We derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror symmetry with respect to the middle layer. We provide a full symmetry analysis of the noninteracting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high-velocity Dirac fermions, and we identify a hidden nonlocal symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of noninteracting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wave functions and derive the full many-body Hamiltonian of the system. We also provide an efficient parametrization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the $\mathrm{U}\left(2\right)\times \mathrm{U}\left(2\right)$ spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large $\mathrm{U}\left(4\right)\times \mathrm{U}\left(4\right)\times \mathrm{U}\left(4\right)\times \mathrm{U}\left(4\right)$ symmetry in the chiral limit. Moreover, by identifying a symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

Topological spin textures can be found in both two-dimensional and three-dimensional nanostructures, which are of great importance to advanced spintronic applications. Here we report the current-induced skyrmion tube dynamics in three-dimensional synthetic antiferromagnetic (SyAF) bilayer and multilayer nanostructures. It is found that the SyAF skyrmion tube made of thinner sublayer skyrmions is more stable during its motion, which ensures that a higher speed of the skyrmion tube can be reached effectively at larger driving current. In the SyAF multilayer with a given total thickness, the current-induced deformation of the SyAF skyrmion tube decreases with an increasing number of interfaces; namely, the rigidity of the SyAF skyrmion tube with a given thickness increases with the number of ferromagnetic (FM) layers. For the SyAF multilayer with an even number of FM layers, the skyrmion Hall effect can be eliminated when the thicknesses of all FM layers are identical. Larger damping parameter leads to smaller deformation and slower speed of the SyAF skyrmion tube. Larger fieldlike torque leads to larger deformation and a higher speed of the SyAF skyrmion tube. Our results are useful for understanding the dynamic behaviors of three-dimensional topological spin textures and may provide guidelines for building SyAF spintronic devices.

Manipulating the spin degrees of freedom of electrons affords an excellent platform for exploring novel quantum states in condensed-matter physics and material science. Based on first-principles calculations and analysis of crystal symmetries, we propose a fully spin-polarized composite semimetal state, which is combined with the 1D nodal lines and 2D nodal surfaces, in the half-metal material ${\mathrm{CaFeO}}_3$. In the nodal line-surface half-metal, the Baguenaudier-like nodal lines feature six rings linked together, which are protected by the three independent symmetry operations: $\mathcal{PT}, {\mathcal{M}}_y$, and ${\tilde{\mathcal{M}}}_z$. Near the Fermi level, 2D nodal surfaces with fully spin-polarized are guaranteed by the joint operation $\mathcal{T}{\mathcal{S}}_{2i}$ in the $k_{i(i=x,y,z)}=\pi$ plane. Furthermore, high-quality ${\mathrm{CaFeO}}_3$ harbors ultraclean energy dispersion, which is rather robust against strong hydrostatic compressional strain and correlation effect. The realization of the Weyl nodal line-surface half-metal presents great potential for spintronics applications with high-speed and low-power consumption.

Majorana zero modes are attracting a lot of attention as a new kind of emergent quasiparticles in condensed-matter physics. Here we propose a new and striking signature of the coupling between Majorana zero modes in a three-terminal Josephson junction made with topological superconductors. Recently three- and four-terminal junctions made either with conventional or with topological superconductors have been shown to exhibit Weyl crossings in their Andreev spectrum that lead to a nonzero quantized transconductance, like in the quantum Hall effect. In contrast with the other types of junctions, where the effect is limited to certain parameter regimes, we predict that, generically, any three-terminal Josephson junction made with topological superconductors is characterized by such a nonzero quantized transconductance. The quantization value is $\pm 2e^2/h$. Based on numerics, we check that this prediction is robust.

We extract local current distributions from interatomic currents calculated using a fully relativistic quantum mechanical scattering formalism by interpolation onto a three-dimensional grid. The method is illustrated with calculations for $\mathrm{Pt}|\mathrm{Ir}$ and $\mathrm{Pt}|\mathrm{Au}$ multilayers as well as for thin films of Pt and Au that include temperature-dependent lattice disorder. The current flow is studied in the “classical” and “Knudsen” limits determined by the sample thickness relative to the mean free path $\lambda$, introducing current streamlines to visualize the results. For periodic multilayers, our results in the classical limit reveal that transport inside a metal can be described using a single value of resistivity $\rho$ combined with a linear variation of $\rho$ at the interface while the Knudsen limit indicates a strong spatial dependence of $\rho$ inside a metal and an anomalous dip of the current density at the interface which is accentuated in a region where shunting is incomplete.

The family of edge-sharing tricoordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin-liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually preempted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-one-dimensional spin chains. Here we present a resonant inelastic x-ray scattering study of the magnetic excitations of the hyperhoneycomb iridate $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under a magnetic field with a record-high-resolution spectrometer. At low temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16 meV. A 2 T magnetic field softens the dispersion around $\mathbf{Q}=0$. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnonlike mode is superimposed by a broad continuum of excitations, centered around 35 meV and extending up to 100 meV. This high-energy continuum survives up to at least 300 K—well above the ordering temperature of 38 K—and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid.

We analyze recently measured nonlinear photoemission spectra from Ag surfaces that reveal resonances whose energies do not scale with the applied photon energy but stay pinned to multiples of bulk plasmon energy $\hslash {\omega }_p$ above the Fermi level. To elucidate these unexpected and peculiar features we investigate the spectra of plasmons generated in a solid by the optically pumped electronic polarization and their effect on photoemission. By combining quadratic response formalism for calculations of photoemission yield, a nonperturbative approach to inelastic electron scattering, and first-principles calculations for the electronic structure, we demonstrate the dependence of probability amplitude for single- and multiplasmon excitations on the basic parameters characterizing the photon pulse and the system. The resulting multiexcitation spectrum evolves towards a truncated plasmonic coherent state. Analogous concept is extrapolated to interpret plasmon generation by multiphoton excited electronic polarization. Based on this we elaborate a scenario that the thus created real plasmons act as supplementary frequency-locked pump field for non-Einsteinian plasmonically assisted channels of photoemission from metals. The established paradigm enables assignment and assessment of the observed linear $\hslash {\omega }_p$ and nonlinear $2\hslash {\omega }_p$ electron yields from Ag. Such effects may be exploited for selective filtering of optical energy conversion in electronic systems.

The quantum magnetism in a three-singlet model (TSM) with singlet crystalline electric field states interacting on a lattice is investigated, motivated by its appearance in compounds with $4f^2$ and $5f^2$ electronic structures. Contrary to conventional (semiclassical) magnetism, there are no preformed moments above the ordering temperature $T_m$. They appear spontaneously as induced or excitonic moments due to singlet-singlet mixing at $T_m$. In most cases, the transition is of second order, however, for large matrix elements between the excited states, it turns into a first-order transition at a critical point. Furthermore, we derive the excitonic mode spectrum and its quantum critical soft mode behavior, which leads to the criticality condition for induced order as expressed in terms of the control parameters of the TSM, and discuss the distinctions to the previously known two-singlet case. We also derive the temperature dependence of order parameters for second- and first-order transitions and the exciton spectrum in the induced magnetic phase.

The question on whether there exists a unique photoelectron reference plane for a stepped solid surface is discussed on the basis of angle-resolved photoelectron spectroscopy data for Ag films grown on Pt(997). Different step morphologies at the surface and interface, revealed by low-energy electron diffraction measurements, result in distinctly different band dispersions of the $sp$-like quantum well states and of the Shockley surface state. Quantum well standing waves form between the parallel optical surface and interface planes, while the surface state follows the orientation of a local plane tilted with respect to the optical surface. These findings show the connection of the photoelectron reference plane with the local morphology of a solid surface and the spatial extent of the electron wave functions.

We present a comprehensive study of magnon excitations in the tetragonal easy-plane antiferromagnet ${\mathrm{Bi}}_2\mathrm{Cu}{\mathrm{O}}_4$ using inelastic neutron scattering and spin-wave analyses. The nature of low-energy magnons, and hence the anisotropy in this material, has been controversial. We show unambiguously that the low-energy magnon spectrum consists of a gapped and a gapless mode, which we attribute to out-of-plane and in-plane spin fluctuations, respectively. We modeled the observed magnon spectrum using linear spin-wave analysis of a minimal anisotropic spin model motivated by the lattice symmetry. By studying the magnetic field dependence of the (1,0,0) Bragg peak intensity and the in-plane magnon intensity, we observed a spin-flop transition in the $ab$ plane at $\sim 0.4$ T, which directly indicates the existence of a small in-plane anisotropy that is classically forbidden. It is only by taking into account magnon zero-point fluctuations beyond the linear spin-wave approximation that we could explain this in-plane anisotropy and its magnitude, the latter of which is deduced from the critical field of the spin-flop transition. The microscopic origins of the observed anisotropic interactions are also discussed. We found that our data are inconsistent with a large Dzyaloshinskii-Moriya interaction, which suggests a potential departure of ${\mathrm{Bi}}_2\mathrm{Cu}{\mathrm{O}}_4$ from the conventional theories of magnetic anisotropy for other cuprates.

Theory predicts that the application of an electric field breaks the inversion symmetry of AB and BA stacked domains in twisted bilayer graphene, resulting in the formation of a triangular network of one-dimensional valley-protected helical states. This two-dimensional network of one-dimensional states has been observed in several studies, but direct experimental evidence that the electronic transport in these one-dimensional states is valley protected is still lacking. In this paper, we report the existence of the network in small-angle twisted bilayer graphene at room temperature. Moreover, by analyzing Fourier transforms of atomically resolved scanning tunneling microscopy images of minimally twisted bilayer graphene, we provide convincing experimental evidence that the electronic transport in the counterpropagating one-dimensional states is indeed valley protected.

Atomistic spin models are of great value for predicting and understanding the magnetic properties of real materials, and extensions of the existing models open routes to new physics and potential applications. The Dzyaloshinskii-Moriya interaction is the prototype for chiral magnetic interactions, and several recent works have uncovered or proposed various types of generalized chiral interactions. However, in some cases the proposed interactions or their interpretation do not comply with basic principles such as being independent of the magnetic configuration from which they are evaluated, or even obeying time-reversal invariance. In this Letter, we present a simple explanation for the origin of these puzzling findings and point out how to resolve them.

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two noninteracting second-order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge $c=1$ and Luttinger parameter $K=1/2$, like the edge modes of a Laughlin $1/2$ state. The bulk and surface topology is characterized by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host an unconventional two-dimensional topological phase. In a clear departure from the physics of a Laughlin $1/2$ state, we find a TEE per surface compatible with $(ln\sqrt{2})/2$, half that of a Laughlin $1/2$ state. This value cannot be obtained from topological quantum field theory for purely two-dimensional systems. For the sake of completeness, we also investigate the topological degeneracy.

A theory of electrically controlled THz-frequency auto-oscillator, based on a trilayer heterostructure comprised of piezoelectric (PZ) ceramics, an NiO-based antiferromagnet, and a heavy metal (HM), is developed in the framework of the well-established antiferromagnetic (AFM) sigma model. It is assumed that the magnetostrictive antiferromagnet is monocrystalline and monodomain, and has mixed biaxial and cubic anisotropy. The frequency of the antiferromagnetic resonance (AFMR) of the heterostructure in a passive subcritical regime is calculated as a function of the following parameters: the choice of the ceramic PZ material and of its poling direction, modulus and orientation of the static electric field applied to the PZ layer, and the magnitude of the driving electric current injected into the HM layer. It is shown that the AFMR frequency of the heterostructure and the threshold value of the driving current for THz-frequency generation depend on the total AFM anisotropy, which can be substantially reduced by the bias electric field in the case when this field is collinear to the PZ poling direction. It is also shown that the variation of the PZ poling direction in respect to the bias electric field provides an additional degree of freedom that can be used to optimize the performance of AFM-based generators and detectors of THz-frequency signals.

The superconducting gap structure of the topological superconductor candidate ZrRuAs with a noncentrosymmetric crystal structure has been investigated using muon-spin rotation/relaxation ($\mu \mathrm{SR}$) measurements in transverse-field (TF) and zero-field (ZF) geometries. Magnetization, electrical resistivity, and heat capacity measurements reveal bulk superconductivity below a superconducting transition temperature $T_{\mathrm{c}}=7.9\left(1\right)$ K. The temperature dependence of the effective penetration depth obtained from the TF-$\mu \mathrm{SR}$ spectra, and the electronic heat capacity in the superconducting state, are well described by an isotropic $s$-wave gap model. Comparison of the electronic mean free path with the superconducting coherence length suggests superconductivity in the dirty limit. ZF $\mu \mathrm{SR}$ data show there is no significant change in the muon-spin relaxation rate above and below $T_{\mathrm{c}}$, indicating that time-reversal symmetry is preserved in the superconducting state.

In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov–de Gennes (BdG) systems. From our theory, we can calculate the generalized Brillouin zone and the energy spectrum in such systems with open boundary conditions in the thermodynamic limit, and we can thus discuss its non-Hermitian nature, despite Hermiticity of an original Hamiltonian. In fact, we find that the bosonic Kitaev-Majorana chain exhibits rich aspects of the non-Hermitian skin effect, such as instability against infinitesimal perturbations and reentrant behavior, in terms of the non-Bloch band theory. This result indicates that our theory is powerful tool for studying non-Hermitian nature in bosonic BdG systems.

Mechanical strain can generate a pseudomagnetic field, and hence Landau levels (LL), for low-energy excitations of quantum matter in two dimensions. We study the collective state of the fractionalized Majorana fermions arising from residual generic spin interactions in the central LL, where the projected Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and particle-hole symmetries forbid any bilinear couplings, leading to an intrinsically strongly interacting system; also, they allow the definition of a filling fraction, which is fixed at 1/2. We argue that the resulting many-body state is gapless within our numerical accuracy, implying ultra-short-ranged spin correlations, while chirality correlators decay algebraically. This amounts to a Kitaev ‘non-Fermi’ spin liquid and shows that interacting Majorana Fermions can exhibit intricate behavior akin to fractional quantum Hall physics in an insulating magnet.

The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev $\left(K\right)$ interaction and a symmetric off-diagonal $\mathrm{\Gamma }$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$\frac{1}{2}{g}_x\text{−}{g}_{y}K\text{−}\mathrm{\Gamma }$ chain by density-matrix renormalization-group method where $g_x$ and $g_y$ are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane $\left(g_x>g_y\right)$ and odd-Haldane $(g_x<g_y)$ phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped $A_x$ and $A_y$ phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a sixfold degenerate ${\mathrm{FM}}_{U_6}$ phase where all the spins are parallel to one of the $\pm \widehat{x}$, $\pm \widehat{y}$, and $\pm \widehat{z}$ axes in a six-site spin-rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-two spin-nematic ordering in the latter is also discussed.

Colossal magnetoresistance is of great fundamental and technological significance and exists mostly in the manganites and a few other materials. Here we report colossal magnetoresistance that is starkly different from that in all other materials. The stoichiometric ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ is an insulator featuring a ferrimagnetic transition at 78 K. The resistivity drops by seven orders of magnitude with an applied magnetic field above 9 T, leading to an insulator-metal transition at up to 130 K. However, the colossal magnetoresistance occurs only when the magnetic field is applied along the magnetic hard axis and is surprisingly absent when the magnetic field is applied along the magnetic easy axis where magnetization is fully saturated. The anisotropy field separating the easy and hard axes is 13 T, unexpected for the Mn ions with nominally negligible orbital momentum and spin-orbit interactions. Double exchange and Jahn-Teller distortions that drive the hole-doped manganites do not exist in ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$. The phenomena fit no existing models, suggesting a unique, intriguing type of electrical transport.

Electronic band matching at the interface between ferromagnetic (FM) and nonmagnetic (NM) metals has been considered a key factor that affects the spin-dependent transport properties such as giant magnetoresistance (GMR) effect. However, to date, there has not been an experimental explanation on the effect of a few monolayer atomic structures at the FM/NM interface on the band matching with a direct observation of the atomic- and element-resolved interfacial microstructure. In this study, we fabricated fully epitaxial current-perpendicular-to-plane GMR pseudo-spin-valve (PSV) films of half-metallic ${\mathrm{Co}}_2\mathrm{Fe}{\mathrm{Ga}}_{0.5}{\mathrm{Ge}}_{0.5}\left(\mathrm{CFGG}\right)/$ Ag spacer/CFGG structure with very thin (0 to 1 nm thick) Ni insertion layers at the CFGG/Ag interfaces. The MR ratio was significantly enhanced (from 23.1% for the PSV without Ni to 32.5% for that) with 0.21 nm-thick Ni insertion. Through an aberration-corrected scanning transmission electron microscopy (STEM), the state-of-the-art atomic-scale microstructure analysis revealed that the Co atoms in a second termination layer from the Ag interface are replaced with Ni monolayer via insertion of 0.21-nm-thick Ni. Our first-principles calculations of ballistic transmittance for the stacking structures modeled by the STEM images indicated that substituting the Co termination layer with Ni improved electronic band matching of majority spin electrons. This study proves that even a monolayer near the interface critically affects the interfacial band matching and MR properties.