${\mathrm{Sr}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$ is a Ruddlesden-Popper compound with triple Ru-O perovskite layers separated by Sr-O rock-salt layers. This compound presents a rare coexistence of interlayer $(c$-axis) ferromagnetism and intralayer (basal-plane) metamagnetism at ambient pressure. Here we report the observation of pressure-induced, intralayer itinerant antiferromagnetism arising from the interlayer ferromagnetism. The application of modest hydrostatic pressure generates an anisotropy that may cause a flattening and a tilting of ${\mathrm{RuO}}_6$ octahedra. All magnetic and transport results from this study indicate these lattice distortions diminish the $c$-axis ferromagnetism and basal-plane metamagnetism, and induce a basal-plane antiferromagnetic state. The unusually large magnetoelastic coupling and pressure tunability of ${\mathrm{Sr}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$ makes it a model system for studies of itinerant magnetism.

We demonstrate spin pumping, i.e., the generation of a pure spin current by precessing magnetization, without the application of microwave radiation commonly used in spin pumping experiments. We use femtosecond laser pulses to simultaneously launch the magnetization precession in each of two ferromagnetic layers of a galfenol-based spin valve and monitor the temporal evolution of the magnetizations. The spin currents generated by the precession cause a dynamic coupling of the two layers. This coupling has a dissipative character and is especially efficient when the precession frequencies in the two layers are in resonance, where coupled modes with strongly different decay rates are formed.

The interplay between different orders is of fundamental importance in physics. The spontaneous, symmetry-breaking charge order, responsible for the stripe or the nematic phase, has been of great interest in many contexts where strong correlations are present, such as high-temperature superconductivity and the quantum Hall effect. In this Rapid Communication, we show the unexpected result that in an interacting two-dimensional electron system, the robustness of the nematic phase, which represents an order in the charge degree of freedom, not only depends on the orbital index of the topmost, half-filled Landau level, but it is also strongly correlated with the magnetic order of the system. Intriguingly, when the system is fully magnetized, the nematic phase is particularly robust and persists to much higher temperatures compared to the nematic phases observed previously in quantum Hall systems. Our results give fundamental insight into the role of magnetization in stabilizing the nematic phase, while also providing a different knob with which it can be effectively tuned.

Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a well-developed Majorana mode.

Driving a quantum system at finite frequency allows one to explore its dynamics. This has become a well-mastered resource for controlling the quantum state of two-level systems in the context of quantum information processing. However, this can also be of fundamental interest, especially with many-body systems which display an intricate finite-frequency behavior. In condensed matter, the Kondo effect epitomizes strong electronic correlations, but the study of its dynamics and the related scaling laws has remained elusive so far. Here, we fill this gap by studying a carbon-nanotube-based Kondo quantum dot at half filling driven by a microwave signal. Our findings not only confirm long-standing theoretical predictions but also allow us to establish a simple ansatz for the scaling laws on the Kondo problem at finite frequency. More generally, our technique opens a path for understanding the dynamics of complex quantum dot circuits in the context of quantum simulation of strongly correlated electron fluids.

We investigate a topological superconducting wire with balanced gain and loss that is effectively described by the non-Hermitian Kitaev/Majorana chain with parity-time symmetry. This system is shown to possess two distinct types of unconventional edge modes, those with complex energies and nonorthogonal Majorana zero modes. The latter edge modes cause nonlocal particle transport with currents that are localized at the edges and absent in the bulk. This anomalous particle transport results from the interplay between parity-time symmetry (non-Hermiticity) and topological superconductivity.

We study the Kitaev-Heisenberg $\mathrm{\Gamma }\text{−}{\mathrm{\Gamma }}^{\prime }$ model that describes the magnetism in spin-orbit coupled honeycomb lattice Mott insulators. In strong magnetic fields perpendicular to the plane of the lattice ([111] direction) that bring the system into the fully polarized paramagnetic phase, we find that the spin-wave bands carry nontrivial Chern numbers over large regions of the phase diagram, implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of anisotropic terms in the Hamiltonian that do not conserve the number of magnons. Since the effects of interactions are suppressed by the exchange scale divided by the applied field strength, the validity of the single-particle picture is tunable, making paramagnetic phases particularly suitable for the exploration of this physics. Using time-dependent density matrix renormalization group methods and interacting spin-wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field.

With the advancement in synthesizing and analyzing Kitaev materials, the Kitaev-Heisenberg model on the honeycomb lattice has attracted a lot of attention in the last few years. Several variations, which include additional anisotropic interactions as well as response to external magnetic field, have been investigated and many exotic ordered phases have been discussed. On the other hand, quantum spin systems are proving to be a fertile ground to realize and study bosonic analogs of fermionic topological states of matter. Using the spin-wave theory we show that the ferromagnetic phase of the extended Kitaev-Heisenberg model hosts topological excitations. Along the zigzag edge of the honeycomb lattice we find chiral edge states, which are protected by a nonzero Chern number topological invariant. We discuss two different scenarios for the direction of the spin polarization, namely, [001] and [111], which are motivated by possible directions of applied field. Dynamic structure factor, accessible in scattering experiments, is shown to exhibit signatures of these topological edge excitations. Furthermore, we show that in the case of spin polarization in the [001] direction, a topological phase transition occurs once the Kitaev couplings are made anisotropic.

The interplay of charge, spin, and lattice degrees of freedom in matter leads to various forms of ordered states through phase transitions. An important subclass of these phenomena of complex materials is charge ordering (CO), mainly driven by mixed-valence states. We discovered by combining the results of electrical resistivity ($\rho$), specific heat, susceptibility ($\chi$), and single crystal x-ray diffraction (SC-XRD) that ${\mathrm{Na}}_{2.7}{\mathrm{Ru}}_4{\mathrm{O}}_9$ with the monoclinic tunnel type lattice (space group $C2/m$) exhibits an unconventional CO at room temperature while retaining metallicity. The temperature-dependent SC-XRD results show successive phase transitions with superlattice reflections at ${\mathbf{q}}_1=(0,\frac{1}{2},0)$ and ${\mathbf{q}}_2=(0,\frac{1}{3},\frac{1}{3})$ below $T_{\mathrm{C}2}$ (365 K) and only at ${\mathbf{q}}_1=(0,\frac{1}{2},0)$ between $T_{\mathrm{C}2}$ and $T_{\mathrm{C}1}$ (630 K). We interpreted these as evidence for the formation of an unconventional CO. It reveals a strong first-order phase transition in the electrical resistivity at $T_{\mathrm{C}2}$ (cooling) = 345 K and $T_{\mathrm{C}2}$ (heating) = 365 K. We argue that the origin of the phase transition is due to the localized $4d$ Ru electrons. The results of our finding reveal an unique example of ${\mathrm{Ru}}^{3+}/{\mathrm{Ru}}^{4+}$ mixed valance heavy $d^4$ ions.

Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wave packet takes to traverse a Brillouin-zone loop. We introduce a new type of Bloch oscillations whose periodicity is an integer $\left(\mu >1\right)$ multiple of the fundamental period. The period multiplier $\mu$ is a topological invariant protected by the space groups of crystals, which include more than just translational symmetries. For example, $\mu$ divides $n$ for crystals with an $n$-fold rotational or screw symmetry; with a reflection, inversion or glide symmetry, $\mu$ equals two. We identify the commonality underlying all period-multiplied oscillations: the multiband Berry-Zak phases, which encode the holonomy of adiabatic transport of Bloch functions in quasimomentum space, differ pairwise by integer multiples of $2\pi /\mu$. For a class of multiband subspaces whose projected-position operators commute, period multiplication has a complementary explanation through the real space distribution of Wannier functions. This complementarity follows from a one-to-one correspondence between Berry-Zak phases and the centers of Wannier functions. A Wannier description of period multiplication does not always exist, as we exemplify with band subspaces with either a nonzero Chern number or ${\mathbb{Z}}_2$ Kane-Mele topological order. In the former case, we present general constraints between Berry-Zak phases and Chern numbers, as well as introduce a recipe to construct nontrivial Chern bands—by splitting elementary band representations. To help identify band subspaces with $\mu >1$, a general theorem is presented that outputs Zak phases that are symmetry-protected to integer multiples of $2\pi /n$, given the point-group symmetry representation of any gapped band subspace. A cold-atomic experiment that has observed period-multiplied Bloch oscillations is discussed, and directions are provided for future experiments.

We present a fully many-body formulation of topological invariants for various topological phases of fermions protected by antiunitary symmetry, which does not refer to single-particle wave functions. For example, we construct the many-body ${\mathbb{Z}}_2$ topological invariant for time-reversal symmetric topological insulators in two spatial dimensions, which is a many-body counterpart of the Kane-Mele ${\mathbb{Z}}_2$ invariant written in terms of single-particle Bloch wave functions. We show that an important ingredient for the construction of the many-body topological invariants is a fermionic partial transpose, which is basically the standard partial transpose equipped with a sign structure to account for anticommuting property of fermion operators. We also report some basic results on various kinds of pin structures—a key concept behind our strategy for constructing many-body topological invariants—such as the obstructions, isomorphism classes, and Dirac quantization conditions.

A class of orbital-dependent exchange-correlation potentials for applications in noncollinear spin-density-functional theory is developed. Starting from the optimized effective potential formalism for the exact exchange potential—generalized to the noncollinear case—correlation effects are added via a self-consistent procedure inspired by the Singwi-Tosi-Land-Sjölander method. The orbital-dependent exchange-correlation potentials are applied to the Hubbard dimer in uniform and noncollinear magnetic fields and compared to exact diagonalization and to the Bethe-ansatz local spin-density approximation. The Singwi-Tosi-Land-Sjölander method gives the overall best performance for total energies, densities, and magnetizations, particularly in the weakly to moderately correlated regime.

Quantum collapse of a small skyrmion in a thin magnetic film with Dzyalishinskii-Moriya (DMI) interaction has been studied. The energy of the skyrmion and the stability threshold determined by the DMI, the external magnetic field, and the underlying atomic lattice are investigated analytically and numerically. The Lagrangian describing the coupled dynamics of the skyrmion size and the chirality angle is derived. Equations of motion possess an instanton solution that corresponds to the skyrmion underbarrier contraction via quantum tunneling with subsequent collapse and decay of the topological charge. The tunneling rate is computed and the conditions needed to observe quantum collapse of a skyrmion in a magnetic film are discussed.

The perovskite ruthenate ${\mathrm{CaRuO}}_3$ has attracted considerable interest due to reports of possible non-Fermi-liquid behavior and its proximity to a magnetic quantum critical point, yet its ground state and electronic structure remain enigmatic. Here, we report measurements of the Fermi surface and quasiparticle dispersion in ${\mathrm{CaRuO}}_3$ through a combination of oxide molecular beam epitaxy and in situ angle-resolved photoemission spectroscopy. Our results reveal a complex and anisotropic Fermi surface consisting of small electron pockets and straight segments, consistent with the bulk orthorhombic crystal structure with large octahedral rotations. We observe a strongly band-dependent mass renormalization, with prominent heavy quasiparticle bands which lie close to the Fermi energy and exhibit a strong temperature dependence. These results are consistent with a heavy Fermi liquid with a complex fermiology and small hybridization gaps near the Fermi energy. Our results provide a unified framework for explaining previous experimental results on ${\mathrm{CaRuO}}_3$, such as its unusual optical conductivity, and demonstrate the importance of octahedral rotations in determining the quasiparticle band structure, and electron correlations in complex transition-metal oxides.

We report the observation of the three-dimensional angular dependence of the spin Hall magnetoresistance (SMR) in a bilayer of the epitaxial antiferromagnetic insulator NiO(001) and the heavy metal Pt, without any ferromagnetic element. The detected angular-dependent longitudinal and transverse magnetoresistances are measured by rotating the sample in magnetic fields up to 11 T, along three orthogonal planes ($xy$-, $yz$-, and $xz$-rotation planes, where the $z$ axis is orthogonal to the sample plane). The total magnetoresistance has contributions arising from both the SMR and ordinary magnetoresistance. The onset of the SMR signal occurs between 1 and 3 T and no saturation is visible up to 11 T. The three-dimensional angular dependence of the SMR can be explained by a model considering the reversible field-induced redistribution of magnetostrictive antiferromagnetic S and T domains in the NiO(001), stemming from the competition between the Zeeman energy and the elastic clamping effect of the nonmagnetic MgO substrate. From the observed SMR ratio, we estimate the spin mixing conductance at the NiO/Pt interface to be greater than $2\times {10}^{14}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$. Our results demonstrate the possibility to electrically detect the Néel vector direction in stable NiO(001) thin films, for rotations in the $xy$ and $xz$ planes. Moreover, we show that a careful subtraction of the ordinary magnetoresistance contribution is crucial to correctly estimate the amplitude of the SMR.

We investigate the Josephson radiation of nanowire (NW)-based Josephson junctions in a parallel magnetic field. The Josephson junction made of an InAs NW with superconducting Al leads shows the emission spectra which follow the Josephson frequency over the range 4–8 GHz at zero magnetic field. We observe an apparent deviation of the emission spectra from the Josephson frequency which is accompanied by a strong enhancement of the switching current above a magnetic field of $\sim 300$ mT. The observed modulations can be understood to reflect trivial changes in the superconducting circuit surrounding the device which is strongly affected by the applied magnetic field. Our findings will provide a way to accurately investigate topological properties in NW-based systems.

We have performed angle-resolved photoemission spectroscopy of ${\mathrm{AlB}}_2$ which is isostructural to high-temperature superconductor ${\mathrm{MgB}}_2$. Using soft-x-ray photons, we accurately determined the three-dimensional bulk band structure and found a highly anisotropic Dirac-cone band at the $K$ point in the bulk hexagonal Brillouin zone. This band disperses downward on approaching the $H$ point while keeping its degeneracy at the Dirac point, producing a characteristic Dirac nodal line along the $KH$ line. We also found that the band structure of ${\mathrm{AlB}}_2$ is regarded as a heavily electron-doped version of ${\mathrm{MgB}}_2$ and is therefore well suited for fully visualizing the predicted Dirac nodal line. The present results suggest that the $(\mathrm{Al},\mathrm{Mg}){\mathrm{B}}_2$ system is a promising platform for studying the interplay among the Dirac nodal line, carrier doping, and possible topological superconducting properties.

The entanglement in a quantum system that possesses an internal symmetry, characterized by the $S^z$ magnetization or $U\left(1\right)$ charge, is distributed among different sectors. The aim of this Rapid Communication is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one-dimensional systems. Surprisingly, we find that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term that depends on the central charge $c$, minus a double logarithmic correction related to the zero-temperature susceptibility. This result provides a method to estimate simultaneously the central charge $c$ and the critical exponents of $U\left(1\right)$-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-$\frac{1}{2}$ quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.

Quenched randomness can have a dramatic effect on the dynamics of isolated 1D quantum many-body systems, even for systems that thermalize. This is because transport, entanglement, and operator spreading can be hindered by “Griffiths” rare regions, which locally resemble the many-body-localized phase and thus act as weak links. We propose coarse-grained models for entanglement growth and for the spreading of quantum operators in the presence of such weak links. We also examine entanglement growth across a single weak link numerically. We show that these weak links have a stronger effect on entanglement growth than previously assumed: entanglement growth is subballistic whenever such weak links have a power-law probability distribution at low couplings, i.e., throughout the entire thermal Griffiths phase. We argue that the probability distribution of the entanglement entropy across a cut can be understood from a simple picture in terms of a classical surface growth model. We also discuss spreading of operators and conserved quantities. Surprisingly, the four length scales associated with (i) production of entanglement, (ii) spreading of conserved quantities, (iii) spreading of operators, and (iv) the width of the “front” of a spreading operator, are characterized by dynamical exponents that in general are all distinct. Our numerical analysis of entanglement growth between weakly coupled systems may be of independent interest.

We study experimentally and theoretically the exciton-phonon interaction in ${\mathrm{MoSe}}_2$ monolayers encapsulated in hexagonal BN, which has an important impact on both optical absorption and emission processes. The exciton transition linewidth down to 1 meV at low temperatures makes it possible to observe high-energy tails in absorption and emission extending over several meV, not masked by inhomogeneous broadening. We develop an analytical theory of the exciton-phonon interaction accounting for the deformation potential induced by the longitudinal acoustic phonons, which plays an important role in exciton formation. The theory allows fitting absorption and emission spectra and permits estimating the deformation potential in ${\mathrm{MoSe}}_2$ monolayers. We underline the reasons why exciton-phonon coupling is much stronger in two-dimensional transition metal dichalcogenides as compared to conventional quantum well structures. The importance of exciton-phonon interactions is further highlighted by the observation of a multitude of Raman features in the photoluminescence excitation experiments.