Stacking order and layer thickness exert significant influence on the physical properties of two-dimensional materials. Here, using first-principles calculations and symmetry analysis, we theoretically investigate the stacking- and layer-dependent Raman responses of InSe and infer the corresponding symmetry-based second-harmonic generation (SHG) selection rules. For bulklike InSe, the calculated low-frequency Raman spectra (below $30 {\mathrm{cm}}^{-1}$) enable direct phase-sensitive spectral fingerprints: no peak is found for $\gamma$-InSe, whereas $\epsilon$- and $\beta$-InSe exhibit peaks near 20.2 and $17.8 {\mathrm{cm}}^{-1}$, respectively. Point-group analysis further indicates that SHG response is symmetry-allowed for bulk $\gamma$- and $\epsilon$-InSe, whereas it is symmetry-forbidden for bulk $\beta$-InSe. For few-layer InSe, the frequencies of the strongest shear modes exhibit a blueshift for the AB-stacked $\epsilon$ and $\beta$ phases, but a redshift for the ABC-stacked $\gamma$ phase, as the layer number increases. SHG response is symmetry-allowed for both odd- and even-layer $\gamma$- and $\epsilon$-InSe, whereas it is allowed for odd layers and forbidden for even layers in $\beta$ phase. This layer-dependent evolution of the low-frequency Raman modes, combined with symmetry-based SHG selection rules, provide an effective route for distinguishing the three InSe polytypes in the few-layer regime. In the high-frequency region, the ${{\mathrm{A}}^{\prime }}_1^1(\sim 110$ ${\mathrm{cm}}^{-1}$) and ${{\mathrm{A}}^{\prime }}_1^2(\sim 235$ ${\mathrm{cm}}^{-1}$) modes display a blueshift and a redshift, respectively, for all three phases with increasing layer thickness. The low-frequency shear modes and the frequency difference between ${{\mathrm{A}}^{\prime }}_1^1$ and ${{\mathrm{A}}^{\prime }}_1^2$ can serve as indicators of layer number in ultrathin films. Combined with analytical lattice-dynamical models, we reveal that the competition between the surface effect and the thickness effect governs the overall evolution of the high-frequency Raman trends. This work clarifies the microscopic origin of Raman responses in InSe and provides theoretical guidance for phase identification, thickness estimation, and elastic modulus characterization of layered materials.

We theoretically study the phase-dependent thermal conductance of a short Josephson junction based on a Rashba semiconducting nanowire with proximity-induced superconductivity. We show that an in-plane Zeeman field induces a quasicontinuum of states inside the superconducting gap, leading to a strong enhancement of the low-temperature thermal conductance. The thermal conductance exhibits a sharp peak precisely at the critical field that separates the trivial and topological superconducting phases, thereby serving as a sensitive probe of the topological phase transition. Moreover, when the Zeeman field acquires a component parallel to the Rashba spin-orbit field, the Andreev bound states experience a Doppler shift, giving rise to an anomalous phase-dependent thermal conductance. This Doppler shift is directly related to an effective finite-momentum pairing of Cooper pairs. Our results establish phase-coherent heat transport as an effective and complementary tool for detecting finite-momentum pairing and topological transitions in nanowire-based Josephson junctions.

Sodium-ion batteries have gained much interest over the past years and especially layered oxides are highly considered as cathodes for the next generation of batteries. However, there are still significant challenges to overcome in these materials for practical applications mainly related to capacity degradation and voltage fading. A key influence factor for these challenges are phase transitions that occur by gliding of layers during operation of these materials. Until now there is limited atomistic-level understanding on such transitions as simulations of these processes are computationally demanding. In this work, we trained a classical pairwise Coulomb-Buckingham potential versus extensive ab initio data using a genetic algorithm to study O2-P2 phase transitions in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$. Our density functional theory (DFT) and classical potential calculations show that phase-transition barriers decrease upon desodiation and are further lowered if dynamic conditions are considered through molecular dynamics simulations. Our developed classical potential is able to capture phase transitions and its related increase in the Na-ion diffusivity under standard laboratory conditions at the $\mu \mathrm{s}$ timescale of molecular dynamics simulation. Furthermore, it is found that the phase transition occurs gradually via various $\mathrm{OP}n$ phases.

As prototypical strongly correlated materials, manganese oxides serve as key platforms for studying electronic correlations. Under high pressure, drastic changes in local coordination, bond lengths, and electronic screening modify the electron correlation strength. However, due to the difficulty in determining the Hubbard $U$ value to correctly describe the localized $d$-electron state for various structures in high-pressure simulations, previous works generally used fixed $U$ values to investigate the pressure-driven phase transition of manganese oxides, resulting in significant controversies. Here, a machine learning approach is developed to fit the Hubbard $U$ parameters for exploring the high-pressure properties of ${\mathrm{Mn}}_{\mathrm{y}}{\mathrm{O}}_{\mathrm{x}}$ and applied to construct convex hulls at pressures of 0–200 GPa. Several new high-pressure phases are found and long-standing controversies about the phase-transition sequence of MnO and ${\mathrm{Mn}}_2{\mathrm{O}}_3$ are resolved by high-throughput structure search and comparing x-ray diffraction patterns. This work provides new insights into the high-pressure behavior of the Mn-O system and contributes to advancing studies of transition metal oxides characterized by localized $d$ electrons.

It has been suggested that the anisotropic behavior of orbital transport can be distinct from that of the spin counterpart. On another front, the microscopic mechanisms underlying the anomalous Hall effect and the spin Hall effect are generally categorized into the intrinsic Berry curvature mechanism and the extrinsic mechanism induced by disorder scattering, each with distinct scaling relations. A similar analysis for orbital transport has rarely been performed. Here, we investigate both aspects of the orbital current generation in a light metal V. The orbital-to-spin conversion is achieved using a heavy metal Pt insertion layer or Ni as the ferromagnetic layer. Benefiting from the epitaxial growth of V with a low disorder strength, the orbital current generation is characterized by a large transverse conductivity and long diffusion length, consistent with the expectation for an intrinsic orbital Hall effect. Across all the heterostructures studied, we confirm the orbital current's isotropic nature, i.e., the orbital current generation is barely affected when the charge current is applied along different crystallographic directions, consistent with the high-symmetry crystal structure. Crucially, the intrinsic nature of the orbital current generation is demonstrated by the scaling analysis, showing a scattering-independent orbital Hall conductivity.

We investigated the rare-earth triangular-lattice antiferromagnet ${\mathrm{NdMgAl}}_{11}{\mathrm{O}}_{19}$ using single-crystal magnetization (1.8 K $\le T\le$ 300 K, ${\mu }_{0}H\le 7\mathrm{T}$) and specific-heat measurements down to 45 mK. The dc susceptibility confirms a well-isolated Kramers doublet ground state with pronounced Ising-type anisotropy, with $g_c\approx 3.7, g_{ab}\approx 1.45$. Curie-Weiss fits yield weak, anisotropic antiferromagnetic exchange, with ${\theta }_c=-0.54\mathrm{K}$ and ${\theta }_{ab}=-0.87\mathrm{K}$. Heat capacity measurements show no long-range magnetic order down to 40 mK. Instead, $C_m/T$ exhibits a broad maximum near 0.081 K whose magnitude and field evolution are consistent with short-range correlations in an anisotropic triangular lattice. Applied magnetic fields open a Zeeman gap where the specific-heat anomaly follows $\mathrm{\Delta }=g{\mu }_B{\mu }_{0}H$, and $M(H,T)$ is well described by a Brillouin function for a $J_{\mathrm{eff}}=\frac{1}{2}$ moment. The field tuning of the low-temperature entropy manifold allows self-cooling from 1.8 K to 53 mK by adiabatic demagnetization from a ${\mu }_{0}H=9\mathrm{T}$ field. These results identify ${\mathrm{NdMgAl}}_{11}{\mathrm{O}}_{19}$ as a nearly ideal weak-exchange triangular magnet with a field-tunable correlated ground state.

A series of Ruddlesden-Popper perovskite solid solutions, ${\mathrm{Ca}}_2{\mathrm{Mn}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_4 (0.25\le x\le 0.65)$, is examined by combining density functional theory (DFT) calculations with local-scale experimental studies conducted at ISOLDE-CERN over a broad temperature range (10–1220 K). Perturbed angular correlation (PAC) spectroscopy probes the $I4/mmm$ to $I{4}_1/acd$ structural phase transitions for all compositions between 900 and 1200 K. For $x=0.65$, measurements below 160 K show that a second structural phase condenses, coexisting with the $I{4}_1/acd$ phase down to 10 K. DFT structural models reproduce a key experimental observation: in the $I{4}_1/acd$ phase, the $c$ lattice parameter shows only a minor increase upon Ti substitution, whereas the $ab$ plane expands significantly, reducing the $c/a$ ratio linearly. This anisotropic response can be attributed to a corkscrewlike mechanism, where the enhancement of in-plane $B{\mathrm{O}}_6$ octahedral rotations induces a contraction of the rocksalt layers, thereby mitigating the expansion of the $c$ axis. PAC data, supported by DFT calculations, demonstrate that Ca sites apically connected to ${\mathrm{MnO}}_6$ octahedra exhibit experimentally distinguishable Electric Field Gradients from those connected to ${\mathrm{TiO}}_6$ octahedra.

The temperature-dependent intrinsic magnetic properties of ${\mathrm{SmCo}}_5$ and its Fe- or Cu-doped compounds are systematically investigated via atomistic spin simulations. For pristine ${\mathrm{SmCo}}_5$, Curie temperature $T_{\text{C}}$ and effective anisotropy constant $K_1^{\text{eff}}$ at 0 K are calculated as 1000 K and $35\mathrm{MJ}\text{/}{\mathrm{m}}^3$, respectively, agreeing with experimental results. The domain-wall width ${\delta }_{\text{w}}$ and exchange stiffness $A_{\text{e}}$ at 0 K are determined as 3.31 nm and 39.3 pJ/m, respectively. As temperature increases, the domain wall broadens and both $K_1^{\text{eff}}\left(T\right)$ and $A_{\text{e}}\left(T\right)$ decrease, with a scaling law as $A_{\text{e}}\propto {[M_{\text{s}}\left(T\right)/M_{\text{s}}\left(0\right)]}^{1.86}$. For the metal-doped $\text{Sm}{\left({\text{Co}}_{1-x}{M}_x\right)}_5$ compounds ($M=\text{Fe},\text{Cu}$; $x=0.2,0.4$), magnetic Fe doping is found to increase $T_{\text{C}}$ through Fe-Co exchange, while nonmagnetic Cu doping decreases $T_{\text{C}}$. Both metal dopants reduce $K_1^{\text{eff}}$ by perturbing the Sm crystal field and Co spin-orbit coupling. Magnetic Fe doping is revealed to improve the thermal stability of the magnetic anisotropy of ${\mathrm{SmCo}}_5$, while nonmagnetic Cu doping weakens it. This work could advance the understanding of ${\mathrm{SmCo}}_5$ permanent magnets and the impact of transition-metal doping through a comprehensive quantification of their temperature-dependent magnetic properties.

Two-dimensional (2D) spintronics has emerged as a rapidly growing field due to its potential for the precise manipulation of electron spins in nanoscale devices. In this work, we investigate the magnetic properties of Janus $\text{CrI}X$ ($X=\mathrm{Cl}$, Br) monolayers using first-principles calculations and atomistic spin simulations. Our study reveals that the magnetic ground state of $\text{CrI}X$ is a helical spin spiral driven by intrachain isotropic Heisenberg frustration. Crucially, the broken inversion symmetry of the Janus structure induces a nonnegligible in-plane Dzyaloshinskii-Moriya interaction (DMI) while the low-symmetry spin-orbit-coupled environment also gives rise to substantial symmetric anisotropic exchange, which modulate the helical spin texture with a tilted spiral plane. By applying an external electric field, we demonstrate the ability to modulate these magnetic interactions through the interplay with the built-in electric field, resulting in a tunable deviation of the spin-spiral plane angle and wavelength. This direct correlation between the electric field and magnetic order highlights the magnetoelectric coupling in $\text{CrI}X$, establishing Janus $\text{CrI}X$ as a model 2D platform for studying electrically tunable noncollinear magnetism.

We study the multifractal criticality in a generalized Su-Schrieffer-Heeger model. The results show that the system supports not only critical phases but also reentrance multifractalization (REM). By mapping the hopping term to an effective potential, we analytically prove that although the model has no explicit unbounded potential, a hidden unbounded potential is actually present—this is the key mechanism driving the emergence of multifractal critical phases. Moreover, one can get a condition where the competition between the explicit and hidden unbounded potentials is exactly balanced. Under this condition, the multifractal critical phase vanishes, and the system returns to the extended phase. Based on this mechanism, we achieve both demultifractalization and reentrant multifractalization. Finally, we double-check the theoretical predictions through wave packet dynamics, and the numerical results are consistent with our theoretical analysis. This work broadens our understanding of how unbounded potentials induce multifractal critical phases, providing a theoretical basis for designing new systems with multifractal critical phases.

We show that electron drag by nonequilibrium phonons describes the actual duration and spectrum of terahertz pulses generated during femtosecond laser irradiation of metals. In contrast to previous models, there is a picosecond delay in the drag force development due to the relatively slow lattice heating and finite phonon lifetime. We also predict that at high pump fluences a macroscopic deformation wave nonlinearly enhances the drag force and terahertz response. Our results establish the terahertz pulse wave form as a direct probe of ultrafast lattice dynamics in metals.

Metallic systems with geometrically frustrated magnetic lattices are of considerable interest due to the exotic ground states that emerge from competing interactions and structural constraints that suppress conventional magnetic order. Here we report the synthesis and magnetic phase diagram of a suitable candidate, ${\mathrm{TbAl}}_2{\mathrm{Ge}}_2$ in a single-crystalline form, where the Tb atoms form a triangular-net arrangement. Magnetization, heat capacity, and electrical resistivity measurements establish an antiferromagnetic ground state in the system with two transitions at $T_{N1}\approx$ 15 K and $T_{N2} \approx$ 11 K, while applied magnetic fields reveal a rich temperature-magnetic field $\left(T\text{−}H\right)$ phase diagram. Both $T_{N1}$ and $T_{N2}$ get suppressed monotonically with increasing $H$, but the magnetic easy plane $(H\perp c)$ has an additional magnetic phase intermediate between the two phases bounded by $T_{N1}$ and $T_{N2}$. The transition of the AFM spins to a spin polarized state at relatively low magnetic fields motivated us to evaluate ${\mathrm{TbAl}}_2{\mathrm{Ge}}_2$ for the magnetocaloric effect. We obtain moderate values of magnetoentropy, rotational magnetocaloric effect, and relative cooling power in this system.

For the van der Waals magnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, although a ferromagnetic ground state has been reported, there are also reports of complex magnetic behavior suggesting coexistence of ferromagnetism and antiferromagnetism due to the intricate interaction between ${\mathrm{Fe}}^{+3}$ and ${\mathrm{Fe}}^{+2}$ ions in this system. The exact nature of the interactions and the origin of antiferromagnetism are still under debate. Here, we report a clear signature of intrinsic intralayer antiferromagnetic coupling coexisting with ferromagnetic couplings between different Fe ions in the anomalous Hall effect measured for devices of mechanically exfoliated ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ nanoflakes of thicknesses of $\sim 20\mathrm{nm}$. Two sharp steplike jumps in the hysteresis loop of anomalous Hall resistance ($R_{\mathrm{xy}}$) measured as a function of external field $\left(H\right)$ at temperatures below the onset temperature of antiferromagnetic coupling. Our detailed analysis of experimental data suggests the jumps in $R_{\mathrm{xy}}\left(H\right)$ correspond to magnetization switching behavior of different Fe ions in individual layers of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. The experimental results are supported by first-principles calculations, suggesting a coexisting intralayer antiferromagnetic coupling between ${\mathrm{Fe}}^{+3}$ and ${\mathrm{Fe}}^{+3}$ ions and ferromagnetic coupling between ${\mathrm{Fe}}^{+3}$ and ${\mathrm{Fe}}^{+2}$ ions in the system.

We show that a planar Josephson junction having $d$-wave superconducting regions, with a skyrmion crystal placed underneath, produces a robust gate-tunable superconducting diode effect. The spatially varying exchange field of the skyrmion crystal breaks both inversion and time-reversal symmetries, leading to an asymmetric current-phase relation with an anomalous phase shift. Our theoretical calculations, obtained using resistively and capacitively shunted junction model combined with the Bogoliubov–de Gennes method, reveal that the diode efficiency is largely tunable by controlling external gate voltage and skyrmion radius. Incorporation of a $d$-wave superconductor such as a high-$T_c$ cuprate enables the diode to function at higher operating temperatures. Planar Josephson junctions coupled with higher-order skyrmion crystals also generate a finite diode efficiency. Our results establish a unique and practically realizable mechanism for devising tunable superconducting diodes that operate without an external magnetic field, based on magnetic texture-superconductor hybrid platforms.

Research on topological phases of matter is a core field in modern condensed matter physics. Free fermion systems, such as topological insulators and superconductors, have been studied using the “tenfold way” and K-theory. Building on Kitaev's idea of $\mathrm{\Omega }$-spectrum and classifying space, as well as Freed–Moore's K-theory, this work demonstrates that free fermionic systems form a genuine $G\text{−}\mathrm{\Omega }$-spectrum and clarifies its connection to several distinct classification schemes appearing in the physical literature. By introducing the ${\mathbb{Z}}_2$-graded algebra $A_{\mathrm{sym}}^V$, the classification problem for systems with general symmetries, including antilinear symmetries, antisymmetries, projective representations, and point group symmetries, is turned into an extension problem in representation theory. To solve this, a computational method for the ${\mathbb{Z}}_2$-graded Wedderburn–Artin decomposition of $A_{\mathrm{sym}}^V$ is developed. This decomposition not only yields a classification but also enables the explicit construction of the corresponding Dirac Hamiltonian. Furthermore, a GAP programming package has been developed to automate these calculations.

The internal low-energy symmetry of the massless Lorentz-invariant Dirac Hamiltonian in (2+1) dimensions is known to be $O\left(2N\right)$, where $N$ is the number of two-component Dirac fermions. Here we point out that there exists an analogous internal symmetry of the single-particle quadratic-band-touching Hamiltonian in two spatial dimensions, and it is the unitary symplectic group, $USp\left(2N\right)$. All fermion bilinears belong to one of the three small irreducible representations of this group. The interacting theory that respects the $USp\left(2N\right)$ symmetry and the spatial rotations is constructed and found to allow two independent interaction terms. When these interactions are infrared relevant the symplectic symmetry either remains preserved or becomes spontaneously broken to $USp\left(N\right)\times USp\left(N\right)$. The symmetry in lattices such as honeycomb to infinite order in the dispersion's expansion in powers of local momentum is given by the overlap of the symplectic and the orthogonal groups. We show that this overlap is $O\left(2N\right)\bigcap USp\left(2N\right)=U\left(N\right)$. Some consequences of the symplectic symmetry and its spontaneous breaking are briefly discussed.

We perform determinant quantum Monte Carlo simulations of the half-filled Hubbard model on a diagonally compressed kagome lattice, introducing exponential decay long-range hopping $t\left(r\right)=t_{0}exp\left(-r/r_0\right)$ to account for the evolving bond length. By varying the lattice angle $\theta$ and the on-site interaction $U$, double occupancy, charge compressibility, and spin-spin correlation functions of the whole system and each sublattice are measured. We find that geometric compression induces a clear sublattice differentiation: For $\theta \gtrsim {52}^{\circ }$, the $A$ sublattice establishes long-range hoppings, which in turn suppresses the metallic behavior of the $B/C$ sublattice and drives a selective Mott transition; for $\theta \lesssim {52}^{\circ }$, the $B-C$ chains develop long-range antiferromagnetic correlations within the finite-size simulations, which in turn suppresses the metallic behavior of the $A$ sublattice and drives a selective Mott transition. The critical interaction $U_A^c$ for the $A$ sites decreases sharply near the onset of $B-C$ antiferromagnetic correlations, while $U_{B/C}^c$ increases. These competing orders give rise to an orbital-selective Mott phase and a rich $U-\theta$ phase diagram featuring paramagnetic-metal, paramagnetic-Mott, antiferromagnetic-metal, and antiferromagnetic-Mott states. Our results highlight the complex interplay between lattice geometry, magnetic frustration, and strong correlations in frustrated two-dimensional systems.

We investigate the electronic structure and Fermi surface of ${\mathrm{Co}}_{1/3}{\mathrm{TaS}}_2$ using angle-resolved photoemission spectroscopy (ARPES) combined with theoretical modeling beyond standard density functional theory ($\mathrm{DFT}+\mathrm{U}$). A shallow electron pocket, the so-called $\beta$ feature, is observed at the Fermi level near the corner of the superlattice Brillouin zone, representing the first experimental observation of this feature in an intercalated ${\mathrm{TaS}}_2$ compound. Similar pockets have been reported in $X_{1/3}{\mathrm{NbS}}_2$ ($X=\mathrm{Co}$, Cr, Ni), where their surface versus bulk origin remains actively debated. Because conventional $\mathrm{DFT}+\mathrm{U}$ does not capture this feature, we employ cluster perturbation theory (CPT) to incorporate an explicit treatment of strong electron correlations ($U$) on the Co sites. CPT successfully reproduces the $\beta$ feature, demonstrating its origin from correlation-driven bulk states rather than surface effects. To further substantiate this conclusion, we studied a reduced Co-content sample, ${\mathrm{Co}}_{0.22}{\mathrm{TaS}}_2$, where the reduced charge transfer modifies the Co-derived states near the Fermi level. Its electronic structure remains largely similar to that of pristine 2H-${\mathrm{TaS}}_2$, showing only a minor overall energy shift and lacking the $\beta$ feature, consistent with disrupted long-range Co ordering and modified orbital character near the Fermi level. We demonstrate that the $\beta$ feature arises from strong local correlations on the Co sites and requires long-range crystallographic order among intercalated Co atoms to maintain coherence. These results highlight the importance of strong electronic correlations in magnetically intercalated transition-metal dichalcogenides and provide a microscopic understanding of features not captured by conventional $\mathrm{DFT}+\mathrm{U}$.