In a recent work [Sharma and Bhosale, Phys. Rev. B 109, 014412 (2024)], an $N$-spin Floquet model with infinite-range Ising interaction was introduced. In this paper, we generalize the strength of interaction to $J$, such that the $J=1$ case reduces to the aforementioned work. We show that for $J=1/2$ the model still exhibits integrability only for an even number of qubits. We analytically solve the cases of 6, 8, 10, and 12 qubits, finding the eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities exhibit the signature of quantum integrability (QI). For the general case of even $N>12$ qubits, we conjuncture the presence of QI using numerical evidence such as spectrum degeneracy and the exact periodic nature of both the entanglement dynamics and the time-evolved unitary operator. We numerically show the absence of QI for odd $N$ by observing a violation of the signatures of QI. We analytically and numerically find that the maximum value of time-evolved concurrence $\left(C_{\max }\right)$ decreases with $N$, indicating the multipartite nature of entanglement. Possible experiments to verify our results are discussed.

In this work, we report that electrically controlled ferroic properties and multistate storage can be achieved in dual-metal trihalide ${\mathrm{WRuCl}}_6$ monolayer from the perspectives of first-principles calculations. We confirm that it is a rare two-dimensional (2D) triferroics, and, particularly, ferromagnetism and ferroelasticity are coupled strongly to the ferroelectricity of 120 ° rotation symmetry. It therefore can enable the flexible and reversible switching of ferroic orders via electric field. In addition, ${\mathrm{WRuCl}}_6$ monolayer is an intrinsic bipolar magnetic semiconductor; thus, the switchable spin-polarized carrier can be obtained by applying an electric gate voltage. Therefore, it provides an extra parameter to further improve the storage density. Our work not only offers a paradigm for the multiferroic coupling physics, but also provides a promising platform for multistate storage and multifunctional nanodevices.

Transition metal dichalcogenides exhibit intrinsic spin-orbit coupling that opens spin splittings in valleys, resulting in spin and orbital polarized bands. Energy valleys driven by electric fields can generate spin (anomalous) Hall effect and orbital Hall effect. Here we focus on ferromagnetic materials and demonstrate that the transport of spin and orbital Hall effects can be attributed to the spin-orbit coupling, which can be characterized by spin-orbital polarization. Driven by an electric field, orbital and spin angular momentum appear at both ends of the sample through corresponding Hall effect, leading to the formation of valley-contrasting spin-orbital polarization states. Based on the spin and orbital transport analysis, we propose the intrinsic magnetic moment as a method to manipulate the spin-orbital polarization states, which enables the four-state switching of the angular momentum at the edge of sample. Moreover, due to the conservation of angular momentum, circularly polarized optical pumping can be used instead of an electric field to selectively excite the orbital and spin angular momentum. Subsequently, we argue that the sign-reversal spin-orbital polarization requires not only spin-orbit coupling effect but also the simultaneous broken time-reversal and inversion symmetries.

We study the Yu-Shiba-Rusinov (YSR) states in materials with bulk band inversion such as iron-based topological superconductors or doped topological insulators. We show that the structure of the YSR state spectrum depends on the doping level relative to the chemical potential at which the band inversion occurs. Moreover, we demonstrate that the transition from ferromagnetic to antiferromagnetic coupling and vice versa, which is caused by the coupling of magnetic impurities through the overlap of YSR states, is highly dependent on the doping level. Additionally, topological edge states may have a substantial impact on the YSR states, leading to a decrease in YSR state energies and the creation of new states when the magnetic impurity approaches the boundary.

We study local density of state (LDOS) oscillations arising from the scattering of electrons at atomic edge defects in topological insulator (TI) surfaces. To create edge scattering on the surface of a TI, we assume that half of its surface is covered with a semiconductor. In addition to modifying the TI states in the covered half, the presence of the semiconductor leads to a localized edge potential at the vacuum-semiconductor boundary. We study the induced LDOS by imposing time-reversal (TR) invariance and current conservation across the boundary. Additionally, we explore how the scattering of TI junctions with dissimilar spin textures and anisotropic Fermi velocities affect the modulations of the LDOS away from the junction edge. In all cases, for energies close to the Dirac point, we find that the decay envelope of the LDOS oscillations is insensitive to the scattering at the atomic edge defect, with a decay power given by $x^{-3/2}$. Quantitative differences in the amplitude of these oscillations depend on the details of the interface and the spin textures, while the period of the oscillations is defined by the size of the Fermi surface.

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, we comprehensively study this system using ab initio and random-phase approximation techniques. Our analysis unveils similarities between this novel ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the $e_g$ orbitals. Pressure primarily increases the bandwidths of the Ni $e_g$ bands, suggesting an enhancement of the itinerant properties of those $e_g$ states. By changing the cell volume ratio $V/V_0$ from 0.9 to 1.10, we found that the bilayer structure in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ always has lower energy than the single-layer trilayer stacking ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per $e_g$ orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading $d_{x^2-y^2}$-wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature $T_c$ in this structure should be much lower than in the bilayer structure.

We study theoretically a setup consisting of excitons formed in two valleys, with proximity-induced Cooper pairing, different in the conduction and valence bands. Due to the combination of a Coulomb interaction with superconducting proximity effects, Cooper pairing between electrons from conduction and valence bands from different valleys is formed. This finite-energy intervalley Cooper pairing has both even- and odd-frequency contributions. We show that there is a phase transition into the formation of a robust macroscopic condensate of such Cooper pairs and present characteristics of the corresponding Higgs modes.

A composite fermion (CF) is a topological quasiparticle that emerges from a nonperturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to noninteracting fermions that form Landau levels in a magnetic field, CFs can fill analogous “Lambda” levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes the low-energy properties of CFs, we show that high-energy features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the noninteracting CF paradigm.

We report on our hard x-ray photoemission study of ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$, wherein the breathing Kagome lattice of Nb provides interesting magnetic properties with spin 1/2 per Nb trimer. The $\mathrm{Nb}3d_{5/2}$ and $3d_{3/2}$ core level peaks are accompanied by satellite peaks, suggesting the importance of $\mathrm{Nb}4d$ charge degrees of freedom. The $\mathrm{Cl}1s$ and $2p$ core level spectra have high binding energy peaks which can be assigned to the Cl site with $\mathrm{Cl}3p$ ligand holes near the center of the Nb trimer. The core level spectra indicate that the Nb-Nb and Nb-Cl charge fluctuations play crucial roles in the magnetic interaction between the trimers.

In this paper, we study the critical behaviors in the non-Hermitian disorder Aubry-André (DAA) model, and we assume the non-Hermiticity is introduced by nonreciprocal hopping. We employ the localization length $\xi$, the inverse participation ratio ($\mathrm{IPR}$), and the energy gap $\mathrm{\Delta }E$ as the characteristic quantities to describe the critical properties of the localization transition. By performing scaling analysis, the critical exponents of the non-Hermitian Anderson model and the non-Hermitian DAA model are obtained, and these critical exponents are different from their Hermitian counterparts, indicating that the Hermitian and non-Hermitian Anderson and DAA models belong to different universality classes. The critical exponents of the non-Hermitian DAA model are remarkably different from both the pure non-Hermitian AA model and the non-Hermitian Anderson model, showing that disorder is an independent relevant direction at the non-Hermitian AA model critical point. We further propose a hybrid scaling law to describe the critical behavior in the overlapping critical region constituted by the critical regions of the non-Hermitian DAA model and the non-Hermitian Anderson localization.

Potential wells are employed to constrain quantum particles into forming discrete energy levels, acting as artificial few-level systems. In contrast, an anti-parity-time-symmetric system can have a single pair of real energy levels, while all the remaining levels are unstable due to the negative imaginary part of the energy. In this work, we investigate the formation of bound states in a tight-binding chain induced by a harmonic imaginary potential. Exact solutions show that the real parts of energy levels are equidistant, while the imaginary parts are semi-negative definite and equidistant. This allows for the formation of an effective two-level system. For a given initial state with a wide range of profiles, the evolved state always converges to a superposition of two stable eigenstates. In addition, these two states are orthogonal under the Dirac inner product and can be mutually switched by applying a $\pi$ pulse of a linear field. Our finding provides an alternative method for fabricating quantum devices through dissipation.

We investigate the magnetic-field dependence of the magnitude of zero-bias conductance peaks (ZBCPs) on some nanoscale bismuth islands grown on the ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ substrate. The ZBCPs exist only on some of the islands with a diameter of 4–8 nm, and are likely to be the Majorana zero modes. Remarkably, the evolution of ZBCPs on these islands exhibits anomalous behavior under varying magnetic fields. The intensity of ZBCPs is first enhanced at weak fields and then suppressed as the fields further increase. We attribute the nonmonotonic evolution of the ZBCPs to the magnetic-field-enhanced topological edge states on these Bi islands. Our findings provide valuable insights into the probable origin of the Majorana zero modes in the Bi-island platform and the magnetic-field response of topological edge states.

Realization of kagome lattice, and hence achieving specific performance, is a challenging issue in condensed matter physics. The corner-sharing triangles of kagome lattice are normally comprised of real atoms occupying certain Wyckoff sites. Here, we propose that the excess electrons in layered electrides ${\mathrm{Mg}}_3\mathrm{N}$ and ${\mathrm{Mg}}_3\mathrm{O}$ build the two-dimensional kagome lattices. The interstitial electrons further contribute to the nontrivial band topology, i.e., the Dirac points and the Dirac nodal lines in ${\mathrm{Mg}}_3\mathrm{N}$ and ${\mathrm{Mg}}_3\mathrm{O}$. Further, the in-plane coupling between the electronic orbitals and the atomic vibrational modes dominate the electron-phonon coupling, and yield superconducting critical temperatures approaching 2.0 and 2.2 K for ${\mathrm{Mg}}_3\mathrm{N}$ and ${\mathrm{Mg}}_3\mathrm{O}$, respectively. This work proposes a feasible scheme to construct kagome lattices by interstitial quasiatoms and provides a promising platform to explore the superconductivity and nontrivial band topology in kagome electrides.

In chaotic quantum systems, the entanglement of a region $A$ can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of $A$. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information “flows” across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various spacetime translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady-state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits and is also present in some special nonstabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature.

Co/Pt multilayers with perpendicular magnetic anisotropy were locally irradiated with a focused beam of $\mathrm{H}{\mathrm{e}}^{+}$ ions to change the magnetic properties of the sample in strictly defined regions. Irradiated regions of 100–400-nm diameter served as pinning centers for chiral magnetic textures, resulting in the formation of magnetic skyrmions of the same diameter. The magnetization topology of such skyrmions was studied by Lorentz transmission electron microscopy. It was found that the helicity of skyrmions depended on its diameter and the ion irradiation fluence. Both Bloch-type skyrmions and Néel-type skyrmions, as well as skyrmions of the intermediate type, were observed. We assume that this behavior is due to a change in the balance of the magnetostatic energy and the Dzyaloshinskii-Moriya energy, which is confirmed by micromagnetic simulations.

We report the magnetic properties of newly synthesized, single crystals of ${\mathrm{TbTi}}_3{\mathrm{Bi}}_4$ whose crystal structure is highlighted by the stacking of terbium-based zigzag chains and titanium-based kagome lattices. This compound demonstrates extreme easy-axis magnetic anisotropy due to the crystalline-electric-field effect which aligns the ${\mathrm{Tb}}^{3+}$ moments along the zigzag chain direction. As the result of the strong single-ion anisotropy and multiple magnetic interactions, ${\mathrm{TbTi}}_3{\mathrm{Bi}}_4$ behaves as a quasi-one-dimensional Ising magnet with a remarkable antiferromagnetic ordering at $T_{\mathrm{N}}=20.4\mathrm{K}$. When a magnetic field is applied along the direction of the zigzag chain, multiple metamagnetic transitions occur between 1/3 and other magnetization plateaus. We have created a field-temperature phase diagram and mapped out the complex magnetic structures resulting from frustration.