Unconventional Weyl and Dirac phonons with topological charges of $\pm 2$ have attracted significant attention due to their exceptional properties. By employing a minimal lattice model, we propose that an ideal topological quasiparticle coexistence system can be achieved in chiral space groups 92 and 96. This system specifically incorporates a charge-2 Weyl phonon and a charge-2 Dirac phonon. Notably, the crystal symmetry restricts these two topological quasiparticles to high-symmetry points within the Brillouin zone, resulting in an ultralong surface arc that extends across the entire surface Brillouin zone. Moreover, the topological surface arcs exhibit a unique saddlelike surface feature. Taking ${\mathrm{BaPt}}_2{\mathrm{S}}_3$ as a representative example, we validate our prediction and reveal the interconnected ultralong surface arc and saddlelike topological surface state. Our work establishes a valuable framework for investigating diverse types of double Weyl nodes and presents a promising approach for detecting ultralong surface arcs.

Current-induced spin-orbit torque (SOT) switching of perpendicular magnetization requires an additional symmetry breaking, calling for modifications of the conventional SOT devices. Here, we have systematically investigated current-induced magnetization switching and dampinglike field in Pt/Co/PtMn trilayer films with a wedged ultrathin antiferromagnetic (AFM) PtMn layer. The symmetry is broken by the effective shape anisotropy in the wedged ultrathin AFM PtMn layer, resulting in the observed field-free SOT switching. Quantitative characterization manifests that the dampinglike (DL) field is boosted up to 30% through wedging the AFM PtMn layer. Additional experiments with in situ magnetic field and micromagnetic simulations indicate the canting of spins caused by the wedge shape accounts for the observed field-free switching and enhancement of SOT efficiency. Our findings provide an easier approach to field-free switching and $H_{\mathrm{D}\mathrm{L}}$ enhancing for magnetic memory devices with high density and low power consumption.

$T{M}_{1/3}M{S}_2$ ($TM=3d$ transition metal, $M=\mathrm{Nb},\mathrm{Ta}$) has recently attracted increasing attention due to its wide variety of fascinating magnetic structures and the chiral arrangement of intercalated $\mathit{TM}$ atoms. We investigated the bulk properties of ${\mathrm{Ni}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ and ${\mathrm{Ni}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ using magnetization, transport, heat capacity, powder neutron diffraction, and x-ray absorption spectroscopy. ${\mathrm{Ni}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ undergoes a phase transition at 84 K, developing an antiferromagnetic helical order with a very long period along the $c$ axis ($33c$). On the other hand, a simple $A$-type spin configuration was observed for ${\mathrm{Ni}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ below 158 K, where the spins are aligned to the $c$ axis. These magnetic structures, combined with lattice chirality and metallicity, can lead to various intriguing transport properties, making ${\mathrm{Ni}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ and ${\mathrm{Ni}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ promising material candidates for future studies on antiferromagnetic spintronics.

It is well known that the electric field can induce phase transitions between superconducting, metallic and insulating states in thin-film materials due to its control of the charge carrier density. Since a similar effect on the charge carriers can also be expected for surfaces of bulk samples, here, we investigate the transformation of the surface states in a superconductor under an applied screened electric field. Our study is performed by numerically solving the self-consistent Bogoliubov–de Gennes equations for the one-dimensional attractive Hubbard model. It is found that the surface insulating regime occurs at sufficiently large (but still experimentally accessible) electric fields. Our calculations yield the phase diagram of the surface superconducting, metallic, and insulating states for a wide range of temperatures and applied fields. Our results are in qualitative agreement with the phase diagram obtained with the transport measurements for (Li, Fe)OHFeSe thin flakes [Ma et al., Sci. Bull. 64, 653 (2019); Yin et al., ACS Nano 14, 7513 (2020)].

We explore critical properties of a chain of interacting Majorana fermions, particles that are their own antiparticles. We study the combined effect of two competing interaction terms of the shortest possible range and show this results in a very rich phase diagram with nine different phases, five of which are critical. In addition, we report a wide variety of quantum phase transitions: the tri-critical Ising lines; the Lifshitz critical line characterized by the dynamical critical exponent $z=3$; two Kosterlitz-Thouless transitions; and an exotic first-order transition between the floating and the gapped phases. However, the most surprising result is the emergence of the commensurate line at which the floating phases collapse into direct transition. We provide numerical evidences that the resulting multicritical point belongs to the universality class of the eight-vertex model. Implications in the context of supersymmetric properties of the Majorana chain are briefly discussed.

Recent advancements in the field of topological band theory have significantly contributed to our understanding of intriguing topological phenomena observed in various classical and quantum systems, encompassing both wave and dissipative systems. In this study, we employ the notion of band theory to establish a profound connection between the spatiotemporal evolution of temperatures and the underlying topological properties of radiative systems. These systems involve the exchange of energy through radiation among a collection of particles. By utilizing the eigenstates of the response matrix of the system, we establish a robust framework for the examination of topological properties in radiative systems, considering both symmetric and asymmetric response matrices. Our formalism is specifically applied to investigate the topological phase transition in a one-dimensional chain composed of an even number of spherical nanoparticles. We provide compelling evidence for the existence and robustness of topological edge states in systems characterized by an asymmetric response matrix. Moreover, we demonstrate that by manipulating the arrangement and volume of particles, it is possible to control the system's structure and achieve desired topological features. Interestingly, we showed that the radiative heat transfer can be controlled and prevented by topological insulation. Additionally, we conduct an analysis of the temperature dynamics and the associated relaxation process in the proposed system. Our research findings demonstrate that the interplay between bulk states and localized states is pivotal in the emergence of distinct eigenstates and provides significant insights into the spatiotemporal dynamics of temperature and the process of thermalization within a system. This interplay holds the potential to be leveraged for the development of structures, facilitating efficient heat transfer even in the presence of perturbation. Consequently, it enables precise experimental measurements of heat transfer and serves as a platform for the exploration of thermal topology, offering new avenues for scientific inquiry in this field.

In this work, using first-principles calculations and Monte Carlo simulations, we investigate the critical (Curie or Néel) temperature $T_{\mathrm{c}}$ and magnetic coupling in two-dimensional multilayer ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6$ (CST). The results indicate that the value of $T_{\mathrm{c}}$ is strongly dependent on thickness. We find that the $T_{\mathrm{c}}$ value of CST increases up to 133 K (bulk CST) from 48 K (monolayer CST), which is significantly greater than that of the homogeneous compounds ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$ and ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. Then, from the perspective of magnetic exchange coupling, it is found that the intralayer ferromagnetic coupling in CST is mostly associated with the competition between direct and superexchange interactions. In particular, the interlayer magnetic coupling is primarily attributed to the supersuperexchange interactions (Cr-Te-Te-Cr) between antiferromagnetically and ferromagnetically coupled multi-nearest neighbors within the layers. In addition, these findings demonstrate that manipulation of the interlayer distance using $z$-directional strain is an efficient way to enhance the $T_{\mathrm{c}}$ value of CST. When the interlayer Cr-Cr distance is decreased to 6.17 Å, the transition temperature of bulk CST increases to 429 K, and an interlayer magnetic coupling transition is observed in which the ferromagnetic layers are coupled antiferromagnetically.

Annealing the collinear antiferromagnet PdMn with excess Pd in a magnetic field produces strongly pinned magnetic moments in the annealing field direction. This behavior can be understood with the help of the magnetic-field-biased diffusion model. Here, the magnetic field creates an energy difference between the two possible occupations of the antiferromagnetic Mn-sublattices by the Pd-excess atoms. This, mediated by diffusion, leads to an imbalance in the amount of the Pd-excess atoms in these sublattices and, subsequently, to an imbalance in the total magnetization of the sublattices. We investigate this effect's dependence on the annealing field, time, and temperature. The results are then compared to the results of the magnetic-field-biased diffusion model, which gives good agreement.

Theoretical analysis of the electronic structure of the high-entropy-type superconductor ${\left(\mathrm{ScZrNb}\right)}_{1-x}{\left(\mathrm{RhPd}\right)}_x, x\in (0.35,0.45)$ is presented. The studied material is a partially ordered CsCl-type structure, with two sublattices, randomly occupied by Sc, Zr, Nb (first sublattice) and Nb, Rh, and Pd (second sublattice). Calculations were done using the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA) and take into account the substitutional disorder. Our total energy calculations confirm the preference for the partially ordered structure over the fully random bcc-type one. Electronic densities of states $N\left(E\right)$, dispersion relations, and McMillan-Hopfield parameters $\eta$ (electronic contribution to electron-phonon coupling) are studied as a function of composition. The computed increasing trends in $N\left(E_F\right)$ and $\eta$ with $x$ are opposite to what we expected based on the experimental results, where the decrease in the critical temperature with increasing $x$ was found. Very strong electron scattering due to disorder is observed, as the electronic dispersion relations are strongly smeared. As a result, the computed electronic lifetimes $\tau$ are very short, leading to a small mean free path of electrons of the order of interatomic distance, which puts ${\left(\mathrm{ScZrNb}\right)}_{1-x}{\left(\mathrm{RhPd}\right)}_x$ near the Mott-Ioffe-Regel limit. The trend in $\tau \left(x\right)$ is similar to the trend observed experimentally in $T_c\left(x\right)$, suggesting that disorder may be the factor that influences $T_c$ in this series of alloys.

We propose an efficient circuit structure of variational quantum circuit Ansätze used for the variational quantum eigensolver (VQE) algorithm in calculating gapped topological phases on the currently feasible noisy intermediate-scale quantum computers. An efficient circuit Ansatz should include two layers: the initialization layer and the variational layer. In the initialization layer, a fixed-depth circuit state with a compatible entanglement structure to the target topological phase is constructed. The circuit state is further adjusted subsequently to capture the details of the local correlations, which is dictated with the Hamiltonian, in the parametrized variational layer. Based on this strategy, we design a circuit Ansatz to investigate the symmetry-protected topological Haldane phase in a nonexactly solvable alternating spin-$\frac{1}{2}$ Heisenberg chain by VQE calculations. Main characterizations of the Haldane phase, including the long-ranged string order, the fourfold nearly degenerate ground states associated with four different localized edge-mode patterns for the system with open boundaries, and the twofold degeneracy of the entanglement spectrum, are all observed for the optimized shallow circuit state with only one-depth variational layer both in numerical simulations and on real quantum computers. We further demonstrate that the computational capacity (i.e., expressibility) of this quantum circuit Ansatz is determined not by the system size but only by the intrinsic correlation length of the system, thus implying that the scalable VQE calculation is possible.

In the creation of Hopf topological matters, the old paradigm is to conceive the Hopf invariant first, and then display its intuitive topology through links. Here we brush aside this effort and put forward a recipe for unraveling the quenched two-dimensional (2D) two-band Chern insulators under a parallel quench protocol, which implies that the quench quantities with different momentum $\mathit{k}$ are parallel or antiparallel to each other. We find that whether the dynamical Hopf invariant exists or not, the links in $(2+1)\mathrm{D}$ space always keep their standard shape even for topological initial states, and trace out the trajectories of phase vortices. The linking number is exactly equal to the difference between pre- and postquench Chern numbers regardless of the construction of homotopy groups. We employ two concrete examples to illustrate these results, highlighting the polarity reversal at fixed points.

We propose an unconventional bulk-edge correspondence for two-dimensional Stiefel-Whitney insulators and Euler insulators, which are topological insulators protected by the $PT$ symmetry. We find that, although the energy spectrum under the open boundary condition is generally gapped, the entanglement spectrum is gapless when the Stiefel-Whitney or Euler class is nonzero. The robustness of the gapless spectrum for Stiefel-Whitney insulator can be understood through an emergent antiunitary particle-hole symmetry. For the Euler insulators, we propose a conjecture, which is supported by our numerical calculation, that the Euler class is equal to the number of crossings in the entanglement spectrum, taking into account the degree of the crossings. We also discuss that these crossings of the entanglement spectrum are related to the gap-closing points in the cutting procedure, which is the energy spectrum as the magnitude of the boundary hopping is varied.

Silicon quantum dot qubits show great promise but suffer from charge noise with a $1/f^{\alpha }$ spectrum, where $f$ is frequency and $\alpha \lesssim 1$. It has recently been proposed that $1/f^{\alpha }$ noise spectra can emerge from a few thermally activated two-level fluctuators in the presence of sub-bath temperature fluctuations associated with a two-dimensional electron gas (2DEG). We investigate this proposal by performing Monte Carlo simulations of a single Ising spin in a bath with a fluctuating temperature. We find that to obtain noise with a $1/f^{\alpha }$ spectrum with $\alpha \lesssim 1$ down to low frequencies, the duration of temperature fluctuations must be comparable to the inverse of the lowest frequency at which the noise is measured. This result is consistent with an analytic calculation in which the fluctuator is a two-state system with dynamics governed by time-dependent switching rates. In this case we find that the noise spectrum follows a Lorentzian at frequencies lower than the inverse of the average duration of the lowest switching rate. We then estimate relaxation times of thermal fluctuations by considering thermal diffusion in an electron gas in a confined geometry. We conclude that temperature fluctuations in a 2DEG sub-bath would require unphysically long durations to be consistent with experimental measurements of $1/f$-like charge noise in quantum dots at frequencies extending well below 1 Hz.

The resonant process of the third-order nonlinear optical response of single-layer graphene has been investigated using various approaches. The complex third-order nonlinear susceptibility (${\chi }^{\left(3\right)}$) directly reflects the resonance effects in third-order nonlinear processes. We measured the modulus and phase of ${\chi }^{\left(3\right)}$ governing the third-harmonic generation (THG) of graphene using the Maker fringe method. First, we observed the incident photon energy dependence of THG in the energy range from 0.57 to 0.81 eV. The modulus values of ${\chi }^{\left(3\right)}$ decreased from $7\times {10}^{-10}$ to $2\times {10}^{-10}$ esu, with an increase in photon energy. The phase values increased from 330 ° to 360 ° in the corresponding energy range. When the experimental result and the model calculation were compared, we found that the THG process in graphene can be described by the superposition of one-, two-, and three-photon resonant components. Experimental results demonstrate that the two-photon resonant process comprising interband and intraband transitions is the most significant among the three components for THG in graphene. Second, we measured the Fermi energy ($E_F$) dependence of THG in the range of $-568\mathrm{meV}\le E_F\le +133\mathrm{meV}$ at incident photon energies of 0.60 and 0.72 eV. The modulus of ${\chi }^{\left(3\right)}$ changed from $5.4\times {10}^{-11}$ to $6.4\times {10}^{-10}$ esu with doping. This result is due to the reduction of the one-photon resonant component by Pauli blocking. The complex ${\chi }^{\left(3\right)}$ has positive real and negative imaginary parts regardless of $E_F$. We also analyzed the laser power dependence of THG intensity via model calculation taking account of the electron temperature. The experimental results and discussion of the complex ${\chi }^{\left(3\right)}$ of graphene can be a basis for understanding nonperturbative harmonic generation and other third-order nonlinear optical responses in Dirac materials.

Particles hopping on a two-dimensional hyperbolic lattice feature unconventional energy spectra and wave functions that provide a largely uncharted platform for topological phases of matter beyond the Euclidean paradigm. Using real-space topological markers as well as Chern numbers defined in the higher-dimensional momentum space of hyperbolic band theory, we construct and investigate hyperbolic Haldane models, which are generalizations of Haldane's honeycomb-lattice model to various hyperbolic lattices. We present a general framework to characterize point-group symmetries in hyperbolic tight-binding models, and use this framework to constrain the multiple first and second Chern numbers in momentum space. We observe several topological gaps characterized by first Chern numbers of value 1 and 2. The momentum-space Chern numbers respect the predicted symmetry constraints and agree with real-space topological markers, indicating a direct connection to observables such as the number of chiral edge modes. With our large repertoire of models, we further demonstrate that the topology of hyperbolic Haldane models is trivialized for lattices with strong negative curvature.

In the average atom (AA) model, the entropy provides a route to compute thermal electronic contributions to the equation of state (EOS). The complete EOS comprises in many modelings an additional 0 K isotherm and a thermal ionic part. Even at low temperature, the AA model is believed to be the best practical approach. However, when it comes to determining the thermal electronic EOS at low temperatures, the numerical implementation of AA models faces convergence issues related to the pressure ionization of bound states. At contrast, the Sommerfeld expansion tells us that the variations with temperature of thermodynamic variables should express in simple terms at these low temperatures. This led us to tackle the AA predictions with respect to the Sommerfeld expansion of the electronic entropy. We performed a comprehensive investigation for various chemical elements belonging to $s, p, d$, and $f$ blocks of the periodic table, at varying densities. This was realized using an inferno-like model since this approach provides the best theoretical framework to address these issues. We found that the Sommerfeld expansion is valid for a ratio of the temperature to the Fermi energy of <0.05. This allows us to extend the study to other atomic numbers at a low enough unique temperature. Comparing the AA results with the free electron gas model, the discrepancies are <10% at very high densities but can reach an order of magnitude at the metal-insulator transition.

The nature of the superconducting pairing state in the pristine phase of the compressed kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ under pressure is studied by the Migdal-Eliashberg formalism and density-functional theory calculations. We find that the superconducting gap distribution driven by electron-phonon coupling is anisotropic and nodeless. It is revealed that the V $3d$ and Sb $5p$ orbitals forming the four Fermi surface sheets are strongly coupled to the V-V bond-stretching and V-Sb bond-bending phonon modes. The resultant superconducting gaps associated with V $3d_{xy,x^2-y^2,z^2}$ and $3d_{xz,yz}$ orbitals is larger in their average magnitude and more widely spread compared to that associated with the Sb $5p_z$ orbital. Meanwhile, we find that unconventional superconductivity driven by electron correlation effects is unlikely because the saddle points at the $M$ point near the Fermi level do not generate van Hove singularities in the total density of states. Our findings demonstrate that the superconductivity of compressed ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ can be explained by the anisotropic multiband pairing mechanism with conventional phonon-mediated $s$-wave symmetry, evidenced by recent experimental observations at ambient pressure and under pressure.

We propose a minimal interacting lattice model for two-dimensional class-$D$ higher-order topological superconductors with no free-fermion counterpart. A Lieb-Schultz-Mattis-type constraint has been proposed and applied to guide our lattice model construction. Our model exhibits a trivial product ground state in the weakly interacting regime, whereas, increasing electron correlations provoke a novel topological quantum phase transition to a $D_4$-symmetric higher-order topological superconducting state. The symmetry-protected Majorana corner modes are numerically confirmed with the matrix-product-state technique. Our theory paves the way for studying correlated higher-order topology with explicit lattice model constructions.

Chiral symmetry (CS) in energy bands appears as perfectly symmetric antibonding and bonding pairs of energy levels. It has only been observed in a few classes of models when bipartite hopping occurs among their pairwise bases. We find that nonbipartite kagome and pyrochlore lattices can host CS when strong spin-orbit coupling is introduced. Unfortunately, the model exhibits an intricate frustrated hopping accompanied by spin rotation with no apparent sign of realizing CS. However, by making use of a local gauge transformation that properly rotates the spin quantization axis site-dependently, complex hopping among up- and down-spin electrons is untangled to bipartite-hopping ones. The clue to find such a transformation and to construct a chiral operator is given by the gauge invariant Wilson loop operator on a triangular unit. The framework allows us to disclose the symmetry and structures of spin-textured CS wave functions and energy bands.