In unconventional superconductors, inversion and/or time-reversal symmetries may be broken, either extrinsically or spontaneously. Here, we consider a simple BCS model with both attractive singlet and attractive triplet pairing channels. We show that when the triplet instability dominates, the model predicts an axionic superconducting state, in which both inversion and time-reversal symmetries are spontaneously broken by the superconductivity without requiring spin-orbit coupling. This leads to characteristic experimental signatures of spontaneous symmetry breaking in superconductors, such as a two-step transition in the specific heat. We critically analyze whether familiar pairing mechanisms such as the electron-phonon interaction and ferromagnetic spin fluctuations could produce such an axionic state.

We demonstrate the emergence of unconventional charged Andreev bound states in a superconductor with a sublattice degree of freedom, where the sign of charge density of the Andreev bound states oscillates between the two sublattices. The oscillating-charged Andreev bound states lead to distinct differences in the spectral features of the electron part of the spectral function, the local density of states, and the tunneling conductance spectrum at energies below the superconducting gap. We also discuss the possible occurrence of such Andreev bound states in ${\mathrm{UTe}}_2$ and locally noncentrosymmetric superconductors.

The realization and manipulation of Majorana zero modes is a key step in achieving topological quantum computation. In this paper, we demonstrate the existence of Majorana corner states in a superconductor-insulators-superconductor vertical Josephson junction. The position of these Majorana corner states can be precisely and easily controlled by the superconducting phase bias, which can be confirmed through both numerical and edge state theoretical analysis. In addition, we propose a protocol for achieving topological braiding of the Majorana corner states in a system of three circular vertical Josephson junctions. Our findings advance the field of topological quantum computation by providing insights into the efficient and precise manipulation of Majorana corner states.

In recent years, there has been growing interest in harnessing noncollinear antiferromagnets (NCAFMs) for applications in antiferromagnetic spintronics. A key requirement for their practical use is the ability to control the spin order in a reliable and tunable manner. In this work, we investigate how the spin order in kagome antiferromagnets—an important class of NCAFMs—can be manipulated via strain. Starting from a microscopic spin Hamiltonian, we derive an effective action for the kagome antiferromagnet that captures the coupling between the spin order and the system's strain tensor. At the microscopic level, this coupling arises from strain-induced modifications of the Dzyaloshinskii-Moriya and exchange interactions. Using this effective description, we explore two strain-driven phenomena: (1) strain-induced switching of the antiferromagnetic spin order and (2) the piezomagnetic response. We numerically show that strain facilitates thermally assisted switching between spin configurations of opposite chirality. Specifically, we find that uniform tensile and compressive strain govern both the average switching time and the preferred switching direction between chiral states. Furthermore, we demonstrate that strain induces a net magnetization and provide an experimentally testable prediction of this effect for a typical NCAFM. Our results provide a theoretical framework for modeling strain-induced manipulation of kagome antiferromagnets, underscoring strain as a promising route for functional control of NCAFMs.

Noncollinear antiferromagnets have emerged as promising platforms for next-generation spintronic devices due to their unique spin textures and unconventional spin-polarized currents. However, the limited understanding of factors governing the out-of-plane spin polarization efficiency (${\xi }_{\mathrm{z}}$) in materials such as $\mathrm{M}{\mathrm{n}}_3\mathrm{Sn}$ hinders their practical application. Here, we demonstrate a strain-engineering strategy to significantly enhance ${\xi }_{\mathrm{z}}$ by tailoring the lattice constant $c$ of $\mathrm{M}{\mathrm{n}}_3\mathrm{Sn}$ thin films. Through controlled annealing processes, we induce tunable crystalline strain in $\mathrm{M}{\mathrm{n}}_3\mathrm{Sn}$ and systematically investigate its impact on spin-to-charge conversion via angle-resolved spin-torque ferromagnetic resonance measurements. Remarkably, the unconventional dampinglike torque efficiency increases by over an order of magnitude when the lattice constant $c$ approaches its equilibrium value, attributed to strain-modulated chiral spin configurations. First-principles calculations corroborate the critical role of lattice strain in amplifying anisotropic spin textures and spin-orbit coupling. This work not only elucidates the structural origin of spin polarization anisotropy in noncollinear antiferromagnets but also establishes a scalable route for designing high-efficiency spin sources compatible with semiconductor integration. The findings advance the development of low-power, all-electric spintronic devices based on strain-engineered antiferromagnetic heterostructures.

Spin-phonon coupling (SPC) is vital in two-dimensional magnetic materials (2DMMs), correlating charge, spin, and lattice vibrations, which is significant for fundamental physics and spintronics. ${\mathrm{CrTe}}_2$, a 2DMM with high Curie temperature, forms self-intercalated ${\mathrm{Cr}}_{1+\mathrm{x}}{\mathrm{Te}}_2$ by interlayer Cr intercalation to easily tune its ground-state properties, promising as a next-generation spintronics device. However, SPC and the microscopic magnetic mechanism (MMM) of ${\mathrm{Cr}}_{1+\mathrm{x}}{\mathrm{Te}}_2$ are still an open issue. Interestingly, studies have found that its magnetic transition temperature is sensitive to the amount of Cr intercalation, while in the critical case of $x_{\mathrm{C}}\sim 0.5$, the coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) interactions enhances magnetic fluctuations, providing a potential platform for studying SPC and MMM. Here, we focus on ${\mathrm{Cr}}_{1.45}{\mathrm{Te}}_2$ crystals near critical doping, systematically investigating their magnetic and thermal properties to clarify related issues. ${\mathrm{Cr}}_{1.45}{\mathrm{Te}}_2$, with a NiAs-type structure ($P\overline{3}m1$), shows pronounced magnetic anisotropy with an out-of-plane FM transition at 232 K and an in-plane AFM transition at 228 K. Lattice dynamics reveal asymmetric $A_{1\mathrm{g}}$ ($\sim 15.1\mathrm{meV}$) and symmetric $E_{\mathrm{g}}$ ($\sim 17.3\mathrm{meV}$) phonon anomalies, attributed to strong SPC, suggesting that ${\mathrm{Cr}}_{1.45}{\mathrm{Te}}_2$ could be a promising candidate for SPC. Furthermore, the strong overlap of Cr $3d_z^2\text{–}\mathrm{Cr}3d_z^2$ induces interlayer FM direct exchange, and in-plane AFM superexchange via near ${180}^{\circ }\mathrm{Cr}\text{–}\mathrm{Te}\text{–}\mathrm{Cr}$ bonding transforms into the plausible Dzyaloshinskii-Moriya interaction due to the robust spin-orbit coupling of Te and relativistic corrections, forming a noncollinear AFM order. Thus, SPC and the competition of magnetic interactions causes intriguing thermomagnetic irreversibilities such as cluster glass, and magnetic thermal hysteresis formed by domain-wall pinning. Notably, ${\mathrm{Cr}}_{1.45}{\mathrm{Te}}_2$ also exhibits a canted noncollinear AFM ground-state and rich excited-state evolution with temperature and applied fields, which will promote the future development of spintronics. This study provides insights to understand SPC and MMM for CrTe-based materials.

We investigate various types of quantum entanglement in the octanuclear heterometallic $3d/4f$ complexes denoted as ${\mathrm{Ni}}_4^{2+}{\mathrm{Gd}}_4^{3+}$ under an external magnetic field, using the exact diagonalization approach. These molecular magnets, which can be effectively described by Heisenberg spin models, consist of two identical {${\mathrm{Ni}}_2^{2+}{\mathrm{Gd}}_2^{3+}$} cubane subunits bridged by acetate and hydroxide ligands. Our analysis reveals that their magnetization exhibits intermediate plateaus at low temperatures, indicating distinct ground states characteristic of Ni-containing compounds. Using negativity as a measure of quantum entanglement, we examine the influence of single-ion anisotropy and magnetic field on tetrapartite, bipartite, 1–3 tangle, and 2–2 tangle entanglements in two families of ${\mathrm{Ni}}_4^{2+}{\mathrm{Gd}}_4^{3+}$ complexes: (1) without anisotropy and (2) with anisotropy. Complex (1) exhibits strong bipartite entanglement between Ni ions, which persists up to $T\approx 3.0\text{K}$ and $B\approx 4.0\text{T}$, but shows significantly weaker tetrapartite entanglement and vanishing bipartite entanglement between $\mathrm{Gd}\cdots \mathrm{Gd}$ and $\mathrm{Ni}\cdots \mathrm{Gd}$ pairs. In contrast, complex (2) displays nonzero and sizable values for all types of entanglement considered. These findings emphasis the crucial role of single-ion anisotropy in generating and shaping the entanglement landscape of heterometallic ${\mathrm{Ni}}_4^{2+}{\mathrm{Gd}}_4^{3+}$ complexes. Notably, we find that the 1–3 tangle entanglement between a Ni ion and the remaining sites in a cubane unit serves as a reliable indicator of ground-state phase transitions, exhibiting distinct changes across phase boundaries irrespective of the presence of single-ion anisotropy.

We investigate aspects of the relation between the quantum geometry of the normal state (NS) and the superconducting phase, through the lens of nonlocality. By relating band theory to quantum estimation theory, we derive a direct momentum-dependent relation between quantum geometry and the quantum fluctuations of the position operator. We then investigate two effects of the NS quantum geometry on superconductivity. On the one hand, we present a physical interpretation of the conventional and geometric contributions to the superfluid weight in terms of two different movements of the normal state charge carriers forming the Cooper pairs. The first contribution stems from their center-of-mass motion while the second stems from their zero-point motion, thereby explaining its persistence in flat-band systems. On the other hand, we phenomenologically derive an emergent Darwin term driven by the NS quantum metric. We show its form in one and two-body problems, derive the effective pairing potential in $s$-wave superconductors, and explicit its form in the case of two-dimensional massive Dirac fermions. We thus show that the NS quantum metric screens the pairing interaction and weakens superconductivity, which could be tested experimentally by doping a superconductor. Our work reveals the ambivalent relationship between noninteracting quantum geometry and superconductivity, and possibly in other correlated phases.

Ultrafast control of confined two-dimensional few-electron systems requires detailed understanding of light-matter interactions at the nanoscale. Twisted light (TL), a special kind of light carrying orbital angular momentum, offers a powerful tool for driving symmetry-resolved transitions in such quantum-confined structures. We consider a simple yet realistic model in which a TL pulse interacts with a nanostructure containing two interacting, charged electrons (e.g. a semiconductor quantum dot containing two electrons) under the influence of a perpendicular magnetic field. Since image charge effects are always present in layered nanostructures, we use an effective electron-electron interaction potential of the form $1/r^{\eta }$. For $\eta =2$, the system acquires an underlying $\mathfrak{su}(1,1)$ dynamical symmetry, which allows for analytical solutions and hence provides a clear framework for interpreting selection rules, parity transitions, and angular momentum resolved absorption features. We show that the bare Coulomb $1/r$ potential also generates similar energy spectra, demonstrating that the twisted-light-driven excitations are remarkably robust against the specific form of the interaction. We analyze the resulting excitation spectrum with emphasis on its chiral properties. We show that TL pulse excitation, unlike conventional dipolar fields, enables direct access to interaction-driven transitions that are otherwise symmetry forbidden. In particular, we demonstrate that TL breaks the generalized Kohn theorem, making the internal nanostructure energetic spectrum accessible through multiple-quanta orbital excitations. More broadly, our findings establish TL as a sensitive future probe of correlations, symmetry, and magneto-optical dynamics in strongly interacting confined quantum systems, revealing features that remain dark in standard low-frequency (e.g. infrared) light absorption.

Nonsymmorphic magnetic Weyl semimetal materials such as $\mathrm{ReAl}X$ (Re = rare earth, $X$ = Si/Ge) provide a unique opportunity to explore the correlated phenomena between Weyl fermions and nontrivial magnetic configurations. To be specific, we study a lattice model in which the magnetic configuration is determined by the competition among ferromagnetic (FM) interaction, the Dzyaloshinskii-Moriya interaction, and the Kondo coupling $K_0$ to the Weyl fermion. Both quantum and finite-temperature phase transitions between FM and correlated nesting helical configurations are found. Different from the uncorrelated helimagnet that decouples from the Weyl fermions, this correlated helimagnet induces a magnetic Brillouin zone with a $K_0$-dependent nesting in the band structure of the conduction electrons instead of the monopolelike Weyl cone. By measuring the current induced by the chiral magnetic effect on the conduction electron with nesting Weyl nodes, one can distinguish the correlated nesting helical order from the ferromagnetism because the chiral magnetic effect is considerably suppressed in the former case. These properties we find here may explain the experimental observations in $\mathrm{ReAl}X$.

We investigate finite-size topological phases in thin films of nodal line semimetals (codimension 2) in three dimensions. By analyzing the hybridization of drumhead surface states, we demonstrate that such systems can transition into either a lower-dimensional nodal line state (codimension 1) or a fully gapped trivial phase. Additionally, we explore the hybridization of bulk states along the nodal loop due to quantum confinement when the system is finite in directions parallel to the loops plane. This generally results in a topologically nontrivial gap. In films that are finite along a single in-plane direction, a partial gap opens, giving rise to two-dimensional Weyl cones characterized by a one-dimensional $\mathbb{Z}$ invariant. When the system is finite along both in-plane directions, a fully gapped phase appears, distinguished by a $\mathbb{Z}$ invariant whose value increases with the thickness of the sample. We further discuss the bulk-boundary correspondence associated with these emergent topological phases.

This study examines the anomalous Hall effect (AHE) in the Heusler series ${\mathrm{Mn}}_{3}Z$ ($Z$=Ga, Ge, Sn), with a particular emphasis on the manipulation of noncollinear antiferromagnetic structures to enhance the AHE. By employing density-functional theory and first-principles calculations, we demonstrate that the anomalous Hall conductivity is markedly responsive to electron filling. By strategically doping Ga into ${\mathrm{Mn}}_3\mathrm{Sn}$ and ${\mathrm{Mn}}_3\mathrm{Ge}$ in order to modulate the electron density, a significant increase in anomalous Hall conductivity (AHC) is achieved. It is noteworthy that a Ga:Sn ratio of 1:5 yields peak AHC values exceeding $700{\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$, while 3:7 Ga-Ge ratios can result in AHC values surpassing $600{\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$. A comparison between the virtual crystal approximation and supercell construction methods for doping has revealed consistent trends. The results of this study pave the way for optimizing the AHE in noncollinear antiferromagnetic materials.

The transport properties of domain wall states in a magnetic topological insulator thin film-based heterostructure are highly sensitive to domain wall configurations. In this work, we identify the existence of the snake state at the magnetic domain wall via electronic transport calculations. We have found the following. (1) The transmission coefficient oscillates periodically with the number of snake state wave cycles, while the wavelength of the snake state is determined by the domain wall profile and its orientation. (2) The transmission through either a slanted or a smoothly curved domain wall is exclusively governed by the domain wall's relative positioning of the endpoints and is impervious to its deformation, a characteristic shared with the electrostatic field. (3) Under heavy disorder, the current splits equally at the termination of the domain wall, independent of the domain wall's profile. (4) The snake state transport through a magnetic domain of finite width can be explained by the combination of two domain walls connected in series. This study offers valuable insights into transport and phase transitions in magnetic topological insulators thin films with complex domain structures.

Weyl semimetal (WSM) thin films exhibit distinct electronic properties compared to their bulk counterparts. In this study, we theoretically investigate the nonreciprocal ballistic transport phenomena arising in WSM thin films due to surface modifications. Our analysis demonstrates that the nonreciprocity is sub-band resolved, where the surface states provide the dominant contribution to the nonreciprocity, whereas the bulk states introduce a negative correction. The striking contrast of the second-order conductance signal may serve as evidence for the existence of surface states. Our calculations further reveal a quantum size effect: overall, the nonreciprocal signal decreases with increasing film thickness, but it undergoes discontinuities as the Fermi energy approaches the bottom of a sub-band. Moreover, we observe a special sub-band-resolved pattern of density of states (DOS), which is common in multilayer systems.

The Rashba effect, characterized by spin splitting in band structures and helical spin textures, plays a pivotal role in various spintronics. However, the nonvolatile modulation of the Rashba splitting magnitude ${\alpha }_R$ in a single material, which potentially gives rise to novel spintronics, still remains unrealized. Here by using density-functional-theory calculations, we theoretically demonstrate the quadruple-well ferroelectrics (FEs) ${\left(\mathrm{Pt},\mathrm{Pd}\right)}_2\mathrm{S}{\mathrm{n}}_2\mathrm{T}{\mathrm{e}}_6$, featured by four stable FE states, $\pm \mathrm{high}$- and $\pm \mathrm{low}$-polarization states ($\pm \mathrm{HP}$ and $\pm \mathrm{LP}$ states), and enable the nonvolatile interconversion between strong and weak Rashba splitting mediated by the HP-LP transformation. Given that the band anticrossing, the typical feature of topologically nontrivial band structures, is associated with the strong Rashba splitting, such HP-LP transformation also enables the topological phase transition between a topological insulator and a conventional semiconductor. The intercoupling between ferroelectricity, Rashba splitting, and band topology provides a unique mechanism for modulating the ${\alpha }_R$ and topological characteristics in a nonvolatile way, paving ways for various novel spintronics and topological electronics.

For a given parent fractional quantum Hall (FQH) state at filling fraction $\nu$, the hierarchy construction produces FQH states at nearby filling fractions $\left\{{\nu }_n\right\}$ by condensing minimally charged quasiholes or quasiparticles of the parent state into their own FQH states. The hierarchy construction has been useful for relating families of FQH states and for the experimental identification of the topological order of parent states via the properties of daughter states. We reinterpret the hierarchy construction as a two-step procedure: stacking with a second FQH state and condensing a condensable algebra of bosons. This two-step procedure can be applied to both Abelian and non-Abelian FQH states, and it does not require calculations with a wave function. We show this construction reproduces the hierarchies for the Laughlin and Pfaffian states, and can be applied further to propose hierarchies for various non-Abelian FQH states.

Thermoelectric transport coefficients up to linear order in the applied magnetic field are microscopically studied using Kubo-Luttinger linear response theory and thermal Green's functions. We derive exact formulas for the thermoelectric conductivity and thermal conductivity in the limit of small relaxation rates for Bloch electrons in terms of Bloch wave functions, which show that the Sommerfeld-Bethe relationship holds. Our final formula contains the Berry curvature contributions as well as the orbital magnetic moment contributions that arise naturally from the microscopic theory. We show that generalized $f$-sum rules containing the Berry curvature and orbital magnetic moment play essential roles in taking into account the interband effects of the magnetic field. As an application, we study a model of a gapped Dirac electron system with broken time-reversal symmetry and show the presence of a linear magnetothermopower in such systems.

By changing the coupling parameter $\alpha$, the $\alpha \text{−}{T}_3$ model lattice varies from honeycomb to dice (or $T_3$) lattice. These lattices are composed of three atomic sites per unit cell, arranged in such a way as to support an additional flat band that touches the conduction and valence bands in the energy spectrum. Slight energetic deviations in the equivalence between their atomic sites result in a band gap opening and the appearance of middle-gap states. Although the sensitivity of these lattices to the breaking equivalence of their atomic sites provides interesting electronic and transport properties, it is unknown how this inequivalence affects the additional intraband states. In this paper, we investigated the appearance of chiral states in $\alpha \text{−}{T}_3$ lattices by applying an asymmetric profile of sublattice symmetry-breaking term as a kink potential. We found one-dimensional interface chiral states morphing as the $\alpha$ parameter is tuned, culminating in a flat band for the dice lattice case. We also demonstrate that the presence of a domain wall (two kink profiles separated by a certain distance), combined with adjustment of the interlattice hopping $\alpha$ parameter, results in two chiral states per valley, which have their dispersion strongly dependent on the $\alpha$ parameter, in addition to the bound states emerging with higher energy-momentum values than the chiral states. Our continuum results are validated with tight-binding results for $\alpha \text{−}{T}_3$ nanoribbons assuming mass-term induced kink and kink-antikink potentials.

Using magnetic force microscopy and Monte Carlo simulations, we investigate the low-energy properties of two artificial kagome ice structures. The two systems differ in that the first series of lattices consists of an assembly of physically disconnected nanomagnets coupled via magnetostatics, whereas the second series is made of fully connected honeycomb networks. Imaging the microstates resulting from a field demagnetization protocol, and analyzing their magnetic correlations in real and reciprocal space, we observe distinct behaviors between the two lattice types. While the former exhibits properties well described by the dipolar kagome ice model equilibrated at a finite fictional temperature, the latter instead is found systematically out of equilibrium. Remarkably, this out-of-equilibrium physics can be reformulated into an at-equilibrium one by strengthening specific coupling terms in the spin Hamiltonian. We interpret this property as a result of the field-induced domain wall propagation that arises when demagnetizing a connected network, i.e., a field driven kinetic process that competes with the formation of local flux-closure configurations that minimize the magnetostatic energy. Our findings highlight how micromagnetic effects bias the selection of spin liquid microstates during a field demagnetization protocol.