We introduce the Zitterbewegung areal rate operator to study the relation between the orientation of trembling motion and band topology. Constructed from the oscillatory interband displacement and velocity, this operator distinguishes clockwise from anticlockwise motion. For a generic gapped two-band Hamiltonian in two dimensions, we show that the Zitterbewegung areal rate is proportional to the Berry curvature. The derivation uses only spectral projectors and is therefore gauge invariant. We also demonstrate that the Zitterbewegung areal rate operator is time independent and a constant of motion at each momentum, although the displacement and velocity from which it is constructed oscillate in time. Its sign distinguishes anticlockwise from clockwise Zitterbewegung and coincides with the sign of the Berry curvature. For wave packets narrowly localized around the isolated massive Dirac points, the Zitterbewegung chirality equals the sign of the local Chern contribution. The Chern number can therefore be reconstructed from the orientations of the Zitterbewegung motion around the individual Dirac points.

Electron–hole plasma in two-dimensional solid-state systems has previously been studied mainly in two limiting cases: the degenerate regime in semimetals with parabolic bands, and the nondegenerate symmetric Dirac regime in graphenelike materials. Here we investigate a third, qualitatively different case realized in a gapless HgTe quantum well: a multicomponent plasma with a hybrid spectrum, in which massless Dirac carriers coexist with thermally activated heavy holes from lateral valence-band valleys. Near the charge-neutrality point we observe a pronounced increase of the resistance with temperature, following an approximately $T^2$ law, in sharp contrast to the nearly temperature-independent resistivity expected for a symmetric two-component Dirac plasma. We show that this behavior originates in the charge-neutrality condition, which, once the heavy holes are populated, pins the chemical potential above the Dirac point: the Dirac electrons remain moderately degenerate, while the heavy holes stay nondegenerate and obey Boltzmann statistics. Because the light degenerate electrons scatter almost elastically off the heavy Boltzmann holes, the interparticle transport admits a relaxation-time description and can be treated nonperturbatively. Using carrier densities from self-consistent band structure calculations, we find that the data are well reproduced by a short-range interaction between Dirac electrons and heavy holes in the weakly disordered limit for which the electronic conductivity scales as $T^{-2}$ and the excess resistivity is proportional to the heavy-hole density, whereas an unscreened Coulomb interaction would leave the conductivity temperature independent. The extracted interaction amplitude is of the Coulomb scale expected at the low charge-neutrality density. Our results establish near-critical HgTe quantum wells as a versatile platform for studying interaction-driven transport in multicomponent systems combining degenerate massless and nondegenerate massive carriers in which the linear Dirac spectrum decouples the current from the total momentum.

Recent numerical and theoretical studies on the two-dimensional $J\text{−}{Q}_3$ model suggest that the deconfined quantum critical point is actually a $\mathrm{SO}\left(5\right)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $\mathrm{O}\left(4\right)$. However, the precise nature of the transition remains under active discussion. Despite extensive studies based on static quantities and entanglement properties, its low-energy excitation spectrum has received comparatively less attention. Here we investigate the dynamical spectra of spin and bond operators at the deconfined critical point of the $J\text{−}{Q}_3$ model using large-scale quantum Monte Carlo simulations and contrast them with the well-established $\mathrm{O}\left(3\right)$ Wilson-Fisher criticality in the $J_1\text{−}{J}_2$ columnar dimerized Heisenberg model. Although both models exhibit two gapless magnon modes in the Néel phase, their critical behaviors diverge strikingly. At the $J_1\text{−}{J}_2$ critical point, the Higgs mode becomes gapless, yielding three gapless modes that reflect the complete restoration of the $\mathrm{O}\left(3\right)$ symmetry. In the $J\text{−}{Q}_3$ model, we instead observe transverse excitations associated with the Néel and VBS order-parameter fluctuations becoming gapless at the transition, a behavior consistent with the emergence of $\mathrm{SO}\left(5\right)$ symmetry. While transverse modes become gapless at the transition, the behavior of the longitudinal (Higgs) mode remains unresolved.

The efficiency of optical cooling of nuclear spins in a CdTe/CdZnTe quantum well is investigated as a function of an external magnetic field. Our results confirm that there is indeed an optimal external magnetic field for optical cooling. We associate it with the kinetic local field $B_{\mathrm{KL}}$ defined by the heating rate of the spin-spin reservoir due to the fluctuations of the hyperfine interaction. We also propose an experimental technique for measuring $B_{\mathrm{KL}}$. For our sample we find that $B_{\mathrm{KL}}=1.0\pm 0.4$ G and it is independent of the electron polarization and pump power. The measured values of the kinetic local fields are in good agreement with the theoretical calculation $B_{\mathrm{KL}}=0.7$ G, taking into account indirect spin-spin interactions of Cd and Te nuclear spins and their considerably different hyperfine constants. The hyperfine constants of the magnetic isotopes of Cd and Te in CdTe are estimated.

Topological zero-line modes (ZLMs) based on valley Hall effect induced by inversion symmetry breaking have attracted significant attention in designing topological quantum devices. Compared with the toy model in monolayer graphene with staggered sublattice potentials, ZLMs in bilayer graphene are more accessible in experiments. However, it is still experimentally challenging to design the fine-tuned electric gates to realize ZLMs, and the introduction of electrodes also makes it difficult to further reduce the device size. In this work, we demonstrate the emergence of ZLMs in bilayer graphene from layer-reversing in-plane electric fields, which are induced by chemical dopants. Our proposal provides an experimentally feasible route to realize electrodeless ZLMs in graphene systems.

We construct the tight-binding model Hamiltonians of transition metals on the basis of $s$, $d$, and $p_z$ orbitals by employing a two-center approximation based on Slater-Koster tables. We systematically investigate the electronic structures of $3d$ and $5d$ transition-metal monolayers, and the material-specific parameters are extracted by fitting the first-principles calculations. We find that, compared with bulk systems, the local environments of atoms in these monolayers have lower symmetries, making $d$ orbitals split into more energy levels. The energy splittings are comparable with the $d$-band width and thus have significant influence on the band structure. Moreover, the lattice constants of these monolayer systems are remarkably smaller than those of corresponding bulk systems, indicating a dramatic change of hopping energies, band widths, and magnetisms. By further invoking the spin degree of freedom, we find that most $3d$ transition metals exhibit magnetizations that are closely related to their lattice constants. By fitting spin-minority and spin-majority bands separately, we find that the spin-majority electron exhibits a smaller $d$-state radius and therefore is more localized. In contrast, most $5d$ monolayers are nonmagnetic while exhibiting strong spin-orbit coupling, whose strength increases approximately linearly as the atomic number increases.

Using the determinant Quantum Monte Carlo method, we investigate the interplay among doping, interlayer tunneling, and on-site Hund's coupling in stabilizing superconductivity (SC) in a two-orbital model for the bilayer nickelate ${\text{La}}_3{\text{Ni}}_2{\text{O}}_7$. With realistic dispersion and for certain values of the interaction parameters, the auxiliary-field-decoupled fermion Hamiltonian has Kramers antiunitary symmetries which guarantee the absence of a sign problem. The same antiunitary symmetries can also be used to show there is a second instability towards the $(\pi ,\pi )$ interlayer bond order (BO) in the strong interaction limit. We indicate the possible connection between this bond order and the enigmatic density wave state observed in experiments and clarify the decisive role played by the interlayer tunneling in the competition between the SC and the BO. Finally, possible directions on how to enhance the SC transition temperature and stabilize the SC phase are also discussed.

Accurate crystal structure prediction (CSP) requires accounting for finite-temperature and nuclear quantum effects, yet first-principles evaluation of the free energy surface (FES) remains prohibitive for high-throughput searches. We observe that the self-consistent harmonic approximation (SCHA) FES, as a function of nuclear centroid positions, shares the same mathematical structure as a potential-energy surface and can therefore be directly learned by a deep neural network potential. The resulting deep free energy (DF) model, constructed via a two-level concurrent-learning workflow, evaluates free energies, forces, and stresses in a single forward pass. Applied to the La-Sc-H system at 200 GPa and 300 K, DF-based CSP reproduces the stability of the experimentally observed ${\mathrm{LaH}}_{10}$ and ${\mathrm{LaSc}}_2{\mathrm{H}}_{24}$, and identifies $P4/mmm$ ${\mathrm{LaScH}}_8$ as thermodynamically stable on the free energy convex hull, a stability absent on the classical potential-energy surface. Benchmarked on the ${\mathrm{LaH}}_{10}$ system, the DF model achieves a $1.72\times {10}^6$-fold cost reduction relative to DFT-level SSCHA. The DF framework provides a scalable route for incorporating finite-temperature and nuclear quantum effects into high-throughput crystal structure prediction.

α-MnTe is a prototypical altermagnet exhibiting a strong anomalous Hall effect (AHE), despite having a nearly vanishing magnetization. ${\mathrm{SrF}}_2\left(111\right)$ has a small lattice mismatch with MnTe and a matching coefficient of thermal expansion; there are, however, no reports on measurements of the AHE in α-MnTe epitaxially grown on this substrate. Here, we report the measurement of an AHE and x-ray magnetic circular dichroism in α-MnTe films grown on ${\mathrm{SrF}}_2$ that have a relaxed crystal structure and nearly vanishing magnetization confirmed experimentally. We study films of varying thickness, all of which exhibit a consistent spontaneous anomalous Hall effect, albeit only at low temperature. With increasing thickness, we find that films become more resistive and that their anomalous Hall conductivity decreases as their longitudinal conductivity decreases. Importantly, a comparison of the anomalous Hall conductivity per unit magnetization with other magnetic semiconductors reveals the colossal amplitude of the AHE of α-MnTe. We carry out this analysis for the films reported here and for previous results from the literature. Such a colossal AHE cannot be explained by a picture where defects induce extrinsic ferromagnetism in this material, and must be a result of the magnetocrystalline symmetry allowing its altermagnetism.

In a recent paper [D. Sahu et al., Phys. Rev. B 112, 144412 (2025)], claims were made about (1) the appearance of noncoplanar and ferromagnetic ordering below 146 K in solid solutions ${\mathrm{Y}}_2\left(\mathrm{T}{\mathrm{i}}_{2-x}\mathrm{C}{\mathrm{r}}_x\right){\mathrm{O}}_7$ with $x=0.03$, 0.07, and 0.1, and (2) discovering an effective way of installing ferromagnetism in nonmagnetic pyrochlores through Cr doping at the nonmagnetic Ti site. In this Comment, we draw attention to the fact that $\mathrm{YCr}{\mathrm{O}}_3$—a well-known antiferromagnetic material with weak ferromagnetic properties—has a Néel temperature ($T_{\mathrm{N}}$) of 140–142 K. The very close match of the magnetic transitions of $\mathrm{YCr}{\mathrm{O}}_3$ and ${\mathrm{Y}}_2\left(\mathrm{T}{\mathrm{i}}_{2-x}\mathrm{C}{\mathrm{r}}_x\right){\mathrm{O}}_7$ gives strong evidence that all ferromagnetism in ${\mathrm{Y}}_2\left(\mathrm{T}{\mathrm{i}}_{2-x}\mathrm{C}{\mathrm{r}}_x\right){\mathrm{O}}_7$ originates from the $\mathrm{YCr}{\mathrm{O}}_3$ impurity. We prepared simple mixtures of ${\mathrm{Y}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ and $\mathrm{YCr}{\mathrm{O}}_3$ compounds containing 0.14 and 0.66 wt. % of $\mathrm{YCr}{\mathrm{O}}_3$ and measured the magnetic properties of such mixtures and individual ${\mathrm{Y}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ and $\mathrm{YCr}{\mathrm{O}}_3$ compounds. Using the reported magnetic irreversibility values and our experimental values, we estimated the amount of $\mathrm{YCr}{\mathrm{O}}_3$ to be below 0.1 wt. % in the original work. It is difficult to detect such levels of impurities with laboratory powder X-ray diffraction. On the other hand, temperature-dependent magnetic measurements at small magnetic fields are much more sensitive to impurities with ferromagneticlike properties.

The position noise spectra of six drums on a single chip were measured on a single cooldown below 1.3 K. Cryostat temperatures as low as 0.7 mK were achieved. The temperature dependence of the resonance frequency and linewidth of the drum modes was analyzed in the framework of the tunneling two-level system (TLS) model. Departures of the resonance frequency and the position noise power from the expected logarithmic and linear temperature dependences, respectively, were interpreted as indications of thermal decoupling from the cryostat. This previously unexplored measurement configuration revealed that similar neighboring drums on a single chip may be at different temperatures. At the lowest temperatures, some drums exhibited excess damping that decreased with temperature. The magnitude of the excess damping of the drums was correlated with the thermal coupling of their TLS to the cryostat. In the case of one drum, a temporary increase in its damping coincided with a decrease in its mode temperature. The thermalization of the TLS to the cold finger was independent of pump power, pulse tube state and temperature of the precooling stages of the cryostat. These results suggest that thermalization of nanomechanics to the cryostat can be mediated by TLS damping rather than clamping loss and may impact efforts to extend the coherence of mechanical resonators.

Ground-state preparation of quantum many-body systems is a fundamental challenge across quantum science, with implications for quantum simulation, quantum computing, and the study of complex quantum matter. The exponential growth of Hilbert space and the complexity of entangled eigenstates motivate the development of new approaches that go beyond conventional strategies based on adiabatic evolution, variational optimization, imaginary-time methods, and engineered dissipative processes. Here, we demonstrate that the recently proposed quantum Landau-Lifshitz-Gilbert (QLLG) dynamics [Phys. Rev. Lett. 133, 266704 (2024)] provides an intrinsic nonlinear dissipative mechanism for real-time ground-state preparation. Unlike engineered dissipative schemes, QLLG encodes relaxation directly into the quantum equation of motion while preserving the underlying quantum structure of the evolution. The QLLG evolution selectively suppresses excited-state contributions, driving the system toward the lowest-energy eigenstate within the accessible symmetry sector. We show that the dynamics admits a monotonic energy functional and a stable ground-state fixed point, and that for generic initial states in an $N$-qubit Hilbert space the characteristic convergence time scales linearly with $N$ and inversely with the spectral gap. Numerical simulations of an interacting spin chain confirm our analytical predictions. These results establish nonlinear dissipative QLLG dynamics as another avenue for quantum state preparation, opening an alternative route for quantum simulation, computation, and state engineering.

Using the Wannier function approach, we develop a gauge-covariant formalism for the orbital angular momentum (OAM) operator and the orbital Hall conductivity (OHC). The Wannier function formulation resolves the position-operator ambiguity inherent to Bloch states, providing a transparent and rigorous theory of orbital transport. Our formalism is validated through a finite-lattice calculation of the Haldane model, where the OAM operator is evaluated exactly from its real-space definition. Our results are also relevant to other orbital phenomena in solids such as the orbital Edelstein effect, orbital torque generation, and the like, where the OAM plays a crucial role.

We have performed muon spin relaxation ($\mu \mathrm{SR}$) and neutron powder diffraction experiments on the ferromagnet ${\mathrm{Sr}}_{1-x}$(${\mathrm{La}}_{0.5}{\mathrm{K}}_{0.5}{)}_x{\mathrm{RuO}}_3$. ${\mathrm{SrRuO}}_3$ shows a ferromagnetic (FM) order below 160 K, and the FM ordering temperature is monotonically suppressed as $x$ increases, eventually vanishing at the critical concentration $x_{\mathrm{c}}$ = 0.5. During this suppression process, the FM ordered state evolves into an FM cluster-glass state for $x \ge$ 0.4. Neutron scattering intensity due to the FM order develops below the magnetic ordering temperatures, but no antiferromagnetic peaks have been observed in either the FM or cluster-glass states within the experimental accuracy. The internal field at lowest temperatures revealed by the $\mu \mathrm{SR}$ experiments is monotonically suppressed as $x$ increases. In contrast, the magnetic volume fraction $V_{\mathrm{f}}$ at lowest temperatures decreases only moderately with $x$ up to $x$ = 0.3, but drops rapidly near the critical concentration. The fact that $V_{\mathrm{f}}$ is less than 1 for $x \ge$ 0.3 is expected to be related to the origin of the cluster-glass state formation. We also found that the muon relaxation rate due to magnetic fluctuations in the cluster-glass state increases as $x$ approaches $x_{\mathrm{c}}$, reflecting progressive destabilization of the cluster-glass state due to the reduction of $V_{\mathrm{f}}$. These results indicate that the magnetically ordered states of ${\mathrm{Sr}}_{1-x}$(${\mathrm{La}}_{0.5}{\mathrm{K}}_{0.5}{)}_x{\mathrm{RuO}}_3$ are strongly affected by the disorder effect, and the suppression process of the FM order is largely different from that in a clean system. We compare the present experimental results with those for other Sr-site substituted systems, and discuss the differences in their magnetic properties and how they are affected by the disorder effect.

Quantum stabilizer codes serve as a promising paradigm for realizing fault-tolerant quantum computation, and their natural mapping to the ground states of exactly solvable spin models strongly motivates the exploration of many-body orders within these systems. In this work, we investigate the fracton topological orders in a specific family of codes derived from a recently proposed general construction. This particular code family can be understood as a class of generalized hypergraph product codes, and we term the corresponding exactly solvable spin models orthoplex models based on the geometry of their stabilizers. In three dimensions, the orthoplex model exhibits a series of intriguing properties, including non-Abelian lattice defects and a nonmonotonic ground-state degeneracy as a function of system size. Most remarkably, in four dimensions we discover fragmented topological excitations: while manifesting as discrete, isolated points in real space, their projections onto lower-dimensional subsystems form connected objects such as loops, thereby revealing their intrinsic topological nature. Consequently, these fragmented excitations constitute an intriguing intermediate class between pointlike and spatially extended topological excitations. More broadly, these rich features establish the underlying general construction framework of stabilizer codes as a versatile and analytically tractable platform for studying many-body orders.

Topological crystalline insulators extend the concept of topological insulators by hosting surface states protected by crystallographic symmetry. Their topological phase transitions arise from spin-orbit-driven band inversion in the bulk electronic structure, reshaping the low-energy electronic environment and its coupling to lattice excitations. While the electronic aspects of band topology are well established, the corresponding dynamics of lattice and electron-phonon interactions remain largely unexplored. Here, we report a pronounced softening of a low-energy surface phonon mode across the topological phase transition in ${\mathrm{Pb}}_{0.77}{\mathrm{Sn}}_{0.23}\mathrm{Se}$, revealed by temperature-dependent time-domain terahertz spectroscopy. Unlike the well-known phonon softening in ferroelectrics, this effect does not signal a structural instability but instead reflects electronic reconstruction. We attribute the softening to the spectroscopic manifestations of a Kohn anomaly, indicating a strong coupling between lattice vibrations and Dirac-like surface electrons in the topological phase. Consistently, the phonon linewidth deviates from the standard anharmonic temperature dependence, further evidencing enhanced electron-phonon coupling. The observed changes in phonon frequency and linewidth at around 120 K are consistent with the reported topological phase transition temperature in this material. Our results thus provide a spectroscopic route for the distinct identification of the onset of a topological phase.

In frustrated magnetism, lattice distortions mediated by magnetoelastic coupling are commonly invoked as an escape route from extensive degeneracy toward an ordered ground state and, in some cases, the onset of multiferroicity. Here we present a simple classical magnetoelastic model that illustrates the converse phenomenon, which we term “magnetic self-frustration.” Monte Carlo simulations reveal that a kagomé lattice with trivial magnetic interactions—namely, nearest-neighbor Ising ferromagnetism—undergoes a magnetostructural transition into a breathinglike phase, characterized by irregular bond dimerization along the three kagomé directions. Structurally, the equilateral triangles belonging to one of the two kagomé sublattices spontaneously distort, expanding into isosceles triangles. An analysis to first order in the magnetoelastic coupling constant $\alpha$ shows that the shape of these triangles is remarkably robust. Acting like rigid building blocks in a puzzle, their vertices determine the geometry of the second sublattice, giving rise to contracted ferromagnetic triangles with a variety of shapes. The magnetic sector can be mapped onto an effective antiferromagnetic triangular lattice, which remains disordered down to low temperatures and retains a finite residual entropy of one-third of that of Wannier. This self-frustrated phase takes place at intermediate values of $\alpha$, separating the conventional undistorted ferromagnetic phase at weak coupling from a strongly coupled ordered phase characterized by a regular dimerized up-up-down-down antiferromagnetic pattern along the three kagomé directions, built from ferromagnetic triangles and hexagons.

Understanding the role of interfacial topography and defects in controlling reactivity remains incomplete because of the difficulty in imaging interfacial topography with nanometric spatial resolution. Here we demonstrate the feasibility of imaging, in three dimensions, the surface topography of calcite ($\mathrm{CaC}{\mathrm{O}}_3$) using coherent x-ray reflectivity (CXR). While these images have a vertical resolution of $\sim 30$ nm, we show that the phase of the interfacial density provides sub-nm sensitivity to the interfacial topography, a $\sim 100$-fold enhancement with respect to resolution limits. This is achieved by extending the concepts of Bragg coherent diffraction imaging (BCDI) to CXR, revealing surfaces with nearly atomically flat and micron-scale topographies. It is demonstrated for surfaces of individual µm-sized particles and extended crystals, including free surfaces and buried interfaces.

Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or large unit cells. Here, we introduce a band unfolding framework that directly generalizes traditional band theory to systems where exact periodicity is absent and remains well-defined for both aperiodic and finite systems. To do so, we employ a pseudospectral approach to identify approximate joint eigenvectors of a system's Hamiltonian and translation operators, thereby yielding an unfolded band structure whose features are directly connected to the manifestation of approximate extended states simultaneously localized in energy and crystalline momentum. To reveal bulk-only spectral phenomena in finite systems, we further show that this pseudospectral framework naturally accommodates additional operators that suppress contributions from boundary-localized states, enabling the systematic isolation of intrinsic bulk behavior. We benchmark the scheme on several representative systems in one and two dimensions, including a Fibonacci chain, where our approach is able to reveal a dispersive envelope while preserving the underlying hierarchy of spectral gaps. Looking forward, this pseudospectral approach may yield a broad framework for predicting momentum-resolved material responses in aperiodic, disordered, and finite systems where conventional band-theoretic methods are not applicable.

A common method to identify the dominant internal material electronic scattering processes that limit transport and conductivity in experimental measurements is to use the scattering exponent approximation. It assumes that the carrier relaxation time follows $\tau ={\tau }_0{E}^r$, where $r$ is a value that depends on a specific scattering mechanism. The exponential trend is also reflected in the temperature dependence for parameters like mobility, following $\mu \propto T^s$. Literature $r$ and $s$ values are defined using simplified assumptions, the most important being single-band parabolic electronic structures. Typical materials beyond simple semiconductors, however, involve complex electronic structures and many scattering processes of various strengths acting simultaneously. Here, we consider transport simulations for a series of electronic structure models, from single parabolic band models, two-band models, and the full band structure of half-Heusler materials, as well as all important scattering mechanisms such as acoustic phonons, optical phonons, polar optical phonons, and ionized impurity scattering through $ab$ $initio$ calculation methods. We show that, in general, the $r$ values that describe transport in such complex cases do not follow the nominal literature values; thus their ability to provide transport characteristics is limited. We also explore the feasibility of using these exponents to extract thermoelectric transport characteristics from the commonly used Pisarenko relation for the Seebeck coefficient in half-Heusler materials. In this case as well, the scattering exponents used to compute the Seebeck coefficient do not correspond to the internal transport processes due to the complexity of the electronic structures. However, despite the band complexities, we have identified a significant negative correlation between the exponents and the material's optical phonon energy.