Papers

Enrico Fermi in 1932 used classical Gauss equation to derive the Coulomb density–density interaction from the longitudinal electromagnetic potential. In this work we extend the Fermi procedure to the transverse component of the vector potential. By using a fully quantum canonical transformation, we replace the transverse vector potential with a current–current and current–current–density interactions. The transformed Hamiltonian is, then, projected in the fermionic space providing a matter–only, totally incoherent and gauge respecting Hamiltonian. The removal of coherence will avoid the breakdown of perturbation theory predicted by Haag's theorem, and make possible to introduce, in the transformed space, the diagrammatic approach. After discussing the implications of the transverse interactions on the current theories based on the Fermi procedure, we conclude by showing how the transverse Hamiltonian provides the quantum origin of the electromagnetic longitudinal–transverse splitting of phonons and other elemental excitations.

We show that an emergent geometric symmetry generates non-trivial topology in quantum-dot-based multi-terminal Josephson junctions. It confines same-spin Andreev bound state crossings to an analytic one-dimensional manifold of the synthetic Brillouin zone, where interdot coupling selects Weyl nodes of charge $\pm1$ in the singlet sector and doubly degenerate cones of charge $\pm2$ in the doublet sector, at gate-tunable locations. The mechanism yields a spectroscopic detection protocol and a design principle for fabricating devices with non-trivial topological signatures.

Metabolic networks play pivotal roles in understanding the evolution of organisms, microbiome dynamics and disease prevention and treatment. This study presents a comprehensive analysis of metabolic network properties across 10912 organisms spanning Bacteria, Archaea, and Eukarya domains. A novel method for the network construction is introduced, emphasizing the chemical transformations of metabolites. Unlike conventional approaches that link every substrate to every product in all chemical reactions, this method aligns more closely with metabolic pathways, linking products only to their generating substrates. Emphasis is placed on investigating the community structure within metabolic networks, employing the Surprise quality function that better addresses some limitations of previous approaches. Through comparisons between real and randomized versions of the networks, we identify characteristics that cannot be explained solely by the network degree distribution, thus identifying topological properties and community structures that arise from additional evolutionary pressures. This highlights the need for evolutionary models to incorporate additional mechanisms beyond the replication of the degree distribution.

The quantum Fisher information (QFI) is widely used to characterize quantum phases and transitions, but its diagnostic power sometimes relies on selecting special generators based on prior knowledge of the underlying physics. We ask whether this requirement can be relaxed in nonequilibrium systems by studying the QFI of the long-time asymptotic state of a two-dimensional p+ip superfluid following an instantaneous quench of the coupling strength, using the particle number within a large subextensive subsystem as the generator. In equilibrium, the ground-state QFI is continuous across the topological transition between the weak-pairing BCS and the strong-pairing BEC phases, showing no direct signature of the transition. After the quench, however, the QFI associated with the same generator distinguishes the three dynamical phases and can encode the topology of the pre-quench state. In phase I, with a vanishing order parameter, the QFI Fourier spectrum consists of a single zero-frequency spike determined by the nonequilibrium distribution function. In phase II, with a constant nonzero order parameter, the QFI spectrum contains a zero-frequency spike and two continua separated by a gap set by the minimum asymptotic quasiparticle energy. The continuum edge behavior reveals whether this minimum occurs at zero or finite momentum. In the former case, the spectral weight vanishes at the edge, with the sign just inside the continuum encoding the pre-quench topology for large subsystem. In phase III, with a time-periodic order parameter, the QFI spectrum exhibits discrete peaks at integer multiples of the oscillation frequency, together with continua associated with the Floquet quasienergy spectrum. Our results show that driving the system out of equilibrium can enhance the diagnostic power of the QFI for a standard physical observable, revealing information inaccessible in equilibrium.

Sliding ferroelectricity widely exists in various van der Waals bilayers or multilayers, which is induced by asymmetric stacking of commensurate interface. The greatly reduced switching barriers via interlayer sliding lead to high speed with low energy cost, while they are still much higher compared with superlubric sliding of incommensurate interfaces. The polarizations of such incommensurate interfaces are not switchable, which is the major obstacle of combing superlubricity and sliding ferroelectricity for ultralow barriers. Here we propose a design of such combination based on previous synthesis of lateral heterojunctions of 2D materials, which can be extensively applicable to various systems including PN junctions. In such long-distance superlubric ferroelectricity, the vertical polarization can be continuously controlled by superlubric sliding of incommensurate interfaces between lateral heterojunction bilayers, where the series of multiple stable states are long-sought for artificial synaptic devices. The unconventionality of our findings does not only include unprecedented barriers down to the magnitude of mu-eV, but also unprecedented long ion displacements distinct from the small deviations in classical paradigm of ferroelectricity. Our predicted superlubric sliding electrically driven by low vertical voltage is also hitherto reported, much more efficient compared with previously reported sliding mechanically driven by tips, resolving a major issue for practical applications.

A theory of the Berry-phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential has been developed by Di Xiao et al in Phys. Rev. Lett. 97, 026603 (2006) based on a field-dependent density of states generating an additional contribution to the current density. We present an alternative derivation of the Berry- phase effect in anomalous transport in altermagnets and noncentrosymmertric metals based on quasiclassic matrix kinetic equation. Along with anomalous Hall effect an anomalous heat flow and anomalous thermalelectric currents are derived.

We study quantum dynamics through the lens of entanglement generation and characterize the underlying unitary evolution by the distinct signatures it imprints on the time-dependent entangling power. For a unitary operator, we characterize ergodicity by the equality between its long-time-averaged entangling power and the Haar-averaged linear entropy. We define mixing more stringently as the convergence of the time-dependent entangling power itself to the Haar value at long times. Within this framework, we establish the ergodic hierarchy of dynamical behavior, showing in particular that mixing implies ergodicity, whereas ergodicity does not necessarily imply mixing. As an application, we find that two-qubit unitary gates are neither ergodic nor mixing: their long-time-averaged entangling power can take only four discrete values, none of which coincides with the Haar average. We then investigate many-body dynamics using the kicked Ising chain and find that the long-time-averaged entangling power converges to the Haar value in both integrable and nonintegrable cases, indicating ergodicity. Remarkably, however, the nonintegrable chain exhibits mixing, whereas the integrable chain, despite being ergodic, is demonstrably nonmixing. We also introduce a Lyapunov-like exponent to characterize the rate at which the time-dependent entangling power approaches its saturation value. We find that this exponent increases systematically with the degree of integrability breaking in the many-body system. Our results establish entanglement generation as a useful framework for characterizing dynamical systems and reveal qualitatively different signatures of integrability beyond conventional diagnostics.

It is a long-established rule for classical ferroelectricity that any ferroelectric crystal must adopt one of the 10 specific polar point groups. Here we predict a unique type of ferroelectricity that can be generated in some crystals belonging to nonpolar noncentrosymmetric groups. This principle can be applicable to many systems including silicon dioxides, the most widely used dielectric materials. Most of their crystalline phases do not belong the polar groups, while the nonlinear Si-O-Si configurations lead to multiple identical states. We show first-principles evidence that the crystal symmetry forbidding the formation of polarizations, can be broken by either parallel surfaces in thin-films or applying a uniaxial strain. As a result, the multiple identical states are endowed with polarizations of different directions, and low-barrier ferroelectric switching can be realized via transition between them, which can be room-temperature robust down to the thickness of 1 nm. Our findings may not only enable low-cost and large-scale manufacture of ferroelectrics directly integrated in silicon chips, but also open a new avenue for exploring ferroelectricity in prevalent nonpolar materials.

We study the semidefinite programs (SDPs) of quantum information whose variables are density operators, measurement operators, or unbounded positive semidefinite operators, together with their thermodynamic regularizations by the von Neumann, Fermi-Dirac, and Bose-Einstein entropies, which have been associated with Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, respectively. We find that this correspondence is exact: the Fermi-Dirac and Bose-Einstein regularized SDPs coincide with the constrained free-energy minimization of an ideal Fermi or Bose gas whose Hamiltonian and non-commuting charges are the second quantizations of the SDP data and whose one-body density matrix is the SDP variable, while the Boltzmann framework corresponds to the single-particle case. We show that the three frameworks can be unified under one framework, in which each entropy-regularized dual is, up to a term linear in the chemical potentials, the grand potential of the corresponding system; the duals are unconstrained and concave in the chemical-potential vector, with gradient and Hessian given by thermal expectation values that hybrid quantum-classical algorithms can estimate. We further identify the Fermi-Dirac and Bose-Einstein relative entropies with the Umegaki relative entropy between quasi-free states, which yields their monotonicity under gauge-covariant Gaussian channels. The result places a wide class of SDPs and their solvers within the thermodynamics of ideal quantum gases and points to extensions to interacting gases.

Nanoscale thermoelectric devices convert tiny amounts of heat into power. But what happens if the external conditions and resulting temperature differences are not a priori known? We propose a feedback mechanism that optimizes the performance of a quantum-point-contact-based heat engine (QPC). A quantum-dot detector measures the external conditions and gives autonomous feedback on the QPC's properties. We expect this feedback mechanism to be experimentally relevant for steady-state engines with unknown external conditions and for adapting dynamic charging processes to the potential buildup.

We investigate the interplay between pairing correlations and quantum geometry in the spin-orbit-coupled BCS-BEC crossover. Working in the helicity basis, we derive the exact pair-size tensor for the two-body bound states and show that it separates into intraband and quantum-geometric interband contributions, with the latter determined by the quantum metric. We extend this decomposition to two distinct many-body length scales at zero temperature: the Cooper-pair size, obtained from mean-field BCS theory, and the coherence length, obtained from the Gaussian fluctuation theory. Although these quantities almost coincide in the BCS regime, they describe distinct physical properties away from it, with the pair size characterizing the internal extent of a pair and the coherence length characterizing the long-wavelength response of the order parameter. We evaluate both quantities for three-dimensional Rashba, three-dimensional Weyl, and two-dimensional Rashba spin-orbit coupling models. We find that the pair size decreases monotonically with increasing spin-orbit coupling as the pair localizes, whereas the coherence length develops a pronounced minimum in the crossover regime before growing again in the BEC regime as the composite bosons become weakly interacting. This minimum is tied to the collapse of the noninteracting Fermi surface onto the ring or sphere of helicity-band minima. The quantum-geometric contributions reach up to nearly one third of the pair size and about 40% of the coherence length, tracking these same changes in the underlying helicity Fermi-surface topology.

We show that living microswimmers mechanically reinforce dense emulsions. Castor-oil-in-water emulsions laden with the microalga Chlamydomonas reinhardtii are compared in three states: without algae, with immobilized algae, and with motile algae, over a broad range of oil fractions spanning the jamming transition. Oscillatory rheology reveals that motile algae systematically increase the yield stress, by up to a factor of two, whereas immobilized cells at the same concentration leave it essentially unchanged. The reinforcement thus originates from activity rather than from the mere presence of inclusions. Single-cell tracking shows that the droplet network confines the swimmers in pores that shrink as the oil fraction increases, and confinement is known to amplify the propulsion force of C. reinhardtii. A simple estimate based on this confinement-enhanced force accounts for the measured excess yield stress and indicates an effective, activity-induced depletion-like attraction between the passive droplets. These results identify a feedback loop: the microstructure confines the swimmers, confinement amplifies the forces they exert, and these forces stiffen the microstructure. Active emulsions thus emerge as a model platform for programming the mechanics of disordered soft solids through activity.

Electrically tunable nonlinear optical responses at the nanoscale remain challenging to achieve because conventional nonlinear materials lack the combination of large susceptibility, nanoscale confinement, and in situ reconfigurability. Here we report electric-field-induced second harmonic (EFISH) generation from a nanoscale tunnel junction defined by conductive atomic force microscope lithography at the LaAlO$_3$/SrTiO$_3$ interface. A conducting channel written at the interface is interrupted by a nanoscale insulating gap, across which applied DC bias produces local electric fields exceeding $10^7$ V/m. The SHG signal is spatially localized at the junction, exhibits a quadratic bias dependence described by $I(2\omega) \propto |\chi^{(2)}_\mathrm{0} + \chi^{(3)} E_\mathrm{DC}|^2$ with no hysteresis, a modulation depth exceeding 380% at $|V_\mathrm{DC}| = 1$ V, and shows a two-lobed input-polarization pattern aligned with the junction axis, consistent with EFISH from a centrosymmetric host. Calibration against a BBO reference crystal gives $|\chi^{(3)}| \approx 1\times10^{-19}$ m$^2$/V$^2$ at 6 K. These results establish cAFM-written oxide nanojunctions as a reconfigurable platform for nanoscale nonlinear optics in which the junction geometry sets the symmetry of the response and the large field-induced $\chi^{(2)}$ of SrTiO$_3$ provides the optical nonlinearity. Because the nonlinearity is both generated and read out within the same nanoscale gap, the junction operates simultaneously as a subwavelength source and a near-field detector of optical nonlinearity.

Sulfur-rich spirofluorene-bridged N-heterotriangulene (FTN) polymers featuring covalently linked oligosulfide units and a terthiophene-based analogue were synthesized via nucleophilic aromatic substitution and Stille cross-coupling polymerization. The resulting materials are amorphous, insoluble solids with high thermal stability and sulfur contents up to 25 wt%. Structural and compositional analyses by combustion analysis, ToF-SIMS, FT-IR, XPS, and solid-state NMR confirm the efficient incorporation of short oligosulfide to disulfide linkages and well-defined terthiophene units in the respective polymers. Electrochemical characterization in lithium half-cells reveals a reversible, high-voltage oxidation of the FTN unit at 3.8-4.0 V (vs. Li/Li+), accompanied by low-voltage sulfur- or terthiophene-based redox processes between 1.5-2.5 V (vs. Li/Li+). Sulfur incorporation markedly increases the theoretical and initial discharge capacities (up to 129 mA h g-1), while the sulfide conversion processes exhibit rapid fading and poor reversibility due to sulfide dissolution. In contrast, the terthiophene-linked polymer shows only transient low-voltage activity while maintaining high Coulombic efficiencies (ca. 99.7%) governed by the persistent FTN backbone redox event. Our results highlight how different redox-active linkers influence the electrochemical behavior of FTN-based polymers and provide insights into the design of functional organic cathode materials featuring multi-redox processes.

We describe the doping-driven Mott transition in the Hubbard model within the framework of steady-state density functional theory, or i-DFT. In order to access the many-body spectral function in i-DFT, an approximation to the exchange-correlation (xc) bias at arbitrary density and current is required. By making use of Fermi-liquid theory, we derive conditions on the xc bias of i-DFT in terms of the quasiparticle weight, thus establishing a clear connection between i-DFT and Fermi-liquid theory. The Fermi liquid conditions are then employed to guide the construction of an approximation to the xc bias functional. Numerical results obtained with this functional demonstrate that the doping-driven Mott transition can indeed be captured with i-DFT. More generally, our i-DFT approach to calculate spectral functions establishes an explicit form for the functional relationship between the many-body spectral function and the ground state electronic density.

Raman scattering measurements confirmed the theoretical prediction that the structural phase transition from the achiral tetragonal to the chiral tetragonal phase, which occurs near 400 K, is induced by a doubly degenerate soft phonon at the Z point of the Brillouin zone. In the low-temperature chiral phase, the soft mode activates in Raman spectra, splits into two components with A1 and B1 symmetries and harden with cooling according to Cochran law. Circularly polarized Raman scattering did not reveal the angular momentum of these singly degenerate phonons at the Gamma point, which is consistent with theory. We also calculated the phonon branches in the whole Brillouin zone for both crystalline phases and compared the results with the phonons observable in the Raman spectra. The calculations revealed that some phonons with nonzero k have angular momentum in the chiral phase. A pronounced circular motion of atoms can be observed, for example, in a Dirac-type topological phonon at the M-point of the Brillouin zone with a frequency of 168 cm-1.

Recently, it was shown that additional material constants of strain gradient elasticity (SGE) can be identified for brittle and quasi-brittle materials based on the analysis of experimental data on the crack size effect. In the present paper, we perform precise numerical simulations within SGE and derive regression relations for processing experimental data from standard fracture mechanics tests under pure Mode I loading conditions (CCT, SENT, SENB). We consider the simplified SGE, whose constitutive relations contain a single length scale parameter $\ell$ in addition to the classical elastic constants. We show that, for brittle materials, this parameter can be explicitly identified as $\ell \approx 0.362 (K_{Ic}/\sigma_{ult})^2$. This identification ensures that the fracture loads predicted by classical linear elastic fracture mechanics (LEFM) and by the simplified SGE coincide for relatively long Mode I cracks. However, within the simplified SGE, these fracture loads are evaluated from the nonsingular stress field using the maximum principal stress criterion. For quasi-brittle materials, we derive regression relations that describe the non-classical size effect on strength. This effect is usually treated within nonlinear fracture mechanics but can be naturally captured by SGE. Examples of identification of the length scale parameter $\ell$ based on the established relations and the experimental data for chopped fiber composites and for porous and dense quasi-brittle ceramics are presented.

{Multislice electron ptychography commonly accounts for inelastic scattering by including an absorptive object potential in the reconstruction forward model that attenuates the elastic signal. However, it remains unclear how the reconstruction is quantitatively impacted by thermal scattering. Here, we use the quantum excitation of phonons (QEP) formalism, which explicitly separates elastic and inelastic (thermal diffuse) scattering within a single multislice propagation, to simulate four-dimensional scanning transmission electron microscopy (4D STEM) datasets of PbTiO$_3$ and SrTiO$_3$ and reconstruct their phase and amplitude. We find that reconstructions of the QEP total and elastic-only datasets are nearly indistinguishable across sample thicknesses from 11 to 40 nm and across atomic species, demonstrating that the reconstruction is largely insensitive to incoherent thermal diffuse scattering within the collected angular range. Reconstructions from multislice phase-only simulations further confirm that appreciable amplitude does not arise from multiple elastic scattering, but instead reflects attenuation of the coherent elastic signal due to thermal scattering. Further comparison of the QEP elastic-only reconstruction with absorptive multislice simulations reveals substantial amplitude contrast deviations for heavy Pb columns (up to 17%), arising from the approximations used to evaluate the absorptive potential for the 4D STEM simulation. These results thus indicate that reconstruction phase and amplitude accuracy are not significantly limited by the absorptive potential forward model, even in the presence of thermal diffuse scattering.

Ultrafast photoexcitation offers a controllable route to steer structural dynamics in solids, yet predicting how nonequilibrium electronic excitation drives lattice motion across extended spatial and temporal scales remains a major computational challenge. Here we introduce time-dependent ab-initio propagation with electronic machine learning (TDAP-eML), a framework that explicitly incorporates electronic evolution into scalable simulations of photoexcitation-induced lattice dynamics. By integrating machine-learned electronic structure with atomistic propagation, TDAP-eML describes how photoexcitation reshapes the evolving energy landscapes and forces governing structural motion. Across representative examples including silicon and FeSe, the framework reproduces key photoexcited lattice responses obtained from first-principles time-dependent density functional theory calculations and captures coherent phonon dynamics together with their dependence on excitation conditions. Its computational advantage increases with system size, reaching nearly three orders of magnitude reduction in computational cost for the large systems examined. TDAP-eML thus establishes a scalable framework for coupled electronic and lattice evolution, linking nonequilibrium excitation to photoinduced forces, predictive structural dynamics, and experimentally accessible observables.

We investigate the topological phases, joint density of states (JDOS), optical conductivities, and magneto-optical responses of a two-dimensional $d$-wave altermagnet with spin-orbit coupling and Zeeman splitting. The system hosts gapped Dirac points at the high-symmetry points $\Gamma$, $\textrm{M}$, $\textrm{X}$, and $\textrm{Y}$. We show that the JDOS exhibits kinks at the corresponding Dirac gap frequencies and pronounced peaks at Van Hove singularities, whose positions can be tuned by the altermagnetic order. These features are reflected in the optical conductivities, with complementary signatures in their real and imaginary parts. In particular, the Van Hove signatures in the transverse optical conductivity disappear in the absence of $d$-wave altermagnetism, revealing an altermagnet-induced optical signature of the Van Hove singularity. Finally, the Faraday and Kerr rotations exhibit characteristic features inherited from the optical conductivity. Our results establish optical and magneto-optical spectroscopy as sensitive probes of Dirac gaps and Van Hove singularities in altermagnetic topological systems.

Quantum error-correcting codes with two-dimensional translation invariance are known to be equivalent to copies of the two-dimensional toric code. Such a simple classification is not possible for quantum codes with higher dimensional translation invariance due to the existence of multiple types of toric codes and infinite families of fracton codes. Here, we focus on D-dimensional translation-invariant quantum codes based on length-D chain complexes. This includes multivariate multicycle codes where the number of variables equals the number of cycles. We show that such codes are equivalent to copies of D-dimensional toric codes. This directly generalizes the classification result for two-dimensional translation-invariant codes.

Artificial intelligence (AI) is redefining the landscape of polymer science. Although numerous AI applications have been introduced in this field, the roles of polymer encoding strategies and different applications of AI models in polymer design remain insufficiently understood. Here, we build upon the foundation of polymer databases to critically examine the performance and applicability of current encoding strategies across different use cases. We then focus on two major AI application domains, property prediction and inverse design, to evaluate the strengths, weaknesses and suitable scenarios for various model architectures. Finally, we emphasize the significance of the online platforms for promoting data accessibility and accelerating the migration from experience-based discovery toward AI-driven innovation in polymer science and engineering. Through these discussions, we aim to provide practical guidance for future research and development in AI-assisted polymer design.

Recent transport experiments reported a quantum spin Hall insulator phase in monolayer 1T-TaIrTe$_4$ gated away from charge neutrality. This phase is not predicted by band structure calculations and has been attributed to an electronic instability induced by strong correlations at a putative van Hove singularity. Here, we investigate the electronic structure of exfoliated monolayer 1T-TaIrTe$_4$ using micro-focus laser angle resolved photoemission. We find a strongly anisotropic band structure susceptible to density wave instabilities. Our data further reveal a saddle point singularity in the density of states. However, we find that the saddle point lies at a density for which transport experiments found no anomalies. Moreover, the quasiparticle line widths suggest weak electron correlations only. This points to a secondary role of van Hove singularities and electron correlations in the transport phase diagram of monolayer 1T-TaIrTe$_4$.

Monolayer transition metal dichalcogenides (TMDs) combine a direct bandgap, strongly bound excitons, and pronounced second-order optical nonlinearity, which makes them promising materials for ultrathin optoelectronic and nanophotonic devices. However, their optical performance is often degraded by environmental exposure and substrate-induced charge trapping, motivating the development of scalable encapsulation strategies. Here, we investigate spin-coated cyclic olefin copolymer (COC) as a scalable encapsulant for TMDs. Room-temperature and cryogenic optical spectroscopy reveal enhanced photoluminescence and second-harmonic generation, accompanied by excitonic linewidth narrowing and an increased exciton-to-trion ratio. In addition, COC encapsulation induces an excitonic peak splitting and an overall spectral blueshift. First-principles calculations attribute these spectral modifications to local symmetry breaking at the chalcogen interface and macroscopic compressive strain, respectively. These findings establish spin-coated COC as an effective, scalable encapsulation strategy and a potential platform for post-growth excitonic and band-structure engineering.

Polar liquid crystals - fluid phases in which molecular dipoles organise into ferro- or antiferroelectric states - present a highly constrained molecular design space, where small changes can entirely suppress polar organisation. Here we demonstrate, contrary to expectations, that installation of a methyl group in the 5-position of a 1,3-dioxane ring substantially increases the onset temperature of polar order. Remarkably, this effect proves transferable across several liquid-crystal families, including examples where the methylated derivative exhibits a polar phase whereas its parent compound does not. Across 8 matched pairs, we find that a 5-methyl group can enhance the onset temperature of polar order in 1,3-dioxane materials by up to 120 {\deg}C. These findings establish a simple and general molecular design strategy for enhancing and enabling spontaneous dipolar ordering in liquid crystals.

We investigate the microscopic conditions that allow for the coupling between opposite quantum spin Hall (QSH) edges in hybrid junctions with superconductors. Using a microscopic Bernevig–Hughes–Zhang model and the Bogoliubov–de Gennes formalism, we model a potential barrier along the NS interface and identify the parameter regimes in which the QSH edges are coupled. In normal–superconductor junctions, such coupling manifests as deviations from the quantized zero-bias Andreev conductance $G=4e^2/h$. These deviations are controlled by the induced gap in the barrier, the barrier geometry, the interface transparency, orbital and Fermi-velocity mismatch, and disorder strength as well as the bias voltage leading to a zero-bias peak. We then analyze the impact of this interedge-coupling mechanism in Josephson junctions at equilibrium and show that it hybridizes the edge-resolved Andreev branches, opens gaps at the time-reversal-invariant phase differences $\varphi=0$ and $\varphi=\pi$, and modifies the superconducting quantum interference pattern. In a reflection-symmetric geometry, the relative sizes of the two gap openings provide complementary information about the interedge dynamical phase, which also determines the parity of the suppressed lobes in the magnetic interference pattern. This investigation sheds light on the microscopic details that control the coupling of helical edge states in actual devices and the resulting consequences for superconducting hybrid systems.

Artificial spin ices (ASIs) are decorations of single domain nanomagnets on geometric lattices allowing for study of magnetic interactions on easily varied lattice geometries. We extend the study of ASIs on single rhomb tilings by simulating an ASI with the aperiodic hexagonal $H_{\frac{1}{2}\frac{1}{2}}$ tiling as the base structure, and the periodic dice lattice for additional comparison. Using a point dipole metropolis Monte Carlo approach, we cool our arrays of nanoislands to form a low energy configuration, assessing individual vertex excitations as identified through complementary micromagnetic simulations. Using the energy and charge landscape of final spin states, we propose a potential ground state spin configuration for the aperiodic system.

The Trachenko-Zaccone equation provides a compact nonlinear dynamical framework for describing non-Debye relaxation in disordered condensed matter. Originally developed to rationalize stretched- and compressed-exponential relaxation in liquids and glasses from the dynamics of interacting local relaxation events, the same equation has subsequently appeared in broader contexts, including polymer relaxation and nonlinear models of global population dynamics. This review retraces the conceptual development of the equation, with particular emphasis on its physical origin in Kostya Trachenko's feed-forward interaction mechanism, its mathematical structure, and its possible generalizations. We also include personal recollections of the work with Kostya Trachenko at Queen Mary University of London in August 2019, during which the equation emerged in essentially its present form. After reviewing applications to stress relaxation, glassy materials, polymer relaxation and population dynamics, we discuss future directions including time-dependent feedback parameters, coupled order parameters, heterogeneous and spatially resolved formulations, flux terms, network versions and stochastic extensions. The central theme of the review is that the Trachenko-Zaccone equation should be viewed not only as a model of glassy relaxation, but as a general nonlinear feedback equation with potential applications across complex systems.

Computing the formation free energies of metastable defects at finite temperature remains challenging due to anharmonicity, the multiplicity of basins and the frequent occurrence of migration events. Using the previously introduced constrained Bayesian Adaptive Biasing Force method (BABFc), we establish a practical thermodynamic integration framework for computing restricted anharmonic formation free energies associated with individual metastable defect basins. We demonstrate that BABFc can be exploited as a robust, systematic and numerically efficient tool for addressing a long standing bottleneck in atomistic materials science: the finite temperature thermodynamic characterization of metastable defects in complex, highly anharmonic energy landscapes. The proposed workflow requires only a reference local minimum and a confinement strategy and does not rely on defect specific collective variables. It therefore provides a general route to assign well-defined free energies to individual metastable basins, even when these basins are separated by low barriers and embedded in a dense landscape of competing configurations. In this setting, BABFc enables stable, bias corrected free energy estimates with statistical accuracies at the meV/atom level and a very low failure rate, including for systems containing approximately one thousand atoms. We demonstrate this capability through thousands of independent free energy calculations covering hundreds of four-interstitial and four-vacancy configurations in bcc $\alpha$-Fe over a broad temperature range, using both a traditional empirical potential and a data driven force field.

We theoretically investigate the performance of a compact matterwave vortex gyroscope formed by a two-component Bose-Einstein condensate in a toroidal potential. Unlike conventional atomic gyroscopes that rely on the Sagnac effect, the topological stability of the vortex state yields rotation sensitivity independent of the enclosed area, making the device robust against geometric drifts. Using fully quantum multimode simulations, we quantify two interaction-driven mechanisms that degrade performance: phase diffusion from one-axis-twisting and four-wave mixing from intercomponent scattering. We identify regimes where tuning interaction and trapping parameters produces a trade-off between these effects, and find that reducing the intercomponent scattering length can counterintuitively worsen sensitivity. Finally, we compare the vortex gyroscope to a guided Sagnac interferometer, demonstrating superior scaling, establishing it as a promising candidate for compact precision rotation sensing.