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At least 127 records · Page 7

Piezomagnetic switching and complex phase equilibria in uranium dioxide

Abstract Actinide materials exhibit strong spin–lattice coupling and electronic correlations, and are predicted to host new emerging ground states. One example is piezomagnetism and magneto-elastic memory effect in the antiferromagnetic Mott-Hubbard insulator uranium dioxide, though its microscopic nature is under debate. Here, we report X-ray diffraction studies of oriented uranium dioxide crystals under strong pulsed magnetic fields. In the antiferromagnetic state a [888] Bragg diffraction peak follows the bulk magnetostriction that expands under magnetic fields. Upon reversal of the field the expansion turns to contraction, before the [888] peak follows the switching effect and piezomagnetic ‘butterfly’ behaviour, characteristic of two structures connected by time reversal symmetry. An unexpected splitting of the [888] peak is observed, indicating the simultaneous presence of time-reversed domains of the 3-k structure and a complex magnetic-field-induced evolution of the microstructure. These findings open the door for a microscopic understanding of the piezomagnetism and magnetic coupling across strong magneto-elastic interactions.

36 MATERIALS SCIENCE↗

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. In this work, we show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

97 MATHEMATICS AND COMPUTING↗

Equilibrium spin polarization arising from chirality

Chirality-induced spin selectivity (CISS) describes how chiral molecules and materials generate spin polarization even at thermal equilibrium. This observation has challenged established principles of microscopic reversibility and Onsager reciprocity. We resolve this paradox by formulating a pseudo-Hermitian quantum framework that separates thermodynamic equilibrium from time-reversal symmetry. Within this approach, structural chirality and electron correlations, irrespective of their microscopic origin, are sufficient to produce CISS observables. Chirality enters through a non-local metric η that couples spin and spatial motion, leading to real spectra, unitary evolution, and thermodynamic consistency. The framework predicts a chirality-induced spin magnetic ordering characterized by a spin-displacement order, which reconciles equilibrium spin polarization with detailed balance and explains the persistence of CISS in materials composed of light elements. We derive generalized Onsager-Casimir relations that respect the observed CISS symmetry, i.e., parity $(\mathscr{P})$-odd and time-reversal $(\mathscr{T})$-odd, but exhibiting $\mathscr{PT}$-even symmetry. This approach establishes a coherent foundation for equilibrium CISS and provides a route to link chemical chirality with measurable spin-to-charge conversion effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fermi surfaces of the topological semimetal CaSn 3 probed through de Haas van Alphen oscillations

Abstract In the search of topological superconductors, nailing down the Fermiology of the normal state is as crucial a prerequisite as unraveling the superconducting pairing symmetry. In particular, the number of time-reversal-invariant momenta (TRIM) in the Brillouin zone enclosed by Fermi surfaces is closely linked to the topological class of time-reversal-invariant systems, and can experimentally be investigated. We report here a detailed study of de Haas van Alphen quantum oscillations in single crystals of the topological semimetal CaSn 3 with torque magnetometry in high magnetic fields up to 35 T. In conjunction with density functional theory based calculations, the observed quantum oscillations frequencies indicate that the Fermi surfaces of CaSn 3 enclose an odd number of TRIM, satisfying one of the proposed criteria to realize topological superconductivity. Nonzero Berry phases extracted from the magnetic oscillations also support the nontrivial topological nature of CaSn 3 .

Physics↗

Kramers' degeneracy for open systems in thermal equilibrium

Kramers' degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a combination of time-reversal symmetry and the microreversibility (detailed balance) property of systems at thermal equilibrium—the degeneracy is lifted if either condition is not met. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the single-particle Green's functions. Furthermore, we show that certain experimental signatures of topological edge modes in open many-body systems can be protected by microreversibility in the same way. Our results highlight the importance of detailed balance in characterizing open topological matter.

36 MATERIALS SCIENCE↗

Imaging orbital ferromagnetism in a moiré Chern insulator

Capturing exotic magnetism Ferromagnetism is associated with the breaking of time-reversal symmetry, most frequently by the spin degree of freedom. Although the orbital motion of electrons can also contribute to ferromagnetism, in most materials, it is small relative to the spin contribution. Tschirhart et al. showed that the reverse is true in an unusual magnetic state hosted by twisted bilayer graphene. Their scanning magnetometry measurements were consistent with ferromagnetism of predominantly orbital origin. Science , abd3190, this issue p. 1323

Science & Technology - Other Topics↗

Enhancing photonic systems using topology and non-Hermiticity

The broad goal of this project was to develop new analytical and numerical insights for how important photonic processes can be improved using recently discovered principles in topological and non-Hermitian physics. In particular, there are two recent discoveries that we aimed to harness to achieve this goal. First, it was discovered in condensed matter physics that crystalline symmetries can protect low-dimensional topologically protected states in lattices without the need for breaking time-reversal symmetry. These so-called ‘higher-order’ topological systems represent an important development for photonic systems, where it is very difficult to break time-reversal symmetry, and which had been previously thought necessary to realize topological phenomena. Second, the last decade has seen a significant amount of interest in phenomena which are unique to non-Hermitian systems, i.e., systems which do not conserve energy. For example, spatially patterned gain and loss can be used to realize exceptional points, which are degeneracies in a system’s spectrum where the system becomes defective, while the existence of radiative losses also enables a new route to confinement through bound states in the continuum. For such non-Hermitian phenomena, photonics again represents a critical platform, as photonic systems naturally lose light to their radiative environments, making them generally non-Hermitian, and it is also possible to incorporate additional gain or loss. Based on these broad principles, we pursued a range of projects to harness bound states in the continuum in a variety of different systems and architectures, develop real-space methods for classifying topological systems to yield better photonic design principles, and a novel Brillouin-based fiber laser for sensing strain.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Theory of strain-induced magnetic order and splitting of $T_c$ and $T_{\text{TRSB}}$ in Sr 2 RuO 4

The internal structure of the superconducting state in Sr 2 RuO 4 remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\text{TRSB}}$ with applied strain. In addition, static magnetic order is induced by the uniaxial strain beyond ~1 GPa, indicating that unstrained Sr 2 RuO 4 is close to a magnetic quantum critical point. Here we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. In this work, it is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain dependence of accidentally degenerate pair states in unstrained Sr 2 RuO 4 . In addition, while unstrained Sr 2 RuO 4 features mainly (2π /3, 2π /3) magnetic fluctuations, uniaxial strain promotes (π, ±π /2) magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exchange coupling in $\mathrm{Bi_2}$ $\mathrm{Se_3}$ / $\mathrm{EuSe}$ heterostructures and evidence of interfacial antiferromagnetic order formation

Spatial confinement of electronic topological surface states (TSSs) in topological insulators poses a formidable challenge because TSSs are protected by time-reversal symmetry. In previous works formation of a gap in the electronic spectrum of TSSs has been successfully demonstrated in topological insulator/magnetic material heterostructures, where ferromagnetic exchange interactions locally lift the time-reversal symmetry. Here we report experimental evidence of exchange interaction between a topological insulator $\mathrm{Bi_2}$ $\mathrm{Se_3}$ and a magnetic insulator EuSe. Spin-polarized neutron reflectometry reveals a reduction of the in-plane magnetic susceptibility within a 2 nm interfacial layer of EuSe, and the combination of superconducting quantum interference device (SQUID) magnetometry and Hall measurements points to the formation of an interfacial layer with a suppressed net magnetic moment. This suppressed magnetization survives up to temperatures five times higher than the Néel temperature of EuSe. Its origin is attributed to the formation of an interfacial antiferromagnetic state. Abrupt resistance changes observed in high magnetic fields are consistent with antiferromagnetic domain reconstruction affecting transport in a TSS via exchange coupling. Importantly, the high-temperature local control of TSSs with zero net magnetization unlocks new opportunities for the design of electronic, spintronic, and quantum computation devices, ranging from quantization of Hall conductance in zero fields to spatial localization of non-Abelian excitations in superconducting topological qubits.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Intrinsic axion insulating behavior in antiferromagnetic MnBi 6 Te 10

A striking feature of time-reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when the surface states are gapped by time-reversal breaking perturbations. While TRS-protected TIs have become increasingly under control, magnetic analogs are still a largely unexplored territory with novel rich structures. In particular, magnetic topological insulators can also host a quantized axion term in the presence of lattice symmetries. Since these symmetries are naturally broken on the boundary, the surface states can develop a gap without external manipulation. In this work, we combine theoretical analysis, density-functional calculations and experimental evidence to reveal intrinsic axion insulating behavior in MnBi 6 Te 10 . Additionally, the quantized axion term arises from the simplest possible mechanism in the antiferromagnetic regime where it is protected by inversion symmetry and the product of a fractional translation and TRS. The anticipated gapping of the Dirac surface state at the edge is subsequently experimentally established using angle resolved photoemission spectroscopy (ARPES). As a result, this system provides the magnetic analog of the simplest TRS-protected TI with a single, gapped Dirac cone at the surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions

Abstract Recent years have witnessed tremendous success in the discovery of topological states of matter. Particularly, sophisticated theoretical methods in time-reversal-invariant topological phases have been developed, leading to the comprehensive search of crystal database and the prediction of thousands of topological materials. In contrast, the discovery of magnetic topological phases that break time reversal is still limited to several exemplary materials because the coexistence of magnetism and topological electronic band structure is rare in a single compound. To overcome this challenge, we propose an alternative approach to realize the quantum anomalous Hall (QAH) effect, a typical example of magnetic topological phase, via engineering two-dimensional (2D) magnetic van der Waals heterojunctions. Instead of a single magnetic topological material, we search for the combinations of two 2D (typically trivial) magnetic insulator compounds with specific band alignment so that they can together form a type-III broken-gap heterojunction with topologically non-trivial band structure. By combining the data-driven materials search, first-principles calculations, and the symmetry-based analytical models, we identify eight type-III broken-gap heterojunctions consisting of 2D ferromagnetic insulators in the MXY compound family as a set of candidates for the QAH effect. In particular, we directly calculate the topological invariant (Chern number) and chiral edge states in the MnNF/MnNCl heterojunction with ferromagnetic stacking. This work illustrates how data-driven material science can be combined with symmetry-based physical principles to guide the search for heterojunction-based quantum materials hosting the QAH effect and other exotic quantum states in general.

36 MATERIALS SCIENCE↗

Signal amplification in a solid-state sensor through asymmetric many-body echo

Electronic spins of nitrogen–vacancy centres in diamond constitute a promising system for micro- and nanoscale magnetic sensing, because of their operation under ambient conditions, ease of placement in close proximity to sensing targets and biological compatibility. At high densities, the electronic spins interact through dipolar coupling, which typically limits but can also potentially enhance sensing performance. Here we report the experimental demonstration of many-body signal amplification in a solid-state, room-temperature quantum sensor. Our approach uses time-reversed two-axis-twisting interactions, engineered through dynamical control of the quantization axis and Floquet engineering in a two-dimensional ensemble of nitrogen–vacancy centres. We observe that optimal amplification occurs when the backward evolution time equals twice the forward evolution time, in sharp contrast to the conventional Loschmidt echo. These observations can be understood as resulting from an underlying time-reversed mirror symmetry of the microscopic dynamics, providing key insights into signal amplification and opportunities for practical entanglement-enhanced quantum sensing.

quantum information↗

Deformation of Lie–Poisson algebras and chirality

Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian symmetric spectra: If λ is an eigenvalue of the linearized generator, -λ and $\barλ$ (hence, -$\barλ$) are also eigenvalues—the former implies a time-reversal symmetry, while the latter guarantees the reality of the solution. However, linearization around a singular equilibrium point (which commonly exists in noncanonical Hamiltonian systems) works out differently, resulting in breaking of the Hamiltonian symmetry of spectra; time-reversal asymmetry causes chirality. This interesting phenomenon was first found in analyzing the chiral motion of the rattleback, a boat-shaped top having misaligned axes of inertia and geometry [Z. Yoshida et al., Phys. Lett. A 381, 2772–2777 (2017)]. To elucidate how chiral spectra are generated, we study the three-dimensional Lie–Poisson systems and classify the prototypes of singularities that cause symmetry breaking. The central idea is the deformation of the underlying Lie algebra; invoking Bianchi’s list of all three-dimensional Lie algebras, we show that the so-called class-B algebras, which are produced by asymmetric deformations of the simple algebra s o ( 3 ) , yield chiral spectra when linearized around their singularities. The theory of deformation is generalized to higher dimensions, including the infinite-dimensional Poisson manifolds relevant to fluid mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

Here, we present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

97 MATHEMATICS AND COMPUTING↗

$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals

In this work, we uncover the properties of complex tensor ($\textit{d}$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $\textit{d}$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $\textit{d}$-wave superconductors where the $\textit{d}$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Colloquium : Quantum anomalous Hall effect

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators—topologically nontrivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, nontrivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. Here, the quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr- and/or V-) doped topological insulators in the (Bi,Sb) 2 T 3 family, (ii) thin films of the intrinsic magnetic topological insulator MnBi 2 Te 4 , (iii) moiré materials formed from graphene, and (iv) moiré materials formed from transition-metal dichalcogenides. In this Colloquium, the physical mechanisms responsible for each class of QAH insulator are reviewed, with both differences and commonalities highlighted, and potential applications of the QAH effect are commented upon.

36 MATERIALS SCIENCE↗

Symmetries and anomalies of Hamiltonian staggered fermions

We review the shift (translation) and time reversal symmetries of Hamiltonian staggered fermions and their connection to continuum symmetries concentrating in particular on the case of massless fermions and (3+1) dimensions. We construct operators using the staggered fields that implement these symmetries on finite lattices. We show that shifts composed of an odd multiple of the elementary shift anticommute with time reversal and are related to continuum axial transformations. We argue that the presence of these nontrivial commutation relations implies the existence of lattice ’t Hooft anomalies. From the shifts we also construct a set of conserved, quantized charges that generate continuous symmetries of the lattice theory. In general these do not commute with the vector charge signaling further ’t Hooft anomalies.

Anomalies↗

First-principles theory of the Dirac semimetal Cd 3 As 2 under Zeeman magnetic field

Time-reversal broken Weyl semimetals have attracted much attention recently, but certain aspects of their behavior, including the evolution of their Fermi surface topology and anomalous Hall conductivity with Fermi-level position, have remained underexplored. A promising route to obtain such materials may be to start with a nonmagnetic Dirac semimetal and break time-reversal symmetry via magnetic doping or magnetic proximity. Here we explore this scenario in the case of the Dirac semimetal Cd 3 As 2 , based on first-principles density-functional calculations and subsequent low-energy modeling of Cd 3 As 2 in the presence of a Zeeman field applied along the symmetry axis. We clarify how each four-fold degenerate Dirac node splits into four Weyl nodes, two with chirality ±1 and two higher-order nodes with chirality ±2. Using a minimal k · p model Hamiltonian whose parameters are fit to the first-principles calculations, we detail the evolution of the Fermi surfaces and their Chern numbers as the Fermi energy is scanned across the region of the Weyl nodes at fixed Zeeman field. We also compute the intrinsic anomalous Hall conductivity as a function of Fermi-level position, finding a characteristic inverted-dome structure. Cd 3 As 2 is especially well suited to such a study because of its high mobility, but the qualitative behavior revealed here should be applicable to other Dirac semimetals as well.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗