$ region, where defects instead result in a peculiar band replacement process within the moiré bands. In the vacancy limit, this process yields a band structure misleadingly similar to the pristine case. Moreover, we show that triple-point fermions, which are the crossing of the Dirac point by a flat band, appearing for single, periodic defects, are generally not preserved when adding extended or multiple defects, and thus likely not experimentally relevant. We further identify two universal length scales for defects, consisting of charge modulations on the atomic scale and on the moiré scale, illustrating the importance of both the atomic and moiré structures for understanding TBG. We show that our conclusions hold beyond the magic angle and for fully isolated defects. In summary, our results demonstrate that the normal state of TBG and its moiré flat bands are extremely sensitive to both the location and strength of nonmagnetic impurities and vacancies, which should have significant implications for any emergent ordered state.

Layered van der Waals ferromagnets, which preserve their magnetic properties down to exfoliated monolayers, are fueling an abundance of fundamental research and nanoscale device demonstration. ${\mathrm{CrGeTe}}_3$ is a prime example of this class of materials. Its temperature-pressure phase diagram features an insulator-to-metal transition and a significant increase in ferromagnetic Curie-Weiss temperatures upon entering the metallic state. We use density functional theory to understand the magnetic exchange interactions in ${\mathrm{CrGeTe}}_3$ at ambient and elevated pressures. We calculate Heisenberg exchange couplings, which provide the correct ferromagnetic ground state and explain the experimentally observed pressure dependence of magnetism in ${\mathrm{CrGeTe}}_3$. Furthermore, we combine density functional theory with dynamical mean-field theory to investigate the effects of electronic correlations and the nature of the high-pressure metallic state in ${\mathrm{CrGeTe}}_3$.

We discuss a nonequilibrium dynamical mean-field framework for simulating inhomogeneous Hubbard models with local disorders. Our approach treats electron interactions and disorders on equal footing, by considering only local dynamical fluctuations. The theory reduces to nonequilibrium dynamical mean-field theory in the presence of only electron-electron interactions and to the coherent potential approximation in noninteracting systems with disorders. Both time-dependent and steady-state problems are treated by implementing the theory on the three-branch Kadanoff-Baym contour and two-branch Schwinger-Keldysh contour, respectively. Benchmarks on a eight-site cube show that the method yields rather accurate spectral functions in both the weakly and strongly interacting regimes. In a cubic lattice, we demonstrate energy conservation after an interaction quench and thermalization after just a few hopping times in both clean and disordered systems. As an application, we study transport through a serial double quantum-dot sandwiched between two leads, focusing on the current and dot occupations after a voltage quench.

The DFT-$\frac{1}{2}$ method is a band-gap correction with GW precision at a density functional theory (DFT) computational cost. The method was also extended to correct the gap between defect levels, allowing for the calculation of optical transitions. However, this method fails when the atomic character of the occupied and unoccupied defect levels is similar as we illustrate by two examples, the tetrahedral hydrogen interstitial and the negatively charged vacancy in diamond. We solve this problem by decoupling the effect of the occupied and unoccupied defect levels and call this the decoupled DFT-$\frac{1}{2}$ method for defects.

An infinitely large Koch fractal is shown to be capable of sustaining only extended, Bloch-like eigenstates if certain parameters of the Hamiltonian describing the lattice are numerically correlated in a special way, and a magnetic flux of a special strength is trapped in every loop of the geometry. We describe the system within a tight-binding formalism and prescribe the desired correlation between the numerical values of the nearest-neighbor overlap integrals, along with a special value of the magnetic flux trapped in the triangular loops decorating the fractal. With such conditions, the lattice, despite the absence of translational order of any kind whatsoever, yields an absolutely continuous eigenvalue spectrum and becomes completely transparent to an incoming electron with any energy within the allowed band. The results are analytically exact. An in-depth numerical study of the inverse participation ratio and the two-terminal transmission coefficient corroborates our findings. Our conclusions remain valid for a large set of lattice models, built with the same structural units, but beyond the specific geometry of a Koch fractal, unraveling a subtle universality in a variety of such low-dimensional systems.

The bidirectional symmetry of electromagnetic wave propagation in optomechanical systems can be effectively disrupted, leading to the achievement of novel devices for unconventional photon transport. This article investigates the near-field radiative heat transfer (NFRHT) between nanoparticles based on moving metasurfaces. The modeling is based on isotropic silicon carbide (SiC) particles and a graphene metasurface and the NFRHT is analyzed using the Green's function and conductivity approximation. This study reveals that when the velocity of the metasurface is sufficiently high, the radiative heat flux in the near field becomes highly nonreciprocal. By selecting appropriate chemical potentials and particle arrangement positions, the thermal conductivity coefficient can be enhanced or suppressed by up to five orders of magnitude. The required threshold velocity for the thermal diode we constructed is also significantly reduced under specific chemical potentials. These findings provide theoretical support for scenarios involving high-speed relative motion in the near field.

Pressure-induced structural transformations up to 8.9 GPa in the perovskite-type ($AB{\mathrm{O}}_3$) $\left(1-x\right){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-x\mathrm{BaTi}{\mathrm{O}}_3$ (NBT-$x\mathrm{BT}$) at the morphotropic phase boundary (MPB), $x_{\mathrm{MPB}}=0.048$, were studied by means of polarized Raman spectroscopy and single-crystal x-ray diffraction. Raman spectroscopic analysis was also performed on reference undoped NBT to reveal the effect of chemical composition on the response of the atomic dynamics to isotropic elastic stress. Our results demonstrate that, like Pb-based relaxors and pure NBT, NBT-0.048BT undergoes multistep structural alteration to a high-pressure state consisting of reduced off-centered displacements of $B$-site cations, enhanced antipolar order of off-centered shifts of $A$-site cations, and induced $B{\mathrm{O}}_6$ tilt order. The comparison between NBT and NBT-0.048BT reveals that Ba doping at the level of the MPB composition smears out the pressure range of ongoing structural transformations, slows down the suppression of off-centering for both $A$- and $B$-site cations, and hardens the $A$-cation subsystem but softens the $B$-cation subsystem. The larger volume compressibility of NBT-0.048BT with respect to NBT suggests that the softening of the $B$-cation subsystem due to the substitution of Ba controls the bulk compressibility at the MBP.

Performing quantum measurements produces not only the expectation value of a physical observable $O$ but also the probability distribution $P\left(o\right)$ of all possible outcomes $o$. The full counting statistics (FCS) $Z(\varphi ,O)\equiv {\sum }_o{e}^{i\varphi o}P\left(o\right)$, a Fourier transform of this distribution, contains the complete information of the measurement outcome. In this work, we study the FCS of $Q_A$, the charge operator in subsystem $A$, for one-dimensional systems described by non-Hermitian Sachdev-Ye-Kitaev-like models, which are solvable in the large-$N$ limit. In both the volume-law entangled phase for interacting systems and the critical phase for noninteracting systems, the conformal symmetry emerges, which gives $F(\varphi ,Q_A)\equiv lnZ(\varphi ,Q_A)\sim {\varphi }^{2}ln\left|A\right|$. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(\varphi ,Q_A)\sim (1-cos\varphi )\left|\partial A\right|$ for $\zeta \gg J$, regardless of the presence of interactions. Our results suggest the FCS is a universal probe of entanglement phase transitions in non-Hermitian systems with conserved charges, which does not require the introduction of multiple replicas. We also discuss the consequences of discrete symmetry, long-range hopping, and generalizations to higher dimensions.

To enable the practical use of skyrmion-based devices, it is essential to achieve a balance between energy efficiency and thermal stability while also ensuring reliable electrical detection against noise. Understanding how a skyrmion interacts with material disorder and external perturbations is thus essential. Here, we investigate the electronic noise of a single skyrmion under the influence of thermal fluctuations and spin currents in a magnetic thin film. We detect the thermally induced noise with a $1/f^{\gamma }$ signature in the strong pinning regime but a random telegraph noise in the intermediate pinning regime. Both the thermally dominated and current-induced telegraphlike signals are detected in the weak pinning regime. Our results provide a comprehensive electronic noise picture of a single skyrmion, demonstrating the potential of noise fluctuation as a valuable tool for characterizing the pinning condition of a skyrmion. These insights could also aid in the development of low-noise and reliable skyrmion-based devices.

The layered van der Waals compound CrOCl is frustrated for antiferromagnetic (AFM) order, because of its orthorhombic $Pmmn$ symmetry that supports a triangular lattice of magnetic ${\mathrm{Cr}}^{3+}$ ions. At ambient pressure, CrOCl develops incommensurate AFM order below $T_c=27.2\mathrm{K}$, and it becomes AFM ordered with a fourfold magnetic supercell below the Néel temperature $T_{N,1\mathrm{bar}}=13.5\mathrm{K}$. This AFM order is facilitated by an $\mathbf{a}$-unique monoclinic lattice distortion. At room temperature, CrOCl remains orthorhombic up to at least 57 GPa. It develops a structural modulation that is the result of the optimization of the packing of Cl atoms within the van der Waals gap. Single-crystal x-ray diffraction (SXRD) at conditions of high pressure and low temperature (HPLT) uncover three novel HPLT phases of CrOCl. Instead of an $\mathbf{a}$-unique monoclinic lattice, major distortions are found for the lattice parameter angles $\beta$ and $\gamma$, resulting in a $\mathbf{c}$-unique HPLT phase at 35 K, a triclinic HPLT phase at both 14 and 35 K, and a structurally modulated, triclinic phase at yet higher pressures. The structurally modulated phases appear at nearly the same critical pressures of $15.0<p_c<16.0\mathrm{GPa}$, and they are of a similar nature at 14, 35, and 293 K, despite the different lattice symmetries. The unmodulated triclinic phase is proposed to lead to more favorable distortions within the double layers CrO than is possible within the high-symmetry structures at equivalent $(p,T)$ conditions. Incommensurate magnetic order or commensurate AFM order may appear with the $\mathbf{c}$-unique HPLT phase at 35 K. This then implies a substantial pressure dependence of the magnetic transitions of $\mathrm{\Delta }{T}_c/\mathrm{\Delta }p=1.42$ K/GPa or $\mathrm{\Delta }{T}_N/\mathrm{\Delta }p=4.1$ K/GPa, respectively. The present finding of substantial lattice distortions involving the angle $\gamma$ may have ramifications for monolayer structures of CrOCl.

Ferroelectricity and metallicity cannot coexist due to the screening effect of conducting electrons, and a large number of stable monolayers with $1\mathrm{T}/1{\mathrm{T}}^{\prime }$ phase lack spontaneous polarization due to inversion symmetry. In this work, we have constructed the $\pi$-bilayer structures for transition metal dichalcogenides ($M{\mathrm{Te}}_2,M=\mathrm{Pt}$, Pd, and Ni) with van der Waals stacking, where two monolayers are related by $C_{2z}$ rotation, and have demonstrated that these $\pi$ bilayers are typical ferroelectric metals (FEMs). The $\pi$-bilayer structure widely exists in nature, such as $1{\mathrm{T}}^{\prime }/{\mathrm{T}}_d\text{−}\mathrm{TMD}$, $\alpha \text{−}{\mathrm{Bi}}_4{\mathrm{Br}}_4$. The computed vertical polarization of ${\mathrm{PtTe}}_2$ and ${\mathrm{MoTe}}_2\pi$ bilayers are 0.46 and 0.25 pC/m, respectively. We show that the switching of polarization can be realized through interlayer sliding, which only requires crossing a low energy barrier. The interlayer charge transfer is the source of both vertical polarization and metallicity, and these properties are closely related to the spatially extended Te-$p_z$ orbital. Finally, we reveal that electron doping can significantly adjust the vertical polarization of these FEMs in both magnitude and direction. Our findings introduce a class of FEMs, which have potential applications in functional nanodevices such as ferroelectric tunneling junction and nonvolatile ferroelectric memory.

An $M$-type hexaferrite is a material with rich physical characteristics, such as magnetism, the dielectric property, and the magnetodielectric (MD) effect. In this paper, we systematically investigated the magnetic, dielectric, and MD properties of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0.0$, 1.2, 1.8, and 2.4) ceramics prepared by a solid-state reaction method. The ${\mathrm{Ga}}^{3+}$ cations with a smaller radius preferentially substitute the ${\mathrm{Fe}}^{3+}$ ions in $\mathrm{Fe}{\mathrm{O}}_6$ octahedra, while the ${\mathrm{In}}^{3+}$ cations with a larger radius tend to replace the ${\mathrm{Fe}}^{3+}$ ions in $\mathrm{Fe}{\mathrm{O}}_5$ bipyramids of $R$ blocks, inducing different physical characteristics. The pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ and Ga-doped samples show ferrimagnetism in the temperature range from 10 to 300 K. The In-doped samples exhibit a transition from noncollinear magnetism to collinear ferrimagnetism at 39, 128, and 144 K for the doping amounts of $x=1.2$, 1.8, and 2.4, respectively. The dielectric decrease of pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ at $\sim 10–175\mathrm{K}$ is attributed to the quantum paraelectric state, and the shoulder peaks of tan $\delta$ at ∼140–200 K are from electron hopping. The dipole glass state is responsible for the dielectric peak of Ga-doped samples at $\sim 20–40\mathrm{K}$. The dielectric increase and plateau of In-doped samples are mainly ascribed to the electron hopping at low temperatures. Their dielectric properties at high temperatures are all attributed to the interfacial polarization caused by the Maxwell-Wagner effect. The MD effect also has different origins for the various samples at low temperatures. For pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$, the negative MD effect at extremely low temperatures and the positive MD effect after warming are ascribed to spin-phonon coupling and field-dependent electron hopping, respectively. The positive MD effect in Ga-doped hexaferrites results from the field-dependent electric dipoles inside $\mathrm{Fe}{\mathrm{O}}_5$ bipyramids. For the In-doped samples, the negative MD effect and subsequent transformation to the positive MD effect originate from the field-dependent noncollinear spin ordering and electron hopping, respectively. The MD effect at high temperatures is attributed to the combination of magnetoresistance and Maxwell-Wagner effects. These research results are helpful for understanding the relationship among doped ions, spin order, dielectric property, and the MD effect in $M$-type hexaferrites.

Ground-state properties, such as energies and double occupancies, of a one-dimensional two-band Hubbard model are calculated using a first-principles Gutzwiller conjugate gradient minimization theory. The favorable agreement with the results from the density matrix renormalization group theory demonstrates the accuracy of our method. A rotationally invariant approach is further incorporated into the method to greatly reduce the computational complexity with a speedup of approximately 50 times. Moreover, we investigate the Mott transition between a metal and a Mott insulator by evaluating the charge gap. With greatly reduced computational effort, our method reproduces the phase diagram in reasonable agreement with the density matrix renormalization group theory.

We propose a general theoretical framework for both constructing and diagnosing inversion-protected higher-order topological superconductors using Kitaev building blocks, a higher-dimensional generalization of Kitaev's one-dimensional Majorana model. For a given crystalline symmetry, the Kitaev building blocks serve as a complete basis to construct all possible Kitaev superconductors that satisfy the symmetry requirements. We derive a simple yet powerful Majorana counting rule that can unambiguously diagnose the existence of higher-order topology for all Kitaev superconductors. We expect this real-space diagnosis to work for general two-dimensional higher-order topological superconductors within this symmetry class. As proof of concept, we have identified two inequivalent stacking strategies using the Kitaev building blocks, based on which we have constructed minimal tight-binding models with symmetry-protected Majorana corner modes. Moreover, we have successfully applied our diagnosis to comprehend the Majorana corner physics in a superconductor model with a fragile Wannier obstruction, confirming the validity of our theory beyond the Kitaev limit. Our work paves the way for interpreting higher-order topological superconductivity from the real-space perspective.

In this study, we present our experimental investigation on the magnetotransport properties of a two-dimensional electron system in GaAs quantum wells utilizing a variety of device geometries, including obstacles with thin barriers and periodic width variations. Our primary focus is to explore the impact of these geometries on the electron viscous flow parameters, enabling precise manipulation of hydrodynamic effects under controlled conditions. Through an analysis of the large negative magnetoresistivity and zero field resistivity, we deduce the scattering times for electron-electron and electron-phonon interactions, as well as the effective channel width. Our findings confirm that the system under investigation serves as a tunable experimental platform for investigating hydrodynamic transport regimes at temperatures above 10 K.

We investigate, using first-principles methods and effective-model simulations, the spin-orbit coupling proximity effects in a bilayer heterostructure comprising phosphorene and ${\mathrm{WSe}}_2$ monolayers. We specifically analyze holes in phosphorene around the $\mathrm{\Gamma }$ point, at which we find a significant increase of the spin-orbit coupling that can be attributed to the strong hybridization of phosphorene with the ${\mathrm{WSe}}_2$ bands. We also propose an effective spin-orbit model based on the ${\mathbf{C}}_{1\mathrm{v}}$ symmetry of the studied heterostructure. The corresponding spin-orbit field can be divided into two parts: the in-plane field, present due to the broken nonsymmorphic horizontal glide mirror plane symmetry, and the dominant out-of-plane field triggered by breaking the out-of-plane rotational symmetry of the phosphorene monolayer. Furthermore, we also demonstrate that a heterostructure with ${60}^{\circ }$ twist angle exhibits an opposite out-of-plane spin-orbit field, indicating that the coupling can effectively be tuned by twisting. The studied phosphorene/${\mathrm{WSe}}_2$ bilayer is a prototypical low common-symmetry heterostructure in which the proximity effect can be used to engineer the spin texture of the desired material.

We report that the strong spin-valley coupling in chiral tellurium can modify the electronic structures, and how it dominates the nonreciprocal transport. The observed nonreciprocal magnetoresistance shows anomalous suppression in high magnetic fields. This behavior contradicts the linearity of nonreciprocal signals to the fields observed in other materials. We find that the magnetic field-induced fully valley polarized states in tellurium trigger the deviation from the linearity. Our results establish the essential role of the valley degree of freedom for the cross-correlation phenomena in chiral materials, in addition to the previously discussed spin-charge coupling.

We have studied magnetic and transport properties of compressively strained ${\mathrm{Eu}}_{1-x}{\mathrm{Gd}}_x\mathrm{Ti}{\mathrm{O}}_3$ (EGTO) thin films up to a high doping level, $x=0.55$, grown by gas-source molecular beam epitaxy. In comparison with a nonmagnetic dopant $\left({\mathrm{La}}^{3+}\right)$ in ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x\mathrm{Ti}{\mathrm{O}}_3$ (ELTO), ${\mathrm{Gd}}^{3+}$ has the same $4f^7$ moment as ${\mathrm{Eu}}^{2+}$, but a smaller ionic radius to induce buckling of the $\mathrm{Ti}{\mathrm{O}}_6$ octahedra and hence reduces the one-electron bandwidth. The evolution of ferromagnetism and electron correlation is more clearly observed in EGTO thin films in the filling $\left(x\right)$ dependence of Curie temperature and the coefficient of temperature-squared resistivity. The systematic comparison of the magnetic phase diagrams for EGTO and ELTO has revealed significant differences caused by the presence (absence) of a magnetic moment in ${\mathrm{Gd}}^{3+}\left({\mathrm{La}}^{3+}\right)$ and an effect due to the difference in electron correlation strength.

The heavy fermion phase is expected to be robust in the periodic Anderson lattice systems when the density of states of conduction electrons at the Fermi energy is finite. In such systems the spin liquid phase driven by geometrical frustration usually coexist with Kondo screening. Here we study a periodic Anderson-Heisenberg triangular lattice model with both geometric and Kondo frustrations, the latter being caused by the on-site and the nearest neighbor site $c\text{−}f$ hybridizations. We show the existence of the Kondo breakdown quantum phase transition at a critical hybridization strength $V_c$ below which the dynamically-decoupled local moment spin liquid phase emerges. Such phase is closely linked to the nodal points of the hybridization function in the presence of Kondo frustration.

$\mathrm{Eu}{\left({\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\right)}_4$ are centrosymmetric systems that have recently been identified as candidates to stabilize topologically nontrivial magnetic phases, such as skyrmion lattices. In this Letter, we present a high-resolution resonant x-ray and neutron scattering study on ${\mathrm{EuGa}}_2{\mathrm{Al}}_2$ that provides new details of the complex coupling between the electronic ordering phenomena. Our results unambiguously demonstrate that the system orders to form a spin density wave with moments aligned perpendicular to the direction of the propagation vector below 19.5 K, and upon further cooling below 15 K, a cycloid with moments in the $ab$ plane, in contrast to what has been reported in the literature. We show that concomitant with the onset of the spin density wave is the suppression of the charge density wave order, indicative of a coupling between the localized $4f$ electrons and itinerant electron density. Furthermore, we demonstrate that the charge density wave order breaks the fourfold symmetry present in the $I4/mmm$ crystal structure, thus declassifying these systems as square-net magnets.