We review the condensation completion of a modular tensor category $\mathcal{C}$, which yields a fusion 2-category $\mathrm{\Sigma }\mathcal{C}$ of separable algebras, bimodules over algebras, and bimodule maps in $\mathcal{C}$. Physically, $\mathrm{\Sigma }\mathcal{C}$ is the fusion 2-category of codimension-1 defects, codimension-2 defects and instantons in the $2+1\mathrm{D}$ topological order $\mathcal{C}$. We realize the rough-rough wall and $e\text{−}m$ exchange wall in the toric code model on the lattice by deforming the Hamiltonian based on the corresponding algebraic data. We apply condensation completion to the toric code, $3\mathbf{F}$, two-layer semion and ${\mathbb{Z}}_4$ topological orders, and explicitly enumerate their $1\mathrm{d}$ and $0\mathrm{d}$ defects along with fusion rules. We also mention other applications of condensation completion: alternative interpretations of condensation completion of a braided fusion category; condensation completion of the category of symmetry charges and its correspondence to gapped phases with symmetry; for a topological order $\mathcal{C}$, one can find all gapped boundaries of the stacking of $\mathcal{C}$ with its time-reversal conjugate through computing the condensation completion of $\mathcal{C}$.

Near-infrared pump and extreme ultraviolet probe transient absorption spectroscopy is employed to unravel the phonon-mode-specific modifications of electronic states near the Fermi energy in molybdenum dioxide. We observe distinct fingerprints of two coherent phonon modes at a frequency of 6 and $11\text{THz}$ which differ vastly in their energy-dependent modulations of the electronic response. By combining our measurements with density functional theory calculations, we show that the measured energy-dependent contrast between the phonon modes is primarily governed by the modification of the projected density of states. These findings highlight the pivotal role of lattice dynamics in the ultrafast electronic response.

We consider the possibility of phonon-mediated unconventional superconductivity in a recently discovered new class of antiferromagnets, dubbed altermagnets. Within a weak-coupling approach, and using a minimal Lieb lattice model for altermagnets, we find a dominant superconducting instability odd in momentum and even in spin with spin-polarized Cooper pairs. We discuss the origin of this unusual result in terms of the spin structure of the altermagnetic Fermi surface, in combination with the momentum-space structure of the effective phonon-mediated electron-electron interactions on the Fermi surface.

Anisotropy-based two-dimensional heterostructures display distinct polarization traits, offering potential for detection and advanced applications. However, common studies often oversimplify anisotropy's properties to the use of anisotropic materials, leaving the true transmission of anisotropy in heterostructures as an unresolved question. Here, we demonstrate that the anisotropy is indeed transferred in the $\mathrm{Re}{\mathrm{S}}_2/\mathrm{WS}{\mathrm{e}}_2$ heterostructure via Raman scattering. The intrinsic anisotropy of the $\mathrm{WS}{\mathrm{e}}_2$ in the as-fabricated heterostructure is clearly enhanced by the overlying $\mathrm{Re}{\mathrm{S}}_2$ layer, while the anisotropy of monolayer $\mathrm{Re}{\mathrm{S}}_2$ is partially erased. The changes in the $E_{\mathrm{g}}$-like modes I and II in the $\mathrm{Re}{\mathrm{S}}_2$ indicate that lattice engineering leads to the formation of regional distortions, potentially causing the weakening of anisotropy in polarized Raman spectroscopy. Furthermore, this anisotropy transferability can be applied to other semiconductor and layered materials. These findings provide insights into interlayer coupling and anisotropy modulation in van der Waals heterostructures, paving the way for future studies on symmetry engineering, anisotropic charge transport, and the design of functional materials with tailored directional properties.

We formulate a scattering theory of the proximity effect in a weakly disordered superconductor–insulating barrier–normal metal–insulating barrier–normal metal (SININ) junction. This allows one to relate the conductance and density of states of the junction to the scattering times $\tau$ (eigenvalues of the Wigner-Smith time-delay matrix). The probability density $P\left(\tau \right)$ has two peaks, at a short time ${\tau }_{\min }$ and a late time ${\tau }_{\max }$. The density of states at the Fermi level is the geometric mean of the two times. The splitting of the zero-bias conductance peak is given by $\hslash /{\tau }_{\max }$.

The one-dimensional Su-Schrieffer-Heeger (SSH) chain is one of the simplest topological models in which nontrivial topological edge states emerge. Recently, semiconductor quantum dots have been proposed as a promising platform for simulating the one-dimensional SSH chain. Consequently, detecting the nontrivial topological edge states of the SSH-type QD chain has become one of the most important topics in condensed matter physics. In this work, the finite-frequency shot noise of electron transport through the SSH-type QD chain is investigated. It is shown that the finite-frequency shot noise in the topological region exhibits a sharp dip, while that in the trivial region exhibits no dip at all. Moreover, the position of the dip of the finite-frequency shot noise is independent of the applied bias voltage, temperature, and strength of the tunnel coupling between the SSH-type QD chain and the two external electrodes. Consequently, the variation of the width of the dip of the finite-frequency shot noise in the weak and relatively strong coupling regimes suggests an alternative way to detect whether the SSH-type QD chain is in the nontrivial topological edge states or not.

We investigate a three-dimensional (3D) topological phase resembling a Weyl semimetal, modulated by a periodic potential and engineered through Floquet dynamics. This system is constructed by stacking two-dimensional Chern insulators and hosts Weyl-like points defined in the parameter space $(k_x,k_y,z)$, distinct from conventional Weyl points in momentum space $(k_x,k_y,k_z)$. The Weyl-semimetal-like phase exhibits characteristics akin to those of Weyl semimetals, including linear dispersion near the Weyl-like points, nontrivial bulk topology, the presence of Fermi arcs connecting the Weyl-like points, and the Berry monopoles. Unlike traditional Weyl semimetals, these features manifest in real space rather than momentum space. Furthermore, we calculate the local density of states, the layer Hall conductance, and the total 3D Hall conductivity, demonstrating that the Weyl-semimetal-like phase remains stable under weak and moderate interlayer couplings. The influence of disorder is also examined: Beyond a critical disorder strength, the Weyl-like points destabilize and the topological phase collapses. Moreover, by computing the Floquet Chern number, we demonstrate that the locations of the Weyl-like points can be tuned via high-frequency laser pumping. Finally, we show that both type-I and II Weyl-like behaviors can arise in a tilted Weyl-like model.

We investigate the possibility of obtaining an infinite-layered superconducting nickel oxide using a topotactic reduction of $R_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_4$ nickelate compounds. We consider the case of reducing ${\mathrm{La}}_{0.8}{\mathrm{Sr}}_{1.2}{\mathrm{NiO}}_4$, which is metallic and with an effective ${\mathrm{Ni}}^{3.2+}$ valence into ${\mathrm{La}}_{0.8}{\mathrm{Sr}}_{1.2}{\mathrm{NiO}}_3$ with an effective ${\mathrm{Ni}}^{1.2+}$ valence similar to the original superconducting nickelate. Here we show that the reduction process is more likely to produce a ${\mathrm{NiO}}_2$ square striped structure instead of a layered structure, yielding an insulating state associated to a charge-ordered pattern of ${\mathrm{Ni}}^{+}$ and ${\mathrm{Ni}}^{2+}$ cations and antiferromagnetism. Although the appropriate valence for Ni cations is reached, it appears that both the crystal structure and the dimensionality of the system are critical for reaching superconductivity in these nickelates.

Barium hydrides are of interest for their potential in both ionic conductivity and superconductivity. Recently, a superconducting hydride ${\mathrm{BaH}}_{12}$ containing ${\mathrm{H}}_2$ and $\mathrm{H}{{}_3}^{-1}$ molecular units was experimentally reported with a critical temperature $T_c$ of 20 K at 140 GPa [W. Chen et al., Nat. Commun. 12, 273 (2021)]. Herein, we combine ab initio methods with a rapid calculator of $T_c$ based on the networking value model to predict that the introduction of light elements, such as Be, can effectively expand the structure diversity and structure space of barium hydrides. Although molecular hydrogen units are still widely present in thermodynamically stable and metastable crystal structures, we find that a metastable phase of ${\mathrm{BeBaH}}_8$ shows a high $T_c$ of 49 K at 100 GPa, which is only 38 meV/atom above the thermodynamic stability energy. This ${\mathrm{BeBaH}}_8$ remains dynamically stable at 15 GPa. Furthermore, our study shows that increasing pressure can further elevate $T_c$ beyond 100 K by enhancing the electron-phonon coupling constant. Our study proposes a feasible method for broadening the structural landscape in the exploration of superconducting phases of barium hydrides.

Prior theoretical studies found a large temperature window around 100 K for hydrodynamic phonon transport to occur in monolayer graphene and other layered materials due to dominant momentum-conserving normal scattering processes. However, these studies have yet to account for high-order phonon scattering processes, especially four-phonon scattering that may play an important role and limit the thermal conductivity of graphene at temperatures above 300 K based on some recent predictions. Here, the predicted four-phonon scattering rates are incorporated into a deviational Monte Carlo solution of the Peierls-Boltzmann equation of phonons in monolayer graphene. The results reveal the apparent weakening of hydrodynamic features, including phonon Poiseuille flow and second sound behaviors, even at 100 K temperature. This effect is connected to the predicted increase of momentum-destroying Umklapp scattering in the calculated four-phonon processes. These findings point to the need for further studies of the effects of high-order phonon scattering, including second-order perturbation theory of three-phonon processes, of various materials in non-Fourier lattice thermal transport phenomena.

While first-principles density functional theory modeling has become a vital tool to investigate defect properties in semiconductors, the lack of crystalline periodicity in pseudobinary random composition alloys, such as ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x\mathrm{As}$, complicates such analyses. We present a simulation strategy to systematically take into account the variability in the local defect environment in order to predict statistical properties of neutral intrinsic defects in ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x\mathrm{As}$. We use a comprehensive sampling from a modest-sized 64-atom special quasirandom structure (SQS) to define a statistically representative set of defects, and use a 512-atom hypercell, a $2\times 2\times 2$ supercell of SQS supercells, to achieve cell-size convergence. We articulate an equivalent site principle and describe how it constrains atomic chemical reference energies in computation of defect formation energies in pseudobinary alloys. A simple protocol for estimating reference energies for the Ga and In atoms sharing the III site succeeds in obtaining the equivalence of defects at Ga-sites and In sites in the SQS supercell, (<30 meV differences in average formation energies). For III-site defects, such as the As antisite ${\mathrm{As}}_{\text{III}}$, the statistical variability in formation energies is modest, $\approx 0.1–0.2\mathrm{eV}$. The variability in formation energy at As-site defects, such as the As vacancy $v_{\text{As}}$, can be much larger, >1 eV. The As antisite is shown to be a low-energy defect and the most likely to be present in as-grown materials, just as in GaAs. All other defects are higher-energy defects unlikely to be important in native material, but potentially important in radiation-damaged material. With a strong variability in defect energies, especially on the As-site, explicit consideration of statistical variability due to compositional randomness will be imperative for meaningful and quantitative comparisons to experiment.

Thermal transport in low-dimensional materials is of great fundamental and applied interest due to their unusual and widely tunable properties, as demonstrated by numerous studies of two- and one-dimensional (1D) crystals. In grim contrast, low-dimensional amorphous materials remain largely unexplored, despite their potentially unique characteristics and applications. Here, we theoretically explore thermal transport in quasi-1D single-walled amorphous carbon nanotubes (a-CNTs) by combining homogeneous nonequilibrium molecular dynamics and lattice dynamics, based on a custom-trained high-accuracy machine-learned potential. For both zigzag and armchair a-CNTs of different diameters, the quantum-corrected thermal conductivity (κ) consistently drops by about an order of magnitude as the degree of disorder increases from 0.01 to 0.08, which is quantified by the concentration of Stone-Wales defects. Spectral analysis reveals the predominant role of the low-frequency (<3 THz) vibrational modes, the mean free paths (MFPs) of which are long but finite, thus leading to converged κ as the tube length reaches several micrometers. Further, lattice dynamics calculations yield much larger MFPs for the longitudinal acoustic modes compared to the transverse acoustic modes, which is primarily attributed to the distinctly higher group velocity of the former. Moreover, the κ suppression appears to be dictated by the structural disorder while anharmonicity barely contributes. Our work expands the understanding of thermal transport in low-dimensional amorphous materials and may help promote their eventual application.

Next generation magnetic memories rely on novel magnetic phases for information storage. Novel spin textures such as skyrmions provide one possible avenue forward due to their topological protection and controllability via electric fields. However, the common signature of these spin textures, the topological Hall effect (THE), can be mimicked by other trivial effects. Competing anomalous Hall effect (AHE) components can produce a peak in the Hall voltage similar to that of the THE, making clear identification of the THE difficult. By applying the first-order reversal curve (FORC) technique to the Hall effect in candidate topological Hall systems, we can clearly distinguish between the THE and AHE. This technique allows for quantitative investigation of the THE and AHE in magnetic materials and heterostructures with topologically nontrivial spin textures. We demonstrate the technique and apply it to several examples.

Magnon spin-orbit coupling (MSOC) has been studied intensively, leading to the findings of a variety of exotic phenomena such as magnon Hall effect and magnon spin Nernst effect. Here we report a new magnon state induced by the MSOC caused by the dipolar interaction, namely, the twisted magnetostatic surface magnons in antiferromagnetic (AFM) and ferromagnetic (FM) cylindrical tubes. We find that magnons lacking orbital angular momentum (OAM) exclusively manifest as bulk modes, while introducing OAM leads to emergence of additional surface magnon modes. In the AFM tube, two twisted surface magnon modes appear—one is localized on the outer surface and another is confined to the inner surface. Both modes show spin-OAM locking propagating characteristics. In the FM tube, only one twisted surface magnon emerges, located on the outer or inner surface depending on the direction of OAM. These characteristics are explained based on the MSOC effect. Micromagnetic simulations verify the theoretical predictions. The polarization-selective propagation of twisted surface magnons, governed by spin-OAM locking, may provide a basis for designing novel magnonic devices.

We have gained a microscopic insight into the phenomenon of double magnetization reversal observed in the $\mathrm{NdFe}{\mathrm{O}}_3$ perovskite compound at compensation temperatures of 6.3 K ($T_{\mathrm{comp}1}$) and 4.3 K ($T_{\mathrm{comp}2}$) through analysis of the evolutions of magnetic moments, magnetic anisotropies, and exchange interactions of Nd and Fe sublattices. This understanding stems from studies involving dc magnetization, neutron depolarization, neutron diffraction, and inelastic neutron scattering (INS) on powder and single-crystal samples. Below 8.6 K, additional (magnetic) Bragg peaks are detected in neutron diffraction patterns, corresponding to the $C_x{F}_z$-type Nd sublattice ordering, which entails C-type antiferromagnetic (AFM) ordering along the $a$ axis and a ferromagnetic (FM) component along the $c$ axis. The FM components ($F_z$) of the $\mathrm{N}{\mathrm{d}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{3+}$ moments are too diminutive to be quantified accurately via powder neutron diffraction; as single-crystal dc magnetization study estimates the FM component (along the $c$ axis) to be approximately 0.09 ${\mu }_{\mathrm{B}}$ at 2 K. Our INS investigations on single-crystal $\mathrm{NdFe}{\mathrm{O}}_3$ sample have unveiled the relative orientations of the $F_z$ components of the Nd and Fe sublattice moments. The INS spectra are found to be consistent with AFM exchange couplings between the Nd-Nd and Nd-Fe sublattices as well as for a planar anisotropy of Nd spins. At 6.3 K, a complete cancellation of the $F_z$ components of the $\mathrm{N}{\mathrm{d}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{3+}$ moments results in $T_{\mathrm{comp}1}$, whereas a reversal in the sign of the total magnetic moment below 5 K leads to $T_{\mathrm{comp}2}$ at 4.3 K. The present comprehensive single-crystal INS investigation thus shed light on the microscopic mechanism for magnetization reversal phenomenon. This microscopic understanding of such a distinctive phenomenon has practical implications for design of magnetic memory and spin-resolving devices.

Nickelates have continued to surprise since their unconventional superconductivity was discovered. Recently, the layered nickelate ${\mathrm{La}}_5{\mathrm{Ni}}_3{\mathrm{O}}_{11}$ with hybrid single-layer and bilayer stacking showed superconductivity under high pressure. This compound combines features of single-layer ${\mathrm{La}}_2{\mathrm{NiO}}_4$ and bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, but its pairing mechanism remains to be understood. Motivated by this finding, here we report a comprehensive theoretical study of this system. Our density functional theory calculations reveal that the undistorted P4/mmm phase without pressure is unstable due to three distortion modes. As pressure increases, these modes are suppressed, leading to the high-symmetry P4/mmm phase without ${\mathrm{NiO}}_6$ octahedron tilting. Moreover, the “charge transfer” between the single-layer and bilayer sublattices was observed, leading to hole doping in the single-layer blocks. Our random-phase approximation calculations indicate a leading $d_{x^2-y^2}$-wave pairing state that arises from spin-fluctuation scattering between Fermi surface states mainly originating from the single-layer blocks and additional weaker contributions from the bilayer blocks. These spin fluctuations could be detected by inelastic neutron scattering as a strong peak at $\mathbf{q}=(\pi ,\pi )$. Our findings distinguish ${\mathrm{La}}_5{\mathrm{Ni}}_3{\mathrm{O}}_{11}$ from other nickelate superconductors discovered so far and the high-$T_c$ cuprates. We also discuss both similarities and differences between ${\mathrm{La}}_5{\mathrm{Ni}}_3{\mathrm{O}}_{11}$ and other hybrid stacking nickelates.

The Higgs mode in superconductors corresponds to oscillations of the amplitude of the order parameter. While its detection typically entails resonant optical excitation, we present a purely transport-based setup wherein it is excited in a voltage biased Josephson junction. Demonstrating the importance of order parameter dynamics, the interplay of Higgs resonance and Josephson physics enhances the second harmonic Josephson current oscillating at twice the usual Josephson frequency in transparent junctions featuring single-band $s$-wave superconductors. If the leads have unequal equilibrium superconducting gaps, this second harmonic component may even eclipse its first harmonic counterpart, thus furnishing a unique hallmark of the Higgs oscillations.