Interfaces between topological insulators and superconductors (SCs) are promising platforms for realizing Majorana zero modes (MZMs) via the superconducting proximity effect. We introduce a bilayer model consisting of the surface states of a three-dimensional topological insulator (3DTI) coupled to an $s$-wave superconductor and systematically study the role of interlayer tunneling strength ($t_{\perp }$) motivated by the recent growth of the $\mathrm{Fe}\left(\mathrm{Te},\mathrm{Se}\right)/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ heterostructure. We find that increasing $t_{\perp }$ shifts the proximity-induced (PrI) gap minimum away from the $\mathrm{\Gamma }$ point, giving rise to momentum-selective interference patterns that manifest as spatial oscillations in the in-gap states. We introduce an antidot with a magnetic vortex in the model and investigate the resulting in-gap states, including MZMs and Caroli–de Gennes–Matricon (CdGM) modes. With increasing hybridization strength, the energy separation between MZMs and CdGM states increases, enhancing the isolation of MZMs. Importantly, in the strong hybridization limit, the leading CdGM separation remains large in spite of the decrease in the PrI gap. Spin- and spatially resolved wavefunction analysis reveals angular momentum asymmetries absent in conventional $s$-wave systems. A direct comparison with a standalone $s$-wave superconductor confirms the emergence of distinct $p$-wave-like features in the bilayer geometry. Our results provide experimentally relevant predictions for tuning the stability of MZMs and their differentiation from the CdGM modes in SC-3DTI heterostructures and offer a theoretical framework for probing unconventional superconductivity in engineered topological systems.

Theoretical and computational studies predict topological charge separation at active-passive interfaces in active nematics, but reliable experimental validation has been lacking. We utilize a synthetic acoustically energized liquid crystal to experimentally investigate the dynamics of topological defects across an active-passive interface. The interference pattern induced by the acoustic wave inside the experimental cell creates a spatial distribution of activity, resulting in the formation of active-passive interfaces with the liquid-crystalline director field aligned parallel to those interfaces. The activity gradient drives the reorientation of positively charged topological defects along its direction, causing them to migrate into the passive zone and form a layer with net topological charge. That layer “discharges” upon cessation of activity through annihilation of positive and negative topological charges, resembling the discharge of a capacitor.

The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full $p\text{−}T$ plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d $\pm J$ random-bond Ising model—corresponding to a surface code under bit-flip noise—and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate $p_c=0.1092212\left(4\right)$ and the associated critical exponents.

Understanding how spin-orbit coupling shapes ultrafast electron dynamics remains a central challenge across atomic, molecular, and condensed-matter systems. Here, we demonstrate that spin-orbit splitting in krypton naturally separates two distinct regimes of attosecond interferometry: a conventional above-threshold process involving interference between continuum pathways and an under-threshold regime in which discrete and continuum intermediate states coexist and interfere. Using spin-orbit and angle-resolved measurements with attosecond precision, supported by ab initio time-dependent simulations, we reveal that the under-threshold channel exhibits dramatic phase and delay variations—up to several hundred attoseconds—highly sensitive to photon energy and emission direction. In contrast, the conventional above-threshold channel shows smooth, featureless behavior. This duality exposes the strong influence of metastable resonances, establishing spin-orbit splitting as a built-in control knob for accessing structured continua. Beyond krypton, our results provide a broadly applicable framework for probing and controlling coupled spin, orbital, and many-body correlation dynamics at the attosecond timescale.

We introduce an active-space embedding framework for core-level spectroscopies that connects localized atomic multiplets to continuum resonances within a plane-wave density functional theory/projector augmented-wave description. The approach is complementary to widely used core-level Bethe-Salpeter implementations based on a two-particle (core-exciton) picture with typically static screening: Here, a correlated multiplet manifold of the absorber (including the core hole and open-shell configurations) is coherently coupled to a plane-wave photoelectron, enabling a unified treatment of localized multiplet structure and continuum lineshapes. Spectra are computed in a general time-domain formulation equivalent to Fermi's golden rule: A transition operator tailored to the specific spectroscopy technique is applied to the correlated ground state to generate an excited wave packet, and the corresponding wave packet autocorrelation function is evaluated without explicit real-time propagation, using Lanczos tridiagonalization or the kernel polynomial method; the spectral intensity follows from its Fourier representation. We validate the method at the Ce $N_{4,5}$ edges, reproducing in quantitative agreement with experiment both high-$Q$ multiplet features and the low-$Q$ giant dipole resonance continuum, including a characteristic low-energy shoulder relevant for robust Ce valence assignments. The implementation is available open source within the quantum espresso xspectra package (xspectruplet mode), together with reproducible inputs and scripts.

We study a fourfold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of $X_9$ type at the Fermi energy. First, we analyze in detail its form, type, and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature $T_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, which has been shown to exhibit this type of singularity.

This paper presents the technical details and commissioning results of a newly upgraded platform for ion-irradiation experiments under multi-GPa static pressure conditions at the GSI Helmholtz Center for Heavy Ion Research (Darmstadt, Germany), now accessible to external users. The GSI SIS18 accelerator provides heavy ions with tens of GeV kinetic energies, capable of penetrating through diamond anvil cells and depositing extremely high energy densities within the pressurized samples. This energy deposition triggers ultrafast, localized structural and phase transformations at the nanoscale. The platform integrates online optical microscopy and Raman spectroscopy, providing real-time monitoring of material modifications during stepwise fluence accumulation. By enabling controlled studies of structural responses and phase transitions under coupled extreme conditions, this setup opens unprecedented opportunities for research across condensed-matter physics, materials science, geoscience, high-pressure chemistry, and planetary science.

Circularly polarized phonons conventionally carry an angular momentum and a magnetic moment arising from circular motions of the atoms. Here, we present three anomalous cases that lead to phonon magnetic moments, which cannot be described in the conventional framework: rotationless axial phonons, which exhibit magnetic responses despite only carrying pseudoangular momentum, divergent gyromagnetic ratios of phonons, in which a magnetic moment is produced despite vanishing angular momentum, and anisotropic gyromagnetic ratios of phonons, which make the phonon angular momentum and magnetic moment noncollinear. Our results shed light on the origin and nature of phonon magnetism and suggest the existence of phononomagnetic hidden order.

We investigate Turing pattern formation in a stochastic reaction-diffusion model defined on $N$ lattice sites, where each lattice site is associated with a reaction vessel of volume $\mathrm{\Omega }$. We focus on a regime where spatial discreteness plays a crucial role, namely, when the characteristic length of patterns is comparable to the lattice spacing. This setting is motivated by mesoscopic and microscopic reaction-diffusion systems, in which continuum descriptions can break down. In this regime, we compare two different limiting procedures and show that they lead to qualitatively different outcomes. If we first take the deterministic limit $\mathrm{\Omega }\to \infty$ and then the long-time limit $t\to \infty$, the stationary solutions of the corresponding spatially discrete deterministic equations become spatially chaotic in the limit $N\to \infty$. In contrast, if we first take the limit $t\to \infty$ and then take an appropriate limit of $\mathrm{\Omega }\to \infty$ and $N\to \infty$, the resulting patterns are spatially periodic.

The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order $\mathcal{O}(1/N)$, where $N$ is the number of projective measurements performed within a fixed evolution time. In this work, we develop higher-order Zeno sequences that achieve faster convergence to Zeno dynamics, yielding an improved error scaling of $\mathcal{O}(1/N^{2k})$, where $k$ describes the order of the Zeno sequence. This is achieved by relating higher-order Zeno sequences to higher-order Trotter formulas that achieve similar convergence behavior. We leverage this relation to develop higher-order Zeno sequences for different manifestations of the quantum Zeno effect, including frequent projective measurements and unitary kicks. We go on to discuss achieving quantum Zeno dynamics through periodic control fields of high frequency. We explicitly develop control fields that yield a second-order type improvement in the Zeno error scaling and present shorter Zeno sequences. Finally, we discuss the connection to randomized and Uhrig dynamical decoupling to develop more efficient implementations in the weak-coupling regime.

Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne measurement. The resulting quantum trajectories, i.e., time evolutions of the quantum state conditioned on the measurement outcome, make the quantum limit cycles apparent. We focus on the paradigmatic model of the quantum van der Pol oscillator and on two-level systems. Our work provides insights into limit cycles in quantum systems, emphasizing their similarity to classical limit cycles subject to noise. Additionally, we connect theoretical measures of quantum synchronization to quantities experimentally accessible via heterodyne detection.

Muonium (Mu), a bound state of a positively charged muon and an electron, can diffuse through crystal lattices and interact with defect centers in insulators and semiconductors. We demonstrate that this Mu’s diffusive property can be used to probe defects in a diamond crystal lattice, specifically, substitutional nitrogen atoms (${\mathrm{N}}_{\text{s}}^0$) and nitrogen-vacancy (NV) centers in type-Ib diamond. Upon interaction with these defects, Mu can exchange its electron’s spin or change its charge state, which results in muon spin relaxation. However, muons in diamond (and semiconductors in general) can be in a few distinctive muonium states, with each state contributing to the muon signal. In addition, these states can undergo site and charge exchange interaction, forming a dynamic network. Hence, to study the Mu interaction with point defects, the muon data have to be deconvoluted to isolate signals from the diffusing species. To achieve this goal, we have modeled the Mu state exchange dynamics and numerically simulated the time evolution of muon spin polarization by the density matrix method. With a global curve fit to a set of longitudinal field scan data, one can extract the Mu transition rates that involve interaction with the defect centers. The diffusing tetrahedral interstitial Mu was found to interact with the paramagnetic ${\mathrm{N}}_{\text{s}}^0$ center via electron spin exchange. In contrast, they are converted to form a diamagnetic center upon interaction with the negatively charged NV center.

Two-color attosecond x-ray pulses are the key to advancing the study of ultrafast dynamics in quantum systems. In this work, we propose a single-pass free-electron laser scheme generating synchronized attosecond two-color x-ray pulses with femtosecond separation and tens-of-gigawatts peak power. By modulating a chirped electron beam with an infrared laser, we create a periodic train of ultrashort current spikes. This scheme utilizes the limited gain bandwidth of the free-electron laser as a filter, allowing only two adjacent current spikes with different resonance wavelengths to lase. This scheme holds promise for delivering sub-300-as two-color x-ray pulses with an intrinsic timing jitter below 100 as. This work provides insights and technical support for generating two-color attosecond x-ray free-electron laser pulses with robust time jitter.

The influence of the quantum state of light on strong-field ionization has emerged as a frontier in attosecond physics. Here, we develop a quantum-optical extension of the quantum-trajectory Monte Carlo framework to study the ionization of hydrogen atoms driven by an orthogonally polarized two-color quantum field, composed of an 800 nm coherent field and a 1600 nm squeezed coherent field. We show that the quantum properties of light significantly influence the subcycle dynamics of photoelectron wave packets. We systematically analyze how the quantum statistics of light influence the photoelectron phase, momentum, yield, and number distribution. Our results reveal a direct correspondence between the quantum fluctuations of the driving field and the electron final state, unveiling an avenue for controlling electron wave packet interference via the quantum properties of light.

Theories of self-organized active fluid surfaces have emerged as an important class of minimal models for the shape dynamics of biological membranes, cells, and tissues. However, due to their inherent geometric nonlinearities and the absence of general minimization principles in active systems, it remains a major challenge to systematically study the emergent shape spaces that such theories give rise to. Here, we introduce a variational approach that allows for a direct computation of stationary surface geometries and flows, which enables the classification of nonequilibrium phase transitions in shape spaces described by active surface theories. To achieve this, we construct a dissipation functional systematically from the entropy production in active surfaces and show how generic symmetries imposed by Onsager relations can be exploited to also account for reactive nondissipative terms in constitutive laws. This functional is supplemented by Lagrange multipliers that relax nonlinear geometric constraints, which leads to a tractable variational problem suitable for implicit dynamic simulations and explicit calculations of nontrivial steady state geometries and flows. We apply this framework to study the dynamics of open fluid membranes and closed active fluid surfaces, and characterize the space of stationary solutions that corresponding surfaces and flows occupy. These analyses rationalize the interplay of first-order shape transitions of internally and externally forced fluid membranes, reveal degenerate regions in stationary shape spaces of mechanochemically active surfaces, and identify a mechanism by which hydrodynamic screening controls the geometry of active surfaces undergoing cell divisionlike shape transformations.