Using spin- and angle-resolved photoemission spectroscopy combined with density functional theory calculations, we investigate the electronic structure of $\alpha$-GeTe grown on a Si(111)-Sb substrate in the ultrathin limit. The full band structure, including the Fermi surface, and spin texture characterizations are presented, with a focus on a film thickness of 5 nm. Well-defined spin-polarized quantum well bulk states are evidenced. This confirms the high quality of elaborated ultrathin films and allows precise determination of the thickness. The Rashba splitting and the in-plane spin texture of GeTe bulk bands are shown to be fully preserved on the Si(111)-Sb substrate. This suggests the persistence of inversion symmetry breaking and ferroelectric properties in the ultrathin limit of GeTe films. Our results demonstrate that device downscaling can be pursued in the context of all-electrically controlled spin-orbitronics applications.

The interplay between moiré flat bands originating from different valleys can give rise to a variety of exotic quantum phases. In this work, we investigate the electronic properties of twisted mono-bilayer (A-AB) and mono-trilayer (A-ABA) ${\mathrm{MoTe}}_2$ using first-principles calculations and continuum models. Unlike previous studies on twisted bilayer systems, in which low-energy flat bands originate solely from the $K/K^{\prime }$ valleys, in A-AB and A-ABA twisted ${\mathrm{MoTe}}_2$ ($t{\mathrm{MoTe}}_2$) the moiré bands at low energies arise from both the $\mathrm{\Gamma }$ and $K/K^{\prime }$ valleys, with spin Chern numbers $C_s=0$ (for $\mathrm{\Gamma }$) and $C_{\uparrow /\downarrow }=\pm 1$ (for $K/K^{\prime }$), respectively. We show that the multivalley moiré flat bands are governed by interlayer hybridization effects, and that different stacking configurations and thicknesses tune the relative energy alignment between the $\mathrm{\Gamma }$ and $K$ valley moiré flat bands. By constructing valley-resolved continuum models and performing Wannierization for the low-energy moiré bands, we further uncover that the Berry curvature and quantum metric distributions can be effectively tuned by the layer number and stacking configuration. Unlike other moiré systems, where only one kind of valley influences the low-energy physics, the simultaneous appearance of two distinct types of valleys with different symmetries establishes A-AB and A-ABA $t{\mathrm{MoTe}}_2$ as ideal platforms for studying layer-controlled multivalley physics.

We uncover a two-stage dynamics during skyrmion formation in chiral magnets and establish its connection to equilibrium phases through the introduction of a Dzyaloshinskii-Moriya interaction (DMI) normalized chiral correlation $\chi$. Stage I involves stripe coarsening governed by the exchange-to-DMI ratio $J^{\prime }$, while stage II entails stripe contraction driven by the synergy between $J^{\prime }$ and the anisotropy-to-DMI ratio $K^{\prime }$. The magnetic field-to-DMI ratio $B^{\prime }$ influences both stages. By combining symbolic regression with neural networks, we establish an interpretable and quantitative framework that captures how microscopic parameters collectively shape the skyrmion formation process. This approach disentangles the distinct roles of different interactions: $J^{\prime }$ sets the stripe width during stage I, $K^{\prime }$ primarily controls the skyrmion size during stage II, and $B^{\prime }$ strongly affects the topological charge. Within the explored parameter space, this framework also yields a field-dependent criterion for skyrmion formation, $0.58J^{\prime }{K}^{\prime }+\mu B^{\prime }{J}^{\prime }>1$. Our results provide a general and interpretable framework for analyzing and controlling skyrmion formation dynamics in chiral magnets.

We report nuclear magnetic resonance Knight shift measurements of the In(1) and In(2) sites in ${\mathrm{CeRhIn}}_5$ as a function of pressure. In contrast to the $c$ axis, the in-plane components of the In(1) Knight shift tensor exhibit little to no pressure dependence. These results indicate that the dipolar component of the tensor is strongly suppressed at the In(1) site, while it remains constant with pressure at the In(2) site. We analyze the hyperfine coupling in terms of a tight-binding model for the electronic structure, and determine that the pressure dependence of the In(1) shift cannot be explained in terms of changes to the crystal field parameters, but rather can be understood in terms of an increase in the $4f$ electron content at the Fermi surface. Our results indicate that the hyperfine coupling reflects changes in the electronic structure near a Kondo breakdown quantum critical point.

We discuss the choice and implementation of intervalley potentials in the so-called two-band $k·p$ model for the opposite $X, Y$, or $Z$ valleys of silicon. We focus on the description of valley splittings in Si/SiGe heterostructures for spin qubits, with a particular attention to alloy disorder. We demonstrate that the two-band $k·p$ model reproduces the valley splittings of atomistic tight-binding calculations in relevant heterostructures (SiGe spikes, wiggle wells, $\cdots$), yet at a much lower cost. We show that the model also captures the effects of valley-orbit mixing and yields the correct intervalley dipole matrix elements that characterize manipulation, dephasing, and relaxation in spin and valley qubits. We simulate a realistic Si/SiGe spin-qubit device as an illustration, and discuss electron-phonon interactions in the two-band $k·p$ model. Beyond spin qubits, this model enables efficient simulations of SiGe heterostructure devices where spin and valley physics are relevant.

Inelastic neutron scattering experiments with a large set of comounted ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ crystals reveal the low-energy magnon dispersion in this candidate material for Kitaev physics. The magnon gap amounts to 1.7(1) meV and can be interpreted similarly to the sister compound $\alpha \text{−}{\mathrm{RuCl}}_3$ to stem from the zone boundaries in the antiferromagnetic zigzag structure. The neutron experiments find no evidence for low-energy excitations with ferromagnetic character, which contrasts with the findings in $\alpha \text{−}{\mathrm{RuCl}}_3$. Our results are consistent with a recently proposed microscopic model that involves an antiferromagnetic Heisenberg nearest-neighbor exchange in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ in contrast to the ferromagnetic one considered for $\alpha \text{−}{\mathrm{RuCl}}_3$. Although the magnetic response shows the signatures of bond-directional anisotropy in both materials the different relative signs of Kitaev and Heisenberg interaction result in different deviations from the initial Kitaev model. Low-energy ferromagnetic fluctuations cannot be considered as a fingerprint of ferromagnetic Kitaev interaction.

Weak localization (WL) and weak antilocalization (WAL) of electrons in a disordered conductor refer to the decrease or increase of the conductivity caused by the quantum interference of the electronic motion. In graphene, the nontrivial Berry phase and the chiral nature of the charge carriers imply that both phenomena can be observed, as it has been firmly established in direct current (DC) magnetotransport experiments. However, studies of alternating current (AC) magnetoconductivity at frequencies comparable to, and much higher than, the dephasing rate (${\tau }_{\varphi }^{-1}$) remain unexplored. Using a combination of transport and spectroscopic measurements at low ($\omega /2\pi <20\mathrm{GHz}$) and high ($\omega /2\pi =90–350\mathrm{GHz}$) frequencies compared to the dephasing rate, we demonstrate a frequency dependence in the optical magnetoconductivity of graphene in the limit $\omega {\tau }_{\varphi }\gg 1$. We prove that spectroscopic measurements at low frequencies are well reproduced by the WL theory in the static limit ($\omega =0$), with no appreciable changes in the magnetoconductivity at different frequencies as long as the condition $\omega {\tau }_{\varphi }<1$ holds. At higher frequencies, the spectra exhibit transitions between WL and WAL induced solely by the external electromagnetic field, as they occur at constant temperature and carrier density. By analyzing the results with a WL model extended to finite frequencies, we observe that the usual decoherence mechanisms of inelastic scattering, in addition to the elastic processes of intervalley and long-range scattering, do not explain the observed behavior. Our results point to the need for a revised model for the decoherence dynamics in the limit $\omega {\tau }_{\varphi }\gg 1$.

In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is characterized by the Rényi-2 correlators. In this work we present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models. In addition to introducing a type of mixed-state topological phases, we provide models of the criticalities between them, including those with gapless symmetry-protected topological order. We clarify that the ground states of lattice gauge theories are purified states of the corresponding mixed SSB states. Our construction can be applied to any finite gauge theory and offers a framework to study quantum operations between mixed quantum phases.

Zigzag chains allow for the formation of topological edge states. Several distinct chain architectures have been developed for this purpose. Here, we report a zigzag superlattice, containing two staggered sublattices, that supports multiple edge states, including higher-order modes. In such lattices, the intra- and intercell coupling is imbalanced by the tunneling effect of the eigenstates or deformation of the higher-order modes. We demonstrate that by arranging the zigzag superlattice into a curved shape, some of the edge states transition into bulk states as the curvature of the lattice increases, while some bulk states become more localized towards edge states. The reason is that a curved superlattice strengthens the intralattice coupling of the inner sublattice because of the separation reduction of the potential wells. We also show that some bulk states at larger curvatures can be transformed into edge states by a repulsive nonlinearity, which also enables the coexistence of different edge states. As a specific and ideal platform for realizing such topological superlattices, we explore exciton-polaritons in semiconductor microcavities with their strong nonlinearity and possibility for optical excitation and control. Our work introduces an additional dimension for the design of complex topological lattices and functional photonic devices.

Deep neural networks can represent very different sorts of functions, including complex quantum many-body states. Tensor networks can also represent these states, have more structure, and are easier to optimize. However, they can be prohibitively costly computationally in two or higher dimensions. Here, we propose a generalization of the perceptron—the perceptrain—which borrows features from the two different formalisms. We construct variational many-body ansatz from a simple network of perceptrains. The network can be thought of as a neural network with a few distinct features inherited from tensor networks. These include efficient local optimization akin to the density matrix renormalization algorithm, instead of optimizing all the parameters at once; the possibility to dynamically increase the number of parameters during the optimization; the possibility to compress the state; and a structure that remains quantum-inspired. We showcase the ansatz using a combination of variational Monte Carlo (VMC) and Green function Monte Carlo (GFMC) on a $10\times 10$ transverse field quantum Ising model with a long-range $1/r^6$ antiferromagnetic interaction. The model corresponds to the Rydberg (cold) atoms platform proposed for quantum annealing. We consistently find a very high relative accuracy for the ground-state energy, around ${10}^{-5}$ for VMC and ${10}^{-6}$ for GFMC in all regimes of parameters, including in the vicinity of the quantum phase transition. We use very small ranks ($\sim 2–5$) of perceptrains, as opposed to multiples of thousand used in matrix product states. The optimization of the energy was very robust. The entire phase diagram was found with a single initial condition and a fixed set of hyperparameters.

We explore gyrotropic effects in the $\mathrm{BaTi}{\mathrm{S}}_3$ system, a quasi-one-dimensional crystal that exhibits giant optical anisotropy [S. Niu et al., Nat. Photon. 12, 392 (2018); B. Zhao et al., Chem. Mater. 34, 5680 (2022)]. In the $P{6}_{3}cm$ phase which is stable under room temperature, we predict two distinct strain-induced phase transitions: (i) a symmetry-lowering transition from the $P{6}_{3}cm$ to chiral $P{6}_3$ phase under tensile strain ($>3.0\%$), which enhances natural optical activity (NOA) and enables electric-field-switchable optical rotation; and an isostructural insulator-to-polar semimetal transition under compressive strain ($\le -3\%$), which activates the nonlinear anomalous Hall effect and exhibits a strain-induced sign reversal. The low-temperature $P{2}_1$ phase also transforms into a $P{2}_1{2}_1{2}_1$ phase under enough compressive strains with such phase transition exhibiting a large NOA. All these results highlight $\mathrm{BaTi}{\mathrm{S}}_3$ as a viable candidate for ferroelectrics, chiral and optical devices with strain enhanced or activated gyrotropic properties.

Long-range electrostatic interactions critically affect polar materials. However, state-of-the-art atomistic potentials, such as neural networks or Gaussian approximation potentials employed in large-scale simulations, often neglect the role of these long-range electrostatic interactions. This study introduces a framework derived from first principles to evaluate the contribution of long-range electrostatic interactions to total energies, forces, and stresses. The model is designed to integrate seamlessly with existing short-range force fields without further first-principles calculations or retraining. The approach relies solely on physical observables, like the dielectric tensor and Born effective charges, that can be consistently calculated from first principles. We demonstrate that the model reproduces critical features, such as the LO-TO splitting and the long-wavelength phonon dispersions of polar materials, with benchmark results on the cubic phase of barium titanate (${\mathrm{BaTiO}}_3$).

We develop a method to fit high-temperature Gibbs free energy data for the development of interatomic potentials for atomic systems. The approach is based on Hamiltonian thermodynamic integration, enabling the identification of suitable potential parameters such that the free energy of the system matches a specified target. The method can be readily combined with conventional fitting techniques for properties such as elastic tensors and liquid pair distribution functions. We validate the effectiveness of the approach using the Uhlenbeck-Ford model and embedded-atom method potentials for pure Ni phases and binary $\mathrm{F}{\mathrm{e}}_{1-x}{\mathrm{O}}_x$ liquids under high-pressure and high-temperature conditions. Our framework provides an efficient strategy for incorporating free energy into interatomic potential fitting.

We investigate the role of quantum geometry in the Meissner response for odd-frequency superconducting pairs in multiband systems. Odd-frequency pairing is traditionally associated with a paramagnetic Meissner response, which raises questions about the stability of the superconducting phase, especially in multiband systems where odd-frequency pairing is ubiquitous. Using analytical calculations in a general two band, we show that the quantum geometric contribution to the Meissner response from odd-frequency pairs is always diamagnetic for its interband processes, while intraband processes always yield a paramagnetic response. With odd-frequency pairing itself generated by interband pairing, an overall diamagnetic response may often be anticipated. We confirm these results with numerical calculations of models with both flat and dispersive bands. In flat-band systems, where geometric effects dominate, the diamagnetic odd-frequency response can even exceed the even-frequency contribution, making odd-frequency pairs the primary source of the diamagnetic Meissner response. In a dispersive two-band system with finite quantum geometry, we similarly find a robust diamagnetic contribution from odd-frequency pairing, even when the total response turns paramagnetic due to even-frequency contributions. These results establish that quantum geometry stabilizes odd-frequency superconductivity and also identify flat-band materials as candidates for realizing odd-frequency superconductivity with a diamagnetic Meissner effect.

The projected ensemble, an ensemble of pure states on a subsystem conditioned on projective measurement outcomes on its complement, provides a finer probe of ergodicity and information structure than the reduced density matrix of the subsystem in bipartite quantum states. This framework can be generalized to partial projected ensembles in tripartite settings, where outcomes from part of the measured subsystem are discarded, leading to ensembles of mixed states. We show that information measures defined for such ensembles, in particular the Holevo information, yield a more detailed characterization of how quantum information is distributed between subsystems compared to conventional entanglement measures. Using exact analytical results supported by numerical results, we uncover a qualitative change in the scaling of the Holevo information with system size in partial projected ensembles generated by Haar-random states, as the relative sizes of the subsystem are varied. In one phase, the Holevo information decays exponentially with system size, while in the other it grows linearly, thereby defining distinct information phases separated by sharp transitions signaled by nonanalyticities in the Holevo information. The exponentially decaying phase rigorously establishes the existence of a measurement-invisible quantum-correlated phase, a manifestation of many-body information scrambling with no bipartite analog. We contrast this information-phase diagram with the entanglement-phase structure of tripartite Haar-random states obtained from logarithmic negativity, and show that the Holevo information reveals additional fine structure beyond conventional entanglement measures. Finally, we show that these information phases, as characterized by the Holevo information, emerge in the dynamics of chaotic quantum circuits and discuss the associated timescales.

We analyze the noise in a multiterminal multichannel conductor under arbitrary time-dependent driving and subject to—possibly large—static potential and temperature biases. We show that the full out-of-equilibrium zero-frequency noise is constrained by a fluctuation-dissipation bound. It consists of an upper bound expressed in terms of weighted current components of the separate Floquet bands arising from the time-dependent driving. In the limit of large static temperature bias, it has an intuitive interpretation in terms of the dissipated powers due to the static potential bias and due to the time-dependent driving. Furthermore, we show the existence of a second bound that relies on the specific shape of the electron distribution resulting from the driving, which can even be tighter than the fluctuation-dissipation bound in some parameter regimes. We show the implications of our bounds at the simple but experimentally relevant example of a two-terminal conductor in the presence of an ac bias.

We study a single component (i.e., single valley, spin-polarized) two-dimensional electron gas with $C_{3v}$ symmetry tuned to a Van-Hove (VH) singularity. Generically, there may be either three or six VH points at the Fermi level, related to each other by symmetry. Using a renormalization group analysis, we show that when the effective interactions between electrons at the VH points are positive, the system is stable. In contrast, if the effective interactions are negative, the system develops an instability toward either pair density wave (PDW) or charge density wave (CDW) orders, depending on the anisotropy of the dispersion at the VH points. The PDW may have either a single wave vector or multiple wave vectors. The PDW phase with three coexisting wave vectors can support fractional $\frac{h}{6e}$ vortices. The interplay between the geometry of the Fermi surface and the singularity of the density of states is the key that enables PDW formation.

Understanding electrical resistivity in metals remains a central challenge in quantifying charge transport at finite temperature. Current first-principles calculations based on the Boltzmann transport equation often match experiments, yet they almost always neglect the effect of thermal expansion and phonon anharmonicity. We show that both effects exert an opposite impact on electron-phonon coupling and on electrical resistivity. Thermal expansion enhances the coupling and leads to overestimation of resistivity, whereas anharmonic effects reduce it. By explicitly incorporating both effects, we establish a more complete description of resistivity in elemental metals, demonstrated here for Pb, Nb, and Al.

The giant and tunneling magnetoresistance effects are widely use in commercial spintronics devices as platform technologies for magnetic-field sensors in magnetic recording. These rely on ferromagnets to spin-polarize and detect an electronic current. The recent discovery of altermagnetism has disrupted this paradigm, demonstrating that even spin-neutral currents can yield significant magnetoresistance. Using first-principles calculations, we confirm the momentum-dependent spin-splitting band structure of the altermagnet ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$ and design an all-metal device, ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}/{\mathrm{BaTi}}_2{\mathrm{Bi}}_2\mathrm{O}/{\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$, displaying tunnel-like transport and the enormous magnetoresistance ratio of $1.5\times {10}^{12}\%$. This is orders of magnitude larger than what was previously reported for altermagnetic tunnel junctions. The underpinning mechanism of this remarkable magnetoresistance is symmetry-driven spin selectivity, which here is explained by computing spin transport across ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$ in different magnetic configurations. Our study expands the possible use of altermagnets in spintronics and suggests a new avenue for high-performing antiferromagnetic devices.

Using first-principles density functional theory (DFT) combined with atomistic spin simulations, we explore the possibility of realizing zero-field isolated skyrmions in three $4d/\mathrm{Co}$ atomic bilayers—Rh/Co, Pd/Co, and Ru/Co—grown on the Re(0001) surface. Our investigation employs an extended atomistic spin model, which goes beyond the standard model by including the multispin higher-order exchange interactions (HOI) in addition to the Heisenberg pairwise exchange interaction, Dzyaloshinskii-Moriya interaction (DMI), and magnetocrystalline anisotropy energy (MAE). All magnetic interactions of the extended spin model are calculated using DFT. The phase diagram obtained from atomistic spin simulations based on this spin model for Rh/Co and Pd/Co on Re(0001) reveals that isolated skyrmions emerge spontaneously on the ferromagnetic background even in the absence of an external magnetic field. The radius of zero-field isolated skyrmions in Rh/Co/Re(0001) is around 6 nm, whereas the radius of those skyrmions in Pd/Co/Re(0001) is about 12 nm. Transition-state theory calculations show that the skyrmions are protected by substantial energy barriers, approximately 150 meV, which predominantly arise from DMI, with a small contribution from the HOI. The height of the barriers suggests that skyrmions could be observed in low-temperature experiments. Based on this work, we propose $4d/\mathrm{Co}$ bilayers on Re(0001) as a new platform to realize nanoscale zero-field isolated skyrmions.