We systematically investigate the Ni-Fe layer thickness ($t$) dependence of the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE). The AHE and ANE show different behavior in the $t$ dependence; the sign of the anomalous Hall resistivity changes around $t=9\mathrm{nm}$, whereas the anomalous Nernst coefficient ($S_{\mathrm{ANE}}$) keeps almost constant regardless of $t$, namely, no sign change of $S_{\mathrm{ANE}}$ with $t$. We analyze $S_{\mathrm{ANE}}$ and separate it into the contribution coming from the transverse thermoelectric conductivity (${\alpha }_{xy}$) and the AHE contribution coming from the Seebeck effect. The detailed analysis for $S_{\mathrm{ANE}}$ concludes that the AHE contribution is negligibly small and ${\alpha }_{xy}$, which is related to the anomalous Hall conductivity (${\sigma }_{xy}$) via the Mott relation, is also independent of $t$. To gain insight into the difference in the $t$ dependence of ${\sigma }_{xy}$ and ${\alpha }_{xy}$, we clarify the origin of sign reversal in the AHE. The sign reversal in the AHE is attributed to the competing contribution of the different sources of the AHE: the extrinsic and intrinsic mechanisms. The present experimental finding of the difference between the $t$ dependence on ${\sigma }_{xy}$ and ${\alpha }_{xy}$ suggests that the relative degree between the extrinsic and intrinsic processes for the AHE is quite different from that for the ANE in the case of Ni-Fe.

Ultrafast photoexcitation can induce a nonequilibrium dynamic with electron-lattice interaction, offering an effective way to study photoinduced phase transitions (PIPTs) in solids. The issue that atomic displacements after photoexcitation belong to a coherent change or disordered process has become controversial in the PIPT community. Using real-time, time-dependent density functional theory (rt-TDDFT) simulations, we obtained both the coherent and the disordered PIPTs (dimer dissociation) in ${\mathrm{IrTe}}_2$ with different electronic occupations. More importantly, we found that in the disordered phase transition there exists a local correlation between different dimers regarding their dissociation status. We define these Ir-Ir dimers directly connected by Te atoms, including intralayer and vertically across the layers, as a group (group I). Other Ir-Ir dimers separated by five Ir atoms from Ir-Ir dimers in group I are divided into another group (group II). The dimers in the same group will dissociate in a correlated fashion; they either all dissociate or all do not dissociate. On the other hand, the dimers in neighboring groups will have an anticorrelation: If the dimers in one group dissociate, the dimers in the neighboring group tend not to be dissociated, and vice versa.

Out-of-time-order correlators (OTOC) in the Ising Floquet system, which can be both integrable and nonintegrable, are studied. Instead of localized spin observables, we study contiguous symmetric blocks of spins or random operators localized on these blocks as observables. We find only power-law growth of OTOC in both integrable and nonintegrable regimes. In the nonintegrable regime, beyond the scrambling time, there is an exponential saturation of the OTOC to values consistent with random matrix theory. This motivates the use of “prescrambled” random block operators as observables. A pure exponential saturation of OTOC in both integrable and nonintegrable system is observed, without a scrambling phase. Averaging over random observables from the Gaussian unitary ensemble, the OTOC is found to be exactly same as the operator entanglement entropy, whose exponential saturation has been observed in previous studies of such spin chains.

Since the beginning of the century, the possibility of having chiral spin textures in magnetic materials has been the subject of intense scientific interest. Chiral spin textures have been observed experimentally and described theoretically, bearing potential applications associated with their topological nature. This work theoretically explores the formation of chiral magnetic order in ultrathin magnetic films, where the antisymmetric Dzyaloshinskii-Moriya interaction induces a conical helix magnetization. By minimizing the internal energy of the helix, a simple model predicts the nucleation field, the pitch vector, and the cone angle that characterize the ground-state magnetization texture. It is further demonstrated that the formation of the helical order is connected with the spin waves excited close to the instability of the field-polarized state. Namely, when an in-plane magnetic field is reduced from saturation, a second-order phase transition arises when the spin-wave frequency approaches zero at a critical point where the conical helix nucleates. Interestingly, the wave vector at which the frequency becomes zero matches the pitch vector of the conical helix texture. Thus the instability point of the magnonic excitations is associated with the spin texture, as if the softened spin-wave modes crystallize in the chiral magnetic film. A critical competition among the magnetostatic and the anisotropy field is also found which influences the orbit described by a dynamic magnetization, changing it from circular to elliptical.

The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semiclassical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the $1/N$ expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in $1/N$, which must be accounted for to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.

A periodic array of topological spin textures, such as skyrmions and hedgehogs, is called the multiple-$Q$ spin texture, as it is represented by a superposition of multiple spin density waves. Depending on the way of superposition, not only the magnetic but also the topological properties are modified, leading to a variety of quantum transport and optical phenomena caused by the emergent electromagnetic fields through the Berry phase. Among others, the phase degree of freedom of the superposed waves is potentially important for such modifications, but its effect has not been fully investigated thus far. Here we perform systematic theoretical analyses of magnetic and topological properties of the multiple-$Q$ spin textures with the phase degree of freedom in two and three dimensions. By introducing a hyperspace with an additional dimension corresponding to the phase degree of freedom, we establish a generic framework to deal with the phase shift in the multiple-$Q$ spin textures. Using the hyperspace representation, we elaborate the complete topological phase diagrams for the superpositions of three proper screws or sinusoidal waves in two dimensions and those of four in three dimensions. In the two-dimensional case, we find that the phase shift as well as the magnetization change can yield the skyrmion lattices with the skyrmion number of $-2$, $-1$, 1, and 2, corresponding to the evolution of the Dirac strings connecting hedgehogs and antihedgehogs in the three-dimensional hyperspace. We show that the high skyrmion numbers $\pm 2$ appear in wider parameter regions for the sinusoidal superpositions than the screw ones. Meanwhile, in the three-dimensional case, we clarify that the topological phase diagrams include various types of the hedgehog lattices whose total number of hedgehogs and antihedgehogs ranges up to 48 in a cubic unit. Interestingly, the phase shift can generate unusual Dirac strings running on the horizontal planes perpendicular to the magnetization direction, which gives rise to unconventional pair creation of hedgehogs and antihedgehogs while increasing the magnetization in the case of the screw superpositions. We also show that the amplitude of the emergent magnetic field is maximized by fusion of hedgehogs and antihedgehogs on the horizontal Dirac strings in both proper screw and sinusoidal cases. In addition, by analyzing the numerical data in the previous studies, we demonstrate that phase shifts are indeed caused by an external magnetic field, associated with the topological transitions in the multiple-$Q$ spin textures. Our results illuminate the topological aspects of the skyrmion and hedgehog lattices with the phase degree of freedom, which would be extended to other multiple-$Q$ textures and useful for the exploration of topologically nontrivial magnetic phases and exotic quantum phenomena.

Majorana zero modes are quasiparticles that hold promise as building blocks for topological quantum computing. However, the litmus test for their detection, the observation of exotic non-Abelian statistics revealed by braiding, has so far eluded experimental efforts. Here, we take advantage of the fact that skyrmion-vortex pairs in superconductor-ferromagnet heterostructures harboring Majorana zero modes can be easily manipulated in two spatial dimensions. We adiabatically braid the hybrid topological structures and explicitly confirm the non-Abelian statistics of the Majorana zero modes numerically using a self-consistent calculation of the superconducting order parameter. Our proposal of controlling skyrmion-vortex pairs provides the necessary leeway toward a scalable topological quantum computing platform.

We use angle-resolved photoemission spectroscopy to revisit the electronic structure of BiTeI, previously identified as a polar semiconductor with giant bulk Rashba splitting. We propose an alternative description, which is based on the experimentally determined crystal structure and agrees well with resistivity, quantum oscillations,and optical measurements. BiTeI emerges as a topological 3D Dirac semimetal hosting only two, well isolated from each other and rest of the band structure, Dirac points. Properly doped bulk material or the controlled synthesis of iodine-terminated surface of the pristine material promise to become a canonical condensed matter system whose physical properties are completely defined by the behavior of fourfold fermions.

We have studied ultrafast dynamics of thin films of ${\mathrm{LaCoO}}_3$ and ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{CoO}}_3$ with femtosecond pump-probe ellipsometry in the energy range of 1.6–3.4 eV. We have observed a large pump-induced transfer of spectral weight in ${\mathrm{LaCoO}}_3$ that corresponds to an insulator-to-metal transition. The photoinduced metallic state initially relaxes via a fast process with a decay constant of about 200 fs. Both ${\mathrm{LaCoO}}_3$ and ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{CoO}}_3$ exhibit a significant secondary peak in the 1–30 ps range. Results of measurements on films with different thicknesses demonstrate that it corresponds to a propagation of an acoustic strain pulse. On timescales longer than 100 ps, heat diffusion to the substrate takes place that can be modeled with a biexponential decay.

Density functional theory has revolutionised our understanding of dense, strongly coupled systems in the condensed-matter limit. At elevated temperatures, such as those found in warm dense matter and dense plasma, the computational cost of calculating enough states to accurately describe a thermal ensemble of electrons is a major obstacle to practical Kohn-Sham calculations. This problem has recently been tackled from a number of approaches, including a plane-wave approximation for electrons at high energy. In this work, we demonstrate how the Thomas-Fermi density of states, equivalent to a local plane-wave approximation, can yield improved results for thermodynamic quantities, electron density profiles, and interatomic forces while requiring fewer states than existing methods.

We present an efficient basis for imaginary time Green's functions based on a low-rank decomposition of the spectral Lehmann representation. The basis functions are simply a set of well-chosen exponentials, so the corresponding expansion may be thought of as a discrete form of the Lehmann representation using an effective spectral density which is a sum of $\delta$ functions. The basis is determined only by an upper bound on the product $\beta {\omega }_{max}$, with $\beta$ the inverse temperature and ${\omega }_{max}$ an energy cutoff, and a user-defined error tolerance $\epsilon$. The number $r$ of basis functions scales as $O(log\left(\beta {\omega }_{max}\right)log(1/\epsilon ))$. The discrete Lehmann representation of a particular imaginary time Green's function can be recovered by interpolation at a set of $r$ imaginary time nodes. Both the basis functions and the interpolation nodes can be obtained rapidly using standard numerical linear algebra routines. Due to the simple form of the basis, the discrete Lehmann representation of a Green's function can be explicitly transformed to the Matsubara frequency domain, or obtained directly by interpolation on a Matsubara frequency grid. We benchmark the efficiency of the representation on simple cases, and with a high-precision solution of the Sachdev-Ye-Kitaev equation at low temperature. We compare our approach with the related intermediate representation method, and introduce an improved algorithm to build the intermediate representation basis and a corresponding sampling grid.

This work aims at addressing an important advanced methodology for twisted graphene in the presence of applied magnetic field, which is the Bloch-basis tight-binding model (TBM) in conjunction with the generalized Peierls substitution. We investigate extensively the band structures, Landau levels (LLs), and quantum Hall conductivity (QHC) of twisted bilayer graphene and twisted double-bilayer graphene, as well as their dependence on the twist angle. Comparison between these crucial properties of monolayer graphene, Bernal bilayer graphene, and the twisted systems is carefully made to highlight the roles played by twisting. The unique selection rules of inter-LL transition, which is crucial for achieving a deep understanding of the step structures of QHC, are identified through the properties of LL wave functions. The effective TBM is combined with the generalized Peierls substitution to investigate the magnetic quantization of twisted graphene systems at magic angle. Our theoretical model opens up an opportunity for comprehension of the interplay between an applied magnetic field and the twisting effect associated with layered graphene. The proposed method is expected to be applicable for the calculation of magnetic quantization problems of other complex systems.

Transmission electron microscopy characterization may damage materials, but an electron beam can also induce interesting dynamics. Elastic knock-on is the main electron irradiation damage mechanism in metals including graphene, and although atomic vibrations influence its cross section, only the out-of-plane direction has been considered so far. Here, we present a full three-dimensional first-principles theory of knock-on displacements including the effect of temperature on vibrations to describe dynamics into arbitrary directions. We validate the model with previously precisely measured knock-on damage of pristine graphene, where we show that the isotropic out-of-plane approximation correctly describes the cross section. We then apply our methodology to reversible jumps of pyridinic nitrogen atoms, whose probability under irradiation is measured at 55 and 60 keV. Direct displacement requiring a high emission angle and an alternative pathway via intermittent N adatom creation and recombination are computationally explored but are unable to explain the observed rates, implying stronger inelastic effects at the defect than in pristine graphene.

Kane fermions are characterized by a linear Dirac cone intersecting with a flat band, resembling a pseudo-spin-1 Dirac semimetal. Similar to relativistic Dirac fermions, Kane fermions satisfy a linear energy-momentum relation and can be classified as being pseudorelativistic. Unlike Dirac fermions, they are not protected by symmetry or by topology, but respect time-reversal symmetry, and can emerge by suitable band engineering, for example, in mercury-telluride compounds. Here we discuss the reminiscences of Berry-phase physics in Kane fermions that emerge in the presence of broken time-reversal symmetry. We discuss anomalous transport in Kane fermions and show its similarity to transport in a Dirac semimetal. Furthermore, we study anisotropy in their response that can be probed in current experiments.

We report on the theoretical electronic spectra of twisted phosphorene bilayers exhibiting moiré patterns, as computed by means of a continuous approximation to the moiré superlattice Hamiltonian. Our model is constructed by interpolating between effective $\mathrm{\Gamma }$-point conduction- and valence-band Hamiltonians for the different stacking configurations approximately realized across the moiré supercell, formulated on symmetry grounds. We predict the realization of three distinct regimes for $\mathrm{\Gamma }$-point electrons and holes at different twist angle ranges: a Hubbard regime for small twist angles $\theta <2^{\circ }$, where the electronic states form arrays of quantum-dot-like states, one per moiré supercell; a Tomonaga-Luttinger regime at intermediate twist angles $2^{\circ }<\theta \lesssim {10}^{\circ }$, characterized by the appearance of arrays of quasi-1D states; and, finally, a ballistic regime at large twist angles $\theta \gtrsim {10}^{\circ }$, where the band-edge states are delocalized, with dispersion anisotropies modulated by the twist angle. Our method correctly reproduces recent results based on large-scale ab initio calculations at a much lower computational cost and with fewer restrictions on the twist angles considered.

The magnetic proximity effect is an imperative tool to comprehend the valley contrasting quantum anomalous Hall (QAH) effect in van der Waals (vdW) heterostructure. The introduction of magnetic exchange and spin orbit interaction together enables to realize topological phases, with a particular emphasis on an interface can be envisioned towards dissipationless electronics. Herein, the proximity coupled valley contrasting QAH effect is predicted in vdW heterostructure consisting of graphene and a ferromagnetic (FM) semiconductor ${\mathrm{CrBr}}_3$ with the implication of relativistic effect, from the ab initio density functional theory (DFT) simulation. The valley contrasting QAH effect is observed with a nonzero Chern number at a high-symmetry point stemming from Berry curvature and Wannier charge center (WCC), leading to a topologically nontrivial state. The occurrence of strong magnetic proximity coupling between graphene and ${\mathrm{CrBr}}_3$ monolayer is realized intrinsically, from shifting of Hall coefficient value near Fermi level. The opening of the global band gap (178 meV) is observed with the inclusion of spin orbit coupling (SOC). The anomalous Hall conductivity (AHC) demonstrates the presence of two maxima peaked at valley $K^{\prime }$ and $K$. The observation of AHC is mainly dominated by nonzero surface charge and localized potential at the heterointerface due to proximity interaction. The Fermi level is found to be located exactly inside the nontrivial global band gap, which can be tuned effectively by applying the external electric field or by introducing a staggered sublattice potential. This robustness makes experimental fabrication highly favorable for developing a valley contrasting QAH device prototype.

We bring together the semiclassical approximation, matrix integrals, and the theory of symmetric polynomials in order to solve a long-standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are present and the number of open channels $M$ is small. In contrast to previous approaches, ours is nonperturbative in $M$; instead, we arrive at an explicit expression in the form of a power series in the barrier's reflectivity, whose coefficients are rational functions of $M$. For higher moments we must require that the barriers are equal and time reversal symmetry is broken, but for conductance we treat the general situation. For equal barriers our method accounts for exponentially small nonperturbative terms, which we call superweak corrections, that were not accessible to previous semiclassical approaches. We also show how to include more than two leads in the system.

Experiments in doped transition metal oxides often show suppression in the single-particle density of states at the Fermi level, but disorder-induced zero-bias anomalies in strongly correlated systems remain poorly understood. Numerical studies of the Anderson-Hubbard model have identified a zero-bias anomaly that is unique to strongly correlated materials, with a width proportional to the intersite hopping amplitude $t$ [S. Chiesa, P. B. Chakraborty, W. E. Pickett, and R. T. Scalettar, Phys. Rev. Lett. 101, 086401 (2008)]. In ensembles of two-site systems, a zero-bias anomaly with the same parameter dependence also occurs, suggesting a similar physical origin R. Wortis and W. A. Atkinson, Phys. Rev. B 82, 073107 (2010)]. We describe how this kinetic-energy-driven zero-bias anomaly in ensembles of two-site systems may be seen in a mesoscopic realization based on double quantum dots. Moreover, the double-quantum-dot measurements provide access not only to the ensemble-average density of states but also to the details of the transitions which give rise to the zero-bias anomaly.