The Weyl fermion – originally proposed to describe neutrinos – arises in a topological semimetallic phase in condensed matter systems, exhibiting such novel properties as surface Fermi arcs and a chiral anomaly. Although Weyl fermions have been observed, it is challenging to find materials that exhibit them near the Fermi level. The authors prove that Weyl fermions can be created in band-inverted materials in a large class of crystal systems by applying a magnetic field along various symmetry axes of the crystal. As the field direction is changed, the Weyl points move in momentum space, during which time pairs are created and annihilated. However, in the highly symmetric $T_d$ point group, the Weyl points cannot completely disappear: at least one pair must remain for any direction of the magnetic field. Furthermore, a semiclassical analysis shows that the magnetoresistance scales differently for Weyl fermions created by a magnetic field compared to intrinsic Weyl points. The ability to create Weyl fermions will lead to new material candidates in these crystal systems; controlling their positions opens the possibility to track and manipulate Fermi arcs.

Skyrmions, swirling magnetic textures with a topological character, have been gaining much attention in spintronics due to the fundamental interest as well as their touted utility as information carriers in ultradense and low-power memory devices. Generally, a skyrmion behaves as a massive particle moving in a viscous medium and experiencing a Magnus force, which is proportional to its winding number and the spin polarization of the magnet. There is a class of tunable ferrimagnets, such as rare-earth transition-metal alloys, exhibiting the angular momentum compensation point at which the spin density changes sign. This raises the possibility to engineer both the magnitude and the sign of the Magnus force acting on the skyrmions in the ferrimagnets. The authors exploit this to suggest that ferrimagnetic skyrmions can exhibit snake trajectories along the line of the vanishing spin density, analogous to the snake orbits of electrons in a nonuniform magnetic field. This can be utilized as dynamically self-focusing racetracks for skyrmions, paving the way for skyrmion-based memory devices.

Quantum effects in magnetic materials are prevalent when the magnetic ions support spin-½ moments, as in Cu${}^{2+}$-based materials. Strong quantum effects can also be achieved when the large angular momentum states are reduced to an effective spin-½ subspace ($S_{\text{eff}}$=½) by the combined effect of spin-orbit coupling and the crystal electric field. A consequence of this is the introduction of anisotropy to the g tensor and the effective exchange interactions. Such anisotropic $S_{\text{eff}}$=½ models have recently been applied successfully to rare-earth based frustrated pyrochlore materials, where they are found to lead to particularly rich phenomenology for XY-like $g$ tensors. Here, it is shown that a similar quantum model should apply to the recently discovered “high temperature” Co${}^{2+}$ pyrochlores, NaCaCo${}_2$F${}_7$ and NaSrCo${}_2$F${}_7$, based on a fit to their single ion levels as measured via inelastic neutron scattering. The effect of the intrinsic crystalline disorder on the anisotropy of the $S_{\text{eff}}$=½ moments in these materials is also estimated.

This work studies the manipulation of photoelectron emission from metallic nanostructures by intense single-cycle terahertz transients. Specifically, the authors employ streaking spectroscopy to study the kinetic energy of photoelectrons emitted from metal nanotips exposed to tailored static and terahertz electrical fields. Supported by detailed numerical simulations, the measurements provide quantitative information on the temporal and spatial properties of terahertz near fields at metal nanotips. The study illustrates far-reaching control over the trajectories and phase-space density evolution of photoelectron wavepackets acted upon by strong static and dynamic near fields. The results are relevant for applications of nanoscopic photoelectron sources employed in ultrafast electron diffraction and microscopy.

In ferromagnetic layers, spin-wave modes can be excited by a laser pulse launching the magnetization out of equilibrium and into precession. The trajectory of the magnetization vector can be fully reconstructed using different magneto-optical effects, generally admitted to give a faithful picture of the dynamics. The authors show that this is not always the case and that magneto-optical effects can indeed be deceiving. For this, they study the case of a weakly absorbing ferromagnet, the semiconductor GaMnAs, in which perpendicular standing spin waves are excited by a laser pulse. Quite counterintuitively, the optical detection shows the first two excited modes to be of opposite chirality, whereas theory tells us the spin waves actually rotate in the same direction. The paper demonstrates that this unexpected and surprising effect is a pure optical illusion. It can perfectly be explained by taking into account absorption and optical phase shift inside the layer, the latter being particularly strong in weakly absorbing layers. These results provide a correct identification of spin-wave modes, enabling a trustworthy estimation of their respective weight as well as an unambiguous determination of the spin stiffness parameter.

Topological pumping, which was originally proposed by Thouless, is a beautiful manifestation of quantum effects in transport phenomena. Thouless’s topological pumping is characterized by the topology of Bloch states in the space of momentum and time, and can be viewed as a dynamical analog of the integer quantum Hall effect of noninteracting fermions. Here, the authors propose a systematic procedure to construct nontrivial classes of topological pumping from strongly correlated quantum Hall states on a thin torus. In particular, this procedure is applied to the bosonic integer quantum Hall (BIQH) state formed by two species of bosons. The BIQH state is an example of a symmetry-protected topological (SPT) state of interacting bosons, and is characterized by nontrivial Hall responses. The authors find that the thin-torus counterpart of the BIQH state is the Haldane state of emergent spin-1 degrees of freedom, which is also a SPT state. The authors further show that an adiabatic change between the Haldane phase and trivial Mott insulators constitute an “off-diagonal” topological pumping, in which the translation of the lattice potential for one component induces a current in the other.

In a set of papers, the authors present a comprehensive investigation of the magnetic, structural, and dynamic properties of thin film Ni-Co, Ni-Fe, and Co-Fe alloys and uncover new phenomena in systems previously thought to be well understood and commonplace. High-precision measurements of saturation magnetization, effective magnetization, spectroscopic $g$ factor, inhomogeneous linewidth broadening, and damping are performed, allowing precise testing of \textit{ab initio} calculations for the orbital magnetic moment and the intrinsic magnetic damping, which is the most integral motivation of this work. Quantitative comparison between experiment and theory is shown and discussed for magnetic damping spanning a broad range of material parameters. Furthermore, a large set of data has been created that will serve as a glossary for alloy magnetic properties in thin films.

One of the challenges in quantum information science is to achieve ultralong spin coherence in naturally grown solid-state systems. So far, isotope engineering is generally needed to suppress the main relaxation mechanism caused by the interaction with nuclear spins. The authors demonstrate here that this ambitious goal can be achieved in binary compounds with natural isotope abundance too. They attain a spin-locked subspace with a drastically reduced spin-decoherence rate through the combination of two effects. First, the suppression of heteronuclear spin cross-talk is achieved by applying a moderate magnetic field. This leads to two dilute and weakly interacting spin baths. Second, because the interaction between nuclei becomes weak, the mutual spin flip-flop processes occur at lower rate, which can be viewed as a reduction of the high-frequency part of the noise spectrum. As a result, dynamic decoupling protocols demonstrate high performance. Using this approach, the authors are able to preserve a coherent spin superposition above 20 ms, which is an improvement by more than one order of magnitude compared to the earlier reported value in SiC.

The historical origins of topological effects in wave equations can be traced to the relativistic Dirac equation, which includes fundamental symmetries related, for example, to spin and charge. Dirac devised his equation to eliminate the deficiencies of a previous theory, and achieved this by effectively taking the square root of the corresponding wave equation. Here, the authors explore the analogue of these considerations for tight-binding models. They show that starting from a suitable parent system, the square-root operation can induce nontrivial topological effects when it reduces the crystal symmetry, as this makes room for additional independent components and emerging fundamental symmetries. The resulting models display an enriched band structure, including additional gaps and controls to induce states into them. These models retain their scope for practical implementations, as the authors explore in the setting of silicon photonics.

Vortices are known to nucleate when classical fluids or superfluids flow past an impenetrable obstacle. Solid-state planar ferromagnets are manifestly not fluids, but their magnetization dynamics can be formulated in terms of dispersive hydrodynamic equations that exhibit peculiar properties such as broken Galilean invariance and support large-amplitude spin-density waves. Here, the authors leverage this fluid interpretation of magnetization dynamics to explore novel large-amplitude nonlinear states. The fluidlike behavior of magnetization dynamics includes quantized vortex-antivortex pair shedding at subsonic conditions and the formation of nonlinear wavefronts and a Mach cone at supersonic conditions. These results are observed both when a spin-density wave interacts with a static obstacle and when an obstacle moves across a homogeneously magnetized ferromagnet. Qualitative agreement with observations in superfluids and quantitative agreement with analytical calculations are found. The results here demonstrate that vortex-antivortex complexes can be nucleated in planar ferromagnets and they exhibit features analogous to fluids and superfluids. The hydrodynamic interpretation of planar magnetic materials yields new insights into magnetization dynamics.

Spin Hall phenomena are a collection of relativistic spin-orbit coupling effects that permit control and detection of magnetization dynamics in magnetic materials with electrical currents. In spintronics, they have been studied extensively in bilayer structures consisting of a magnetically ordered material interfaced by a current-carrying paramagnetic metal with strong spin-orbit coupling. In this work, the authors propose the magnetic phase qubit, the macroscopic quantum spintronic device that can be built from such bilayers and that permits full electrical control and readout via spin Hall phenomena. The device is an example of a macroscopic qubit that can be constructed from solid-state materials and so should offer the same advantages as the superconducting qubits of strong inter-qubit coupling and scalability. An estimate of the relevant physical parameters based on current spintronic technology gives a qubit operational temperature that is more than an order of magnitude higher than for existing superconducting qubits, thus opening the possibility of macroscopic quantum information processing at temperatures above the dilution refrigerator range. The authors also show that a coupled array of these qubits can realize a quantum annealer, which could be used to solve certain hard optimization problems and machine learning tasks.

Quantum systems are known to exhibit several types of exotic behavior beyond classical physics, including quantum entanglement, which describes a web of nonlocal correlations among the constituents of the system. Despite numerous advances in understanding and quantifying the bipartite entanglement entropy of a pure state, where the whole system is described by a wave function, less is understood about quantum entanglement of a mixed state, where the system is described by a density matrix. The partial transpose of the density matrix, in which one takes the transpose only for a subsystem, and its corresponding entanglement measure – called the (logarithmic) negativity – have been introduced as an effective probe for the quantum entanglement in bosonic mixed states. In this work, the authors present a scheme to compute an analog of the entanglement negativity in the fermionic mixed states using a partial time-reversal transformation. Various examples are investigated. In particular, it is shown that the partial time reversal is an intrinsically fermionic construction, in that it can capture the formation of the edge Majorana fermions, while the partial transpose obtained from the bosonic partial transpose through the Jordan-Wigner transformation fails.

Computer simulations show that a uniform but not periodic arrangement of tiny, wave-scattering pillars can host an efficient acoustic channel of arbitrary shape.

Quantum mechanics nominally works in a space of infinite dimensions. In practice, however, the computer-based solution of quantum-mechanical problems relies on a restriction of that space to a high but finite number of dimensions. This is important since computational quantum-mechanical simulations have a huge presence in today’s physical science. In many instances, the finite-dimensional space needs to evolve during a simulation. In this work, the authors extend the formalism used for finite spaces to that of evolving spaces. Here, well-known equations acquire a new meaning in the language of the curved spaces familiar to general relativity. The authors provide a novel geometric approach to calculating tensorially well-defined derivatives of quantum-mechanical state and operator representations with respect to arbitrary external parameters. Contributions due to basis function evolution play the role of the Christoffel symbol terms of Riemannian geometry. The curvature of the resulting geometry is equivalent to Berry’s curvature, but generalized for possibly nonorthogonal, smoothly varying basis functions. This work provides insights into dynamical quantum simulations that enable the development of improved simulation algorithms. It also opens up new scientific horizons, as is ever the case when establishing formal links between different subfields of physics.

Weyl points in photonic systems have gained much attention for their novel properties, such as topologically protected robustness and gapless surface states. However, many Weyl photonic crystal structures designed previously are probably too complicated for nanofabrication. Here, the authors discover that Weyl points can be found in metallic chiral woodpile photonic crystals, which can be fabricated using current nanotechnology. Weyl points with topological charge not only 1 but also 2 can be found in these photonic crystals. When the constituent materials change from the air-in-metal to metal-in-air configuration, the sign of the topological charge will change, leading to a topological phase transition, and the bands change from topologically trivial to nontrivial. Gapless surface states exist in the latter case and robust transport properties have also been demonstrated numerically. When the metallic component is replaced by dielectric materials, such as silicon, the Weyl points still exist. These woodpile photonic crystals should become promising platforms for exploring Weyl point related physics at optical frequencies.

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model for randomly interaction fermions in a quantum dot. This paper studies the properties of the many-body spectrum of the SYK model and finds a periodicity of the spectral properties in term of the number of fermion modes in the quantum dot. In particular, the level statistics of SYK spectrum are investigated. It is found that the many-body level spacing of the SYK model follows Wigner-Dyson statistics, consistent with the thermalizing nature of the SYK model. Interestingly, the level statistics goes through those of different random matrix ensembles periodically. The periodicity can be explained by viewing the SYK model as an effective model for the boundary of 1D interacting fermionic symmetry-protected topological states. The periodicity in the SYK spectrum is therefore tied to the classification of fermionic topological states in one dimension.

The superconducting ferromagnet UCoGe is a versatile laboratory tool to investigate the interplay of ferromagnetism ($T_{\text{c}}$ = 3.0 K) and superconductivity ($T_{\text{sc}}$ = 0.6 K). Here, the authors report the superconducting and magnetic phase diagram in the field-temperature plane determined by thermal expansion measurements. The use of the thermal expansion technique has the advantage that it involves a thermodynamic bulk probe. The experiments were carried out on a single crystal in fixed magnetic fields applied along the principal axes of the orthorhombic crystal. Since the phase diagram depends sensitively on the orientation of the magnetic field with respect to the crystal axes, the thermal expansion cell was mounted on a piezoelectric rotator to enable $in$ $situ$ tuning of the magnetic field angle. The authors observe that the Curie point for $B$ || $b$ shifts gradually to lower temperatures and present bulk-sensitive evidence for the unusual S-shaped $B_{\text{c2}}$ curve for the same field orientation. The results lend further support to theoretical proposals of spin-fluctuation mediated enhancement of superconductivity in a magnetic field ($B$ || $b$).

Localization and transport of a quantum particle in fractal lattices with random-site connectivity and without any diagonal disorder are investigated. It is the random hopping terms that introduce disorder-causing localization of a single-particle wave function. The lattices are generated so that their fractal (Hausdorff and spectral) dimensions are independently controlled. Therefore, it is possible to analyze how different fractal dimensions influence the localization properties, which is the main purpose of this paper.

Skyrmions are topological knots in the magnetization, and they can be stabilized as particle-like states in a ferromagnetic environment. Due to their noncollinear spin texture, the local density of states is modified, and they are thus electronically different from their ferromagnetic surroundings. Exploiting the spatial and energy resolution of scanning tunneling microscopy and spectroscopy this work demonstrates how the local spin configuration within a skyrmion modifies the respective differential conductance. This noncollinear magnetoresistance (NCMR) can reach values of 50% in Pd/Fe/Ir(111) and allows imaging of skyrmions with nonmagnetic probe electrodes. Because of its large signal and the reduced technical requirements, NCMR is expected to be useful for the detection of the magnetic state with planar tunnel junctions in skyrmionic spintronics applications.

Entanglement entropy is a widely applicable indicator of the onset of quantum chaos. In particular, the entanglement entropy of the wave function after a quench from an initial state with low entanglement can be used to study the thermalization of the system. Here, the authors propose an initial-state independent quantity called the “operator entanglement entropy” (opEE) to extract the properties of the unitary evolution operator. They study the growth of the opEE in Floquet, chaotic, and many-body localized systems. They respectively have a linear, power-law, and logarithmic growth before reaching extensive saturation values. The most chaotic Floquet spin model has the maximal saturation value among the three classes and is identical to the value of a random unitary operator (the Page value). The authors interpret the opEE as the state EE of a quenched state living in a doubled Hilbert space, thus establishing its consistency with the existing state EE results. They conclude that the EE of the evolution operator should characterize the propagation of information in these systems.