Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational cost associated with evaluating the free-energy density and its gradient. This process requires contracting a triple-layer tensor network composed of a projected entangled pair operator and projected entangled pair states. In this paper, we employ a split corner-transfer renormalization group scheme tailored for the contraction of such a triple-layer network, which reduces the computational complexity while keeping high accuracy. Through numerical benchmarks on the three-dimensional classical Ising model, we demonstrate that the proposed scheme achieves numerical results comparable to the most recent Monte Carlo simulations, providing a substantial speedup over previous variational tensor network approaches. This makes this method well-suited for efficient gradient-based optimization in three-dimensional tensor network simulations.

The spin Hall effect in ferromagnets is of great interest in the field of spintronics, and while the effect has been quantified in many materials, the dependence of the spin Hall angle on the relative orientation of spin polarization and the magnetization is less well studied. Of equal importance for the purpose of spin-charge interconversion in ferromagnets is the spin relaxation length, which is predicted to be highly anisotropic with respect to magnetization. Using a modified lateral spin valve geometry with a copper channel and permalloy spin injector, we measure the dependence of the spin Hall angle and spin relaxation length on magnetization orientation in permalloy and nickel, using two distinct device geometries. This allows us to disentangle the contributions of the spin relaxation length and spin Hall angle to the measured spin-charge interconversion voltage output. Our results indicate a large anisotropy in both the spin relaxation length and spin Hall angle in both permalloy and nickel, in agreement with theoretical calculations. The quantities change in opposite directions, with the spin relaxation length rising as the magnetization is moved parallel to the spin polarization and the spin Hall angle falling, leading to a near total cancellation of the spin-charge interconversion output.

We propose a way to generate a one-dimensional topological superconductor from a monolayer of a transition metal dichalcogenide coupled to a Bernal-stacked bilayer of graphene under a displacement field. With proper gating, this structure may be tuned to form three parallel pads of superconductors creating two planar Josephson junctions in series, in which normal regions separate the superconductors. Two characteristics of the system, which are essential for our discussion, are spin orbit coupling induced by the transition metal dichalcogenides and the variation of the Fermi velocities along the Fermi surface. We demonstrate that these two characteristics lead to one-dimensional topological superconductivity occupying large parts in the parameter space defined by the two phase differences across the two junctions and the relative angle between the junctions and the lattice. An angle-shaped device in which this angle varies in space, combined with proper phase tuning, can lead to the formation of domain walls between topological and trivial phases, supporting a zero-energy Majorana mode, within the bulk of carefully designed devices. We derive the spectrum of the Andreev bound states and show that Ising spin-orbit coupling leaves the topological superconductor gapless, and the Rashba spin-orbit coupling opens a gap in its spectrum. Our analysis shows that the transition to a gapped topological state is a result of the band inversion of Andreev states.

We investigate the magnetization dynamics of an ultrathin Co (1.5 nm)/Py (1.5 nm) bilayer system from femtosecond (fs) to nanosecond (ns) timescales. Magnetization dynamics in the fs timescales is characterized as a highly nonequilibrium regime due to an ultrafast reduction of magnetization by laser excitation. On the other hand, the dynamics in the ns timescales is characterized as a close-to-equilibrium regime involving the excitation of coherent magnons. We demonstrate that the interfacial interaction between the Co and Py layers in these two nonequilibrium regimes across the timescales is dynamic and simultaneously influences the magnetization loss in the fs timescales and the magnon dynamics in the ns timescales. On ultrafast (fs) timescales, comparison between time-resolved magneto-optical Kerr effect (TR-MOKE) measurements and temperature-based $\mu T$ model simulations reveals that the bilayer exhibits demagnetization dynamics intermediate between those of its individual layers. When driven far from equilibrium by ultrashort laser pulse excitation, the magnetization dynamics of the individual Co and Py layers appear to remain decoupled and evolve independently in the initial stages of the ultrafast response. On the other hand, in the ns regime, the two individual layers of the bilayer precess together at the same frequency in a coupled manner as one effective single layer. These results improve our understanding of magnetization dynamics across timescales in ultrathin exchanged-coupled ferromagnetic bilayers and provide valuable insights for the design of high-frequency and energy-efficient spintronic device concepts.

The recent identification of altermagnets (AMs) and their associated physical phenomenon have drawn considerable interest in the field of spintronics. In this study, we conducted a comprehensive investigation on the vibrational and thermal transport properties of the altermagnetic semiconductor MnTe based on first-principles calculations with phonon Boltzmann transport theory. Our findings revealed that the lattice thermal conductivity (κ) of MnTe exhibits a unique spin-dependent anisotropy, with values along the [100], [001], and [210] directions at the magnetic transition temperature ($T_N=310$ K) being 1.87, 3.05, and 1.63 W/mK, respectively. In contrast, the lattice thermal conductivity in the [100], [001], and [210] directions for nonmagnetic (NM) MnTe are 6.90, 6.78, and 0.32 W/mK at 310 K. Our phonon analysis revealed that the lowest thermal conductivity along the [210] direction in both AM and NM MnTe is a consequence of the intrinsically smallest group velocities in this crystallographic orientation. Remarkably, the [210] direction inherits the AM crystal symmetry of MnTe, and the magnetization and spin arrangement significantly weaken the directional anisotropy from ${\mathit{k}}_{\left[\mathbf{100}\right]}/{\mathit{k}}_{\left[\mathbf{210}\right]}=21.56$ in the NM state to ${\mathit{k}}_{\left[\mathbf{00}\mathbf{1}\right]}/{\mathit{k}}_{\left[\mathbf{210}\right]}=1.87$ in the AM state. The higher $k_{\left[210\right]}$ in the AM state compared to the NM state predominantly originates from its enhanced phonon lifetime and weaker phonon anharmonicity. These results deepen our understanding of the mechanisms driving spin-dependent anisotropic thermal transport in altermagnetic semiconductors and provide valuable insights for the design of AM based spin-caloritronic devices, spintronic memristors, and cryogenic magnetic sensors.

In this paper we theoretically describe a distinct class of two-dimensional Néel ordered metallic antiferromagnets on a honeycomblike lattice in which the two magnetic sublattices are connected only by a combination of time-reversal and mirror symmetry operations. As a result of this symmetry, conducting fermions have antiferromagnetic spin splitting consistent with the symmetry, mirror-symmetric spin splitting. It is shown that the anomalous spin Hall effect is expected in such antiferromagnets. We also consider a Néel ordered metallic antiferromagnet in which there are no symmetries between the magnetic sublattices and obtain asymmetric spin splitting of conducting fermions. Such systems are ferrimagnets and show the anomalous Hall effect.

We theoretically investigate near-field radiative heat transfer (NFRHT) between subwavelength Mie-resonators supporting a supercavity mode with vanishing far-field coupling—a manifestation of quasibound states in the continuum (quasi-BICs). Employing the quasinormal mode (QNM) expansion formalism, we achieve complete spectral reconstruction of NFRHT in strongly coupled resonator systems. Through precise gap engineering, we demonstrate activation of high-order hybridized gap modes that coherently amplify the supercavity resonance. Moreover, incoherent superposition between the supercavity mode and adjacent gap-perturbed scattering modes yields an integrated enhancement effect with substantially augmented radiative power. Numerical simulations show an order-of-magnitude enhancement in NFRHT power density relative to conventional Mie-Fabry-Pérot scattering modes. We validate quantitative agreement between QNM superposition and analytical expansion methods, while confirming the spectral robustness of supercavity modes against realistic geometric perturbations. This study provides fundamental insights into non-Hermitian thermal photonics and offers practical design principles for thermal radiation resonators and metasurfaces.

We propose a scheme for performing Majorana zero mode (MZM) braiding utilizing cotunneling processes in a three-MZM system incorporating reference arms. This approach relies on the interference between cotunneling paths through the MZMs and reference arms, establishing an effective, tunable coupling between the MZMs. The strength and sign of this coupling can be manipulated via the reference arms and applied magnetic flux. Notably, the introduction of a half-quantum flux reverses the coupling sign, enabling an echolike protocol to eliminate dynamic phases during braiding. Our setup, requiring only three MZMs, represents a minimal platform for demonstrating non-Abelian braiding statistics. We demonstrate that this system facilitates the implementation of Clifford gates via braiding and, significantly, permits the realization of non-Clifford gates, such as the $T$ gate, by geometric phase, thereby offering a potential pathway toward universal topological quantum computation.

Floquet engineering of electronic states by light is a central topic in modern experiments. However, the impact of many-body interactions on the single-electron properties remains unclear in this nonequilibrium situation. We propose that interaction effects could be reasonably understood by performing perturbative expansion in both the pump field and the electron-electron interaction when computing physical quantities. As an example, we apply this approach to semiconductors and show analytically that excitonic effects, i.e., effects of electron-hole interaction, lead to dramatic corrections to the single-electron Floquet spectra even when the excitons are only virtually excited by the pump light. We compute these effects in phosphorene and monolayer ${\mathrm{MoS}}_2$ for time- and angle-resolved photoemission spectroscopy and ultrafast optical experiments.

The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts. In this work, we focus on one such aspect, the difference of evolving quantum ensembles under $H_{\mathrm{nh}}$ (right ensemble) versus its Hermitian conjugate, $H_{\mathrm{nh}}^{†}$ (left ensemble). We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties. Such a comparison gives us a scope to measure the extent to which non-Hermiticity gets translated from the Hamiltonian into physically observable properties. We test the formalism in two cases: First, we construct a non-Hermitian Hamiltonian using a set of imperfect Bell states, showing that the non-Hermiticity of the Hamiltonian does not automatically comply with the non-Hermiticity at the level of observables. Second, we study the interacting Hatano-Nelson model with asymmetric hopping as a paradigmatic quantum many-body Hamiltonian. Interestingly, we identify situations where the measures of non-Hermiticity computed for the Hamiltonian, for single-, and for many-particle quantum properties behave distinctly from each other. Thus, different notions of non-Hermiticity can become useful in different physical scenarios. Furthermore, we demonstrate that the measures can qualitatively mark the model's parity-time symmetry-breaking transition. Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems as well as in preparing resourceful states for quantum technologies.

The ultrathin tungsten (W) layer has been utilized as a spin-generating source for memory application in magnetic heterostructures. We investigate the spin Hall conductivity (SHC, ${\sigma }_{xy}^z$) of W-N compounds, focusing on WN and ${\mathrm{W}}_2\mathrm{N}$, employing first-principles calculations. We evaluate the SHC, formation energy ($\mathrm{\Delta }F$), and phonon frequencies for all cases. Three possible structures, including NaCl, hexagonal, and NbO type, are considered for WN. While the SHC of WN in NaCl and a hexagonal structure are substantial, the thermodynamic average of WN is $-194(\hslash /e)\text{S/cm}$, much smaller than pure W. However, ${\mathrm{W}}_2\mathrm{N}$, whose stability is confirmed by phonon calculations, shows a large SHC of ${\sigma }_{xy}^z=-966(\hslash /e)\text{S/cm}$ with a spin Hall angle (${\theta }_{\text{SH}}$) of $-0.44$, in good agreement with the experiment, enhanced by 18% over $\beta \text{−}\mathrm{W}$. Most of the spin Berry curvature, responsible for such large ${\sigma }_{xy}^z$, stems from the $\left[1\overline{1}0\right]$ ($k_x=k_y$) plane and is analyzed from a symmetry perspective using representations of group theory.

With its huge entropy change and a strong interplay between magnetic order, structural and electrical properties, the first-order antiferromagnetic/ferromagnetic phase transition is a paradigmatic example of the multicaloric effect. The unraveling of the physics underlying the phase transition needs a better understanding of the thermal hysteresis of FeRh within the AF-FM phase coexistence region. In this work, we compare the effect of two very different types of thermal cycling on the hysteresis of the magnetic order: quasistatic heating, and cooling of the entire $195\mathrm{nm}$ thick film, and a $f=100\mathrm{kHz}$ modulated heating driven by a laser focused down to a spot of about 10 $\mu {\mathrm{m}}^2$ at the film surface. Taking advantage of the reflectivity difference between both phases to probe optically their respective fraction, we show that whereas only temperature-driven reflectivity variations ($dR/dT$, thermoreflectance) are detected in the pure phases, a huge modulation of the phase-dependent reflectance at the driving frequency $f$ is detected in the phase coexistence temperature range. This is quantitatively described as resulting from a substantial modulation of the FM fraction (up to $90\%$) with increasing laser power. A simplified rate-independent hysteresis model with return-point-memory (RPM), represented in terms of bistable units that undergo a temperature excursion corresponding to a given laser power, reproduces very well the optically measured FM phase modulation characteristics for a broad range of temperature excursions. This offers an insight into the leading role of quenched disorder in defining thermal hysteresis in FeRh under high excitation frequency, when the material is periodically driven out-of-equilibrium.

Planar Josephson junctions are theoretically predicted to harbor zero-energy Majorana bound states (MBS) in a tunable two-dimensional geometry, at the two ends of the middle metallic channel. Here we show that three distinct topological superconducting regimes, governing the localization of the near-zero-energy MBS, appear in these planar Josephson junctions. The topologically protected MBS appear near the narrow edges of the junction, not only in the middle metallic channel but also in the superconducting leads which have widths similar to the values used in recent experiments. We incorporate random fluctuation in the chemical potential to investigate the influence of nonmagnetic disorder on the localization of the MBS in different topological regimes and find that the MBS are quite robust against disorder because of the two-dimensional geometry. Interestingly, moderate amount of disorder reduces the splitting between the MBS pairs, possibly by minimizing the wave-function overlap of the MBS. We also discuss the changes in the topological superconducting phases when the superconducting lead width is varied. Our results reveal a rich structure of the localization of topologically protected multiple MBS in experimentally accessible planar Josephson junctions, and call for their experimental confirmation.

Ductile high-temperature superconductors are essential for engineering applications such as superconducting tapes and wires. However, materials that simultaneously exhibit mechanical ductility and a superconducting transition temperature ($T_c$) above liquid nitrogen temperature remain scarce. In this study, we start with the experimentally reported ${\mathrm{Al}}_7\mathrm{Mg}$ alloy and investigate the structures, electron-phonon coupling (EPC), and superconducting properties of various ${\mathrm{Al}}_7{\mathrm{MgH}}_2$ configurations through first-principles calculations combined with statistical methods. Statistical analysis reveals that the percentage contribution of H density of states at the Fermi level ($E_F$) and the H local space are two factors determining superconductivity. While the hydrogen occupation site has a negligible effect on the electronic structure, it significantly alters the phonon spectra. Specifically, the intrinsic vibrational modes of H are primarily associated with phonon frequencies, whereas the local chemical environment of H strongly influences EPC through phonon spectra softening or hardening, as demonstrated through our analysis of H phonon splitting and vibrational mode visualization. The predicted ${\mathrm{Al}}_7{\mathrm{MgH}}_2$ crystal can sustain superconductivity up to 64 K at ambient pressure while exhibiting excellent ductility comparable to that of Al and AlMg alloys. Our results show that AlMg-based hydrides may bridge the gap in the absence of ductile superconductors near the liquid-nitrogen temperature and offer a different perspective on how interstitial hydrogen configurations affect conventional $s$-wave superconductivity.

Recently, the superconducting properties of Fibonacci quasicrystals have attracted considerable attention. By numerically solving the self-consistent Bogoliubov-de Gennes equations for an $s$-wave superconducting Fibonacci chain, we find that the system exhibits universal end superconductivity, where the pair potential at the chain ends can persist at higher temperatures compared to the bulk critical temperature ($T_{cb}$) of the condensate in the chain center. Furthermore, our study reveals two distinct critical temperatures at the left ($T_{cL}$) and right ($T_{cR}$) ends of the chain. This complex behavior arises from the competition between topological bound states and critical states, a characteristic of quasicrystals. With the chosen parameters, the maximal enhancement of $T_{cR}$ reaches up to $66\%$ relative to $T_{cb}$, while $T_{cL}$ can increase by up to $31\%$. Our study sheds light on the phenomenon of end superconductivity in Fibonacci quasicrystals, pointing to alternative pathways for increasing the superconducting critical temperature.

The spectral properties of the Heisenberg spin-1/2 chain with random fields are analyzed in light of recent works on the renormalization-group flow of the Anderson model in infinite dimension. We reconstruct the $\beta$ function of the order parameter from the numerical data, and observe that it may not admit a one-parameter scaling form and a simple Wilson-Fisher fixed point. Rather, it appears to be more compatible with a two-parameter, Berezinskii–Kosterlitz-Thouless-like flow with a line of fixed points (the many-body localized phase) terminating at the localization transition critical point. We argue that this renormalization group framework provides a more coherent and intuitive explanation of numerical data, up to the system sizes available with the present technology.