The quantum behavior of light particles in solids gives rise to phenomena that cannot be captured by a classical description. We show that muon spin spectroscopy (& micro;SR), when paired with a quantum-mechanical treatment of the implanted muon, becomes a sensitive and direct probe of nuclear quantum effects. By modeling the muon as a spatially extended quantum particle, our approach captures strong anharmonic behavior. We demonstrate this in Zn-barlowite, which serves as a nontrivial test case due to its structurally complex lattice and the presence of both fluorine and hydroxyl groups. Our results establish a route for extracting nuclear quantum signatures from & micro;SR data and open different opportunities for studying light nuclei such as hydrogen and lithium in systems where quantum fluctuations shape structure and function.
As a powerful theoretical construct, the entanglement Hamiltonian (EH) encapsulates the essential entanglement properties of a quantum many-body system. From the EH, one can extract a variety of entanglement quantities, such as entanglement entropies, negativity, and the entanglement spectrum. However, its general analytical form remains largely unknown. While the Bisognano-Wichmann theorem gives an exact EH form for Lorentz-invariant field theories, its validity on lattice systems is limited, especially when Lorentz invariance is absent. In this work, we propose a general scheme based on the lattice-Bisognano-Wichmann (LBW) ansatz and multi-replica-trick quantum Monte Carlo methods to numerically reconstruct the entanglement Hamiltonian in two-dimensional systems and systematically explore its applicability to systems without translational invariance, going beyond the scope of the original Bisognano-Wichmann theorem. Various quantum phases-including gapped and gapless phases, critical points, and phases with either discrete or continuous symmetry breaking- are investigated, demonstrating the versatility of our method in reconstructing entanglement Hamiltonians. Furthermore, we find that when the entanglement boundary of a system is ordinary (i.e., free from surface anomalies), the LBW ansatz provides an accurate approximation well beyond Lorentz-invariant cases. Our work thus establishes a general framework for investigating the analytical structure of entanglement in the complex quantum many-body systems.
We report the experimental observation of oscillations in the critical current Ic of SNS Josephson junctions as a function of in-plane magnetic field B|| (where S is Nb and N is Al above its critical temperature). Our theoretical calculations within the Ginzburg-Landau framework demonstrate that at sufficiently large B||, in-plane vortices enter the N layer, pin on the SN interface, and partially penetrate the S layer in the banks of the SNS junction. These interface vortices significantly affect the proximity-induced superconductivity in the normal weak link, leading to pronounced oscillations in the critical current Ic(B||). We also observe a superconducting diode effect of orbital origin that undergoes sign reversal with variations in the magnetic field.
Symmetry analysis is a cornerstone of modern physics, with charge- and spacetime-orientation-reversal (CRT) symmetry being a subject of particular interest. Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the 7LC2 & times; 7LR2 & times; 7LT2 symmetry for scalar bosons. In fact, the CRT symmetry for fermions can be extended by internal symmetries such as fermion parity 7LF2 , chiral symmetry 7L chi 2 , and continuous symmetries, thereby forming a group extension of the aforementioned 7L2 direct product, and suffices to rule out bilinear mass terms. In the conventional framework, a Majorana fermion is defined by a single Dirac fermion with trivial charge conjugation. However, this definition encounters a fundamental challenge when the spacetime dimension d + 1 = 5, 6, 7 mod 8, where the real dimension of Majorana fermion (dimR chi Cl(d,0)) aligns with the real dimension of Dirac fermion (dimR psi Cl(d)), rather than being half as in other dimensions. This peculiarity necessitates the introduction of a symplectic Majorana fermion, defined by a pair of Dirac fermions with trivial charge conjugation, to account for the discrepancy. To include these two types of Majorana fermions, we embed the Majorana theory in nR and define the Majorana fermion field as a representation of the real Clifford algebra, which exhibits an eightfold Bott periodicity. Within the Hamiltonian formalism, we identify the eightfold CRT-internal symmetry groups across general spatial dimensions. In the case of Dirac fermions, the fermion field is defined as a representation of the complex Clifford algebra, which has a twofold Bott periodicity. Interestingly, we discover that the CRT-internal symmetry groups exhibit an eightfold periodicity that is distinct from that of the complex Clifford algebra. In certain dimensions where distinct mass terms can span a mass manifold, the CRT-internal symmetries can act nontrivially upon this mass manifold. Employing domain wall reduction method, we are able to elucidate the relationships between symmetries across different dimensions.
Herein, we report spectroscopic, electronic, and magnetic investigation of the mixed-cation pyrochlores Ca3R3Ta2Ti7O26.5 (R = Dy3+, Nd3+), elucidating key signatures of A-and B-site cation disorder and oxygen nonstoichiometry. Structural characterization, Raman and infrared spectroscopy, complemented by lattice dynamical analysis, reveal disorder-induced distortions of the pyrochlore lattice and relaxation of the vibrational selection rules. The ab initio density-functional theory computations using LDA+U and LDA-1/2 approaches reproduce experimentally observed wide optical band gaps (approximate to 3 eV), highlighting the sensitivity of the electronic states near band edges to oxygen rearrangements and cation mixing. Crystal-field (CF) calculations employing the exchange charge model reproduce UV-visible and photoluminescence spectra, yielding reliable CF energy levels and wavefunctions for R3+ ions. Dy3+ ions in Ca3Dy3Ta2Ti7O26.5 retain a well-isolated (111) Ising-like Kramers doublet with large magnetic moment. The dc and ac magnetic susceptibility measurements reveal absence of long-range spin-ice freezing, with only slow spin dynamics and short-range correlations persisting arising from disorder-induced disruption of exchange interactions. Nd3+ ions in Ca3Nd3Ta2Ti7O26.5 exhibit pronounced CF-induced J mixing, reduced Ising anisotropy, and dominant antiferromagnetic interactions, leading to short-range "all-in, all-out" correlations that are enhanced under applied magnetic fields. Mean-field modeling incorporating CF effects, anisotropic exchange, and long-range dipolar interactions quantitatively accounts for the magnetic response of both compounds. Electrical resistivity measurements on Nd-based compound reveal thermally activated hopping transport, consistent with a wide-gap insulating state and disorder-induced electronic localization. Our results establish chemical disorder as an effective tuning factor controlling the spectroscopic, electronic, magnetic, and transport properties of rare-earth pyrochlores and provide a robust platform for exploring emergent phenomena in frustrated materials.
The magnetic behavior of the Fe sublattice in the pseudobinary Laves phase materials (Hf,Mo)Fe2 was thoroughly investigated in the paramagnetic regime as well as in the magnetically ordered state. The analysis of the paramagnetic phase has led to the determination of the Curie-Weiss temperature and effective paramagnetic moment whereas the spontaneous magnetic moment was obtained at temperatures ranging from 4 K up to the Curie point. The number of magnetic charge carriers was calculated both above and below the ferromagnetic ordering temperature in order to evaluate the degree of itinerancy (degree of delocalization) of Fe magnetism in the Hf1-xMoxFe2 series of intermetallic compounds. It is shown that the Curie and Curie-Weiss temperatures decrease strongly upon increasing Mo concentration. Of particular interest is the thermal dependence of the reciprocal magnetic susceptibility in the intermediate composition range (0.05 x 0.15): an unusual transition between two distinct Curie-Weiss behaviors is observed at a critical temperature T & lowast;. The experimental data were analyzed and discussed within the framework of the Kuz'min's model, the self-consistent renormalization and Takahashi's theory of spin fluctuations. T0 and TA parameters characterizing the widths of the spin fluctuation spectrum in energy and wave-vector space, respectively, have been estimated. The transverse spin fluctuations are predominant for the parent intermetallic HfFe2, in contrast, the longitudinal spin fluctuations gradually grow for the richest Mo compositions. Furthermore, Mo for Hf substitution induces a weakening of ferromagnetic exchange interactions: a change from long-range ferromagnetism (for HfFe2) towards systems with competing exchange interactions (for Mo-rich side) is observed. In this family of compounds, the generalized RhodesWohlfarth ratio points out an itinerant magnetism. The 3d Fe magnetism evolves from nearly localized character to strongly delocalized one as the Mo fraction is increased.
We report on ultrasonic measurements of the rare-earth altermagnet TbPt6Al3 in which the Tb magnetic moments in a honeycomb lattice form a collinear antiferromagnetic structure below TN = 3.4 K. All elastic moduli show a distinct downward peak at TQ = 1.6 K, suggesting an additional phase transition. The transverse moduli C44 and C66 exhibit significant softening toward TQ, accompanied by ultrasound attenuation. Crystal field analysis of the temperature dependences of elastic moduli reveals that the elastic softening arises from quadrupole-mediated interactions of the ground non-Kramers doublet of the Tb ions. The field-temperature phase diagram in a magnetic field applied along [001] shows an increase in TQ with increasing field up to 0.8 T. Our crystal field model with the mean-field approximation displays spontaneous occurrence of an expectation value of electric quadrupole at TQ. The agreement between our experimental and calculated results suggests quadrupolar ordering in an altermagnetic ordered state.
Chaotic lattice models at high temperature are generically expected to exhibit diffusive transport of all local conserved charges. Such diffusive transport is usually associated with overdamped relaxation of the associated currents. Here we show that by appropriately tuning the interparticle interactions, lattice models of chaotic fermions at infinite temperature can be made to cross over from an overdamped regime of diffusion to an underdamped regime of hot band sound. We study a family of one-dimensional spinless fermion chains with long-range density-density interactions, in which the damping time of sound waves can be made arbitrarily long even as an effective interaction strength is held fixed. Our results demonstrate that underdamped sound waves of charge density can arise within a single band, with strong interactions and far from integrability, and at very high temperature.
High thermoelectric efficiency has been reported in several antiperovskites, but strongly unbalanced n- and p-type thermoelectric performances still limit practical device integration. Here, we show that Ag3SX (X = Cl, Br, I) antiperovskites exhibit simultaneously favorable p- and n-type transport, and that halogen substitution further improves this ambipolar behavior through coupled lattice and electronic mechanisms. On the lattice side, heavier halogens soften the Ag-X framework and strengthen anharmonic phonon scattering, which markedly lowers the lattice thermal conductivity and helps drive the materials toward a glasslike transport regime. On the electronic side, halogen substitution modifies the relative contributions and hybridization of Ag-4d and chalcogen/halogen p states near the valence-band edge; together with the stronger spin-orbit coupling in the iodide, this leads to enhanced valence-band degeneracy while retaining sufficient band dispersion. As a result, Ag3SI exhibits ultralow lattice thermal conductivity (0.29 W/m K) and high carrier mobility (10-200 cm2/V s), achieving a maximum power factor of 2.5 mW/m K2. Under optimal doping, ZT at 800 K reaches approximate to 2.42 for p-type and approximate to 1.87 for n-type carriers. These results identify Ag3SX compounds as promising ambipolar thermoelectric materials and highlight how lattice anharmonicity and band-edge reconstruction can be combined to optimize heat and charge transport.
The atomic-scale structure and melting curve of liquid mercury was measured using in situ synchrotron x-ray diffraction (SXRD) at pressure and temperature (p-T ) conditions up to 9.44(2) GPa and 651(1) K. Ab initio molecular dynamics (AIMD) simulations were employed to obtain a detailed atomistic model of the liquid structure. The results reveal a pronounced flattening, and potential maximum, in the measured melting curve between 6 and 9 GPa. The structure factors SHgHg(Q) and pair distribution functions gHgHg(r) calculated from the AIMD simulations are in good overall agreement with the SXRD measurements under comparable reduced densities and temperatures, indicating that the atomistic structure of liquid Hg is well captured by AIMD. With increasing pressure, the principal peak in SHgHg(Q) shifts to higher Q, with the subsidiary peak at Q = 2kF experiencing a concomitant shift consistent with the increased electron density. Considering the Evans t-matrix formulation of the Ziman theory of liquid metals, the structural S(2kF) term is expected to have only a weak influence on the electrical resistivity under compression. In contrast, the pressure-induced broadening and shift of the d-projected density of states towards the Fermi level is consistent with enhanced near-resonant d-electron scattering, and a corresponding increase in resistivity, analogous to the behavior of first-row transition metals. Analysis of the measured gHgHg(r) functions, and AIMD trajectories in real space, indicates that the liquid structure experiences a progressive development towards simple hard-sphere-like behavior at increasing p-T along the melting curve. However, topological cluster classification analysis shows that while the structural fingerprint of liquid Hg strongly resembles an effective hard-sphere system, even at the highest pressures investigated it contains more many-body motifs than expected for this simple model.
Accurate characterization of thermodynamic phases and domain structures is crucial for the engineering of polar-textured thin-film electronic devices. In an improvement to the phase prediction, a Landau-GinzburgDevonshire thermodynamic model of ferroic materials is extended to generalized elastic and electromagnetic boundary conditions. The proposed mathematical framework allows for the implementation of a modular computational model which can analyze composite systems with solid solutions, multiple material layers, and domain structures. The model is applied to epitaxially constrained solid solutions of barium and strontium titanates, with the results illustrating the similarity in the evolution of the single-domain and polydomain ferroelectric phases across a wide range of material compositions. In the applications where barium titanate is placed near a phase boundary, further refinement of the characterization of the boundary can be achieved with the inclusion of the inequality of domain sizes and the tilting of the domain wall within the computational model.
We employ functional derivatives to calculate spectroscopy in nonequilibrium many-body systems. This allows for all vertex correction effects to be properly incorporated. We focus on electronic Raman scattering. As a concrete example, we present numerical results for the nonresonant contribution to the time-resolved electronic Raman scattering cross section in the A 1 g symmetry channel solved with dynamical mean-field theory. To do this, we add a small field to the Hamiltonian and take the functional derivative of the “Raman current” operator with respect to this field, which results in an exact expression for the greater Green's function that determines the Raman scattering cross section. This approach avoids the need to set up and solve Bethe-Salpeter equations, which are notoriously difficult to work with in nonequilibrium. We also work out formal expressions for the optical conductivity in the Appendix.
Several recent x-ray diffraction studies have focused on whether the high-pressure body-centered cubic (bcc) phase of zirconium undergoes an isostructural bcc-bcc transition at 58 GPa. The consensus of these studies is that there is no such transition and that a previous claim by Stavrou et al. resulted from issues with the pressure calibration. However, a close analysis of the data from one of the most recent of these diffraction studies by Anzellini et al. shows unremarked evidence of a discontinuity in both atomic volume and compressibility at 83 GPa indicating an isostructural transition is present. Unfortunately, no other previous studies have reached this pressure, and so the question of the bcc-bcc transition is still open. Here we describe a diffraction study of Zr to 240 GPa looking for a bcc-bcc isostructural transition. Our data show no evidence of any discontinuous change in volume or compressibility at 83 GPa. We observe no evidence of a ,B -> ,B' transition above 80 GPa, and suggest a possible cause of the discontinuity observed by Anzellini et al.
The zero-mode corner states in the gap of a two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of midgap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.
Type-II multiferroics offer a promising route to strong magnetoelectric coupling due to the magnetic-order-driven ferroelectricity. Most experimentally realized type-II multiferroics exhibit noncollinear magnetic order, whose complex interaction with external fields can impede the practical control of magnetoelectric effects. In contrast, type-II multiferroics with collinear magnetic order remain underexplored, with prior work largely limited to conventional antiferromagnets. In this work, using Landau theory and symmetry analysis, we investigate spin-order-induced ferroelectricity in collinear ferrimagnetic systems and derive the criteria in the minimal-case scenario. According to these criteria, we perform a rapid and efficient search and ultimately identify three promising ferrimagnetic multiferroic candidates from the Inorganic Crystal Structure Database (ICSD). Among them, the largest net magnetic moment per unit cell (u.c.) reaches 3.0 & micro;(B), and the maximum polarization reaches 0.08 & micro;C/cm(2), comparable to the typical multiferroics material TbMnO3. In addition, for the altermagnetic system, we searched for known magnetic structures in the MAGNDATA database and identified MnSe2 as a promising candidate material, exhibiting a polarization as high as 0.07 & micro;C/cm(2). Notably, our results show that ferroelectric polarization behavior provides a clear criterion for distinguishing the two experimentally reported magnetic structures of MnSe2.
Topological phase transitions in photonic systems are traditionally realized by geometrically modifying the unit cell. Here, we introduce a cavity-based mechanism that enables dynamic control of topological phases without structural alterations. Specifically, we study the topological phase of electric dipolar arrays placed between two parallel metal plates. Using the image-charge method, we demonstrate that the coupling strength between dipoles is strongly influenced not only by their distances to the two plates but also by the orientation of the dipoles themselves. Exploiting this feature, we construct an equally spaced Su-Schrieffer-Heeger (SSH) chain composed of dipoles with tailored orientations. We show that when the chain is closer (farther) to the top plate than to the bottom plate, the system exhibits a topologically trivial (nontrivial) phase. Hence, the topological phase of the array can be controlled simply by tuning the relative position of the chain between the two plates. We further generalize this approach to two-dimensional dipolar arrays, demonstrating its applicability to a Kagome lattice. This cavity-enabled strategy offers a practical route for achieving topological phase transitions in photonic systems without the need for lattice geometry modification, paving the way for more versatile implementations of topological photonics.
We propose an interlayer-engineering scheme to realize a two-dimensional hybrid-order topological insulator, characterized by the coexistence of first-order and second-order topological phases, in a coupled trilayer Chern system. Starting from three quantum anomalous Hall layers with Chern numbers C1/2/3 = +1/ - 1/ + 1 in the decoupled limit, interlayer tunneling hybridizes their edge states into a single chiral edge mode, while simultaneously opening a gap that supports corner states. Consequently, the system exhibits the coexistence of one-dimensional chiral edge states and zero-dimensional corner states within the same bulk gap, a hallmark of the hybrid-order topology. Furthermore, we map out the topological phase diagram, and show that the hybrid-order phase is robust against mass-type disorder. Our results identify interlayer hybridization as a minimal and broadly applicable strategy for engineering coexisting edge and corner states within a topological platform.
CoxTaS2 (x approximate to 1/3) exhibits a spontaneous Hall effect from spin texture in antiferromagnets, with a tetrahedral triple-Q(3Q) order and uniform spin scalar chirality. Upon Co overdoping (x> 1/3), it undergoes a shift in magnetic ordering vectors from Q(m) = (1/2, 0, 0) to (1/3, 0, 0). Interestingly, the spontaneous Hall effect disappeared in the overdoped regime, which was originally attributed to the loss of 3Q order. However, a question remains whether a new type of 3Q order can exist with alternating chirality in the overdoped regime. To address this, we investigated Co0.336TaS2 using inelastic neutron scattering (INS), neutron diffraction, and optical dichroism, and found that INS data and spin-wave simulations support a 3Q order with alternating chirality. Moreover, neutron diffraction data show field-independent Bragg peaks, while linear dichroism detects no in-plane anisotropy, consistent with threefold rotation symmetry. Our data support the scenario of an alternating-chirality 3Q order in Co0.336TaS2, canceling the spontaneous Hall effect. This study highlights a combined neutron-optical approach to identify complex spin textures.
Manifolds with nontrivial topology play an essential role in the study of topological phases of matter. In this paper, we study the nontrivial symmetry response of the (2+1)-dimensional Z2 symmetry-protected topological (SPT) phase when the system is put on a nonorientable manifold: the Klein bottle. In particular, we find that when a symmetry defect is inserted along the orientation-reversing cycle of the Klein bottle, the ground state of the system gets an extra charge. This response remains well defined at transition points into the trivial SPT phase, resulting in an exact twofold degeneracy in the ground state independent of the system size. We demonstrate the symmetry response using exactly solvable lattice models of the SPT phase, as well as numerical work across the transition. We explore the connection of this result to the modular transformation of the (3+1)-dimensional Z2 gauge theory and the emergent nature of the parity symmetry in the Z2 SPT phase.
A systematic structural investigation of Fe2Mo3O8 as a function of pressure, temperature, and magnetic field reveals that the P63mc space group remains robust over a wide range of conditions. No changes in the long-range crystal structure are observed for pressures up to 10 GPa, temperatures between 11 K and 300 K, and magnetic fields up to 9 T. The magnetostructural response, quantified by Ac/c, is determined for magnetic fields applied transverse to the crystallographic c axis, demonstrating strong magnetoelastic coupling. The well-known magnetic-field-induced transition is confirmed to be first order and isostructural, occurring between two distinct altermagnetic states. Importantly, this transition can also be accessed using magnetic fields applied within the ab plane. When expressed in terms of the c/a ratio, the structural evolution under pressure (0-10 GPa) maps continuously onto that observed across the full Zn substitution range in (Fe1-yZny)2Mo3O8 (0 y 1), indicating a common underlying structural control parameter. These results demonstrate that the c-axis lattice parameter is the primary structural degree of freedom governing magnetic behavior under external tuning parameters. More broadly, they indicate that magnetic order in this family of complex oxides (A2Mo3O8, A = Co, Mn, Ni) can be systematically tuned via pressure. This tunability highlights these materials as promising platforms for controllable magnetic switching, particularly in thin films integrated with piezoelectric substrates.
