Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap $\mathrm{\Delta }$ and of the critical temperature $T_c$, the ratio $\mathrm{\Delta }$/$k_B{T}_c$ remaining roughly constant. In addition, in most films, an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature $T_c$ and the energy gap $\mathrm{\Delta }$ starts decoupling from $T_c$. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of an NbN film with scanning tunneling spectroscopy (STS), we show that the inhomogeneous spatial distribution of $\mathrm{\Delta }$ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modeling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of $\mathrm{\Delta }$ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now.

Contrary to the usual assumption, the electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-$1/2$ states. This has profound consequences for the symmetry properties and nodal structure of superconductors, especially for the interband gap functions. Focusing on tetragonal superconductors, we show that the interband pairing in the conventional ($s$-wave) channel can have features which are traditionally associated with unconventional pairing, such as triplet components and odd parity, and can produce line nodes in the excitation energy gap. In the $d$-wave case, the interband pairing, which can also be odd in momentum and have a triplet component, changes the positions and topology of the nodal lines.

Muon spin rotation and resonant soft x-ray scattering experiments on prototype multiferroics $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ ($R$ = Y, Sm) are used to demonstrate that the local electric displacements are driven by the spin-current (SC) mechanism. Small local electric displacements were evaluated by observing spin polarization at ligand O ions, for which implanted muons served as an extremely sensitive probe. Our results for ${\mathrm{YMn}}_2{\mathrm{O}}_5$ provide evidence that the spin polarization of O ions forming a spin cycloid chain with Mn spins increases in proportion to the vector spin chirality (${\mathbf{S}}_i\times {\mathbf{S}}_j$) of the Mn ions. This relationship strongly indicates that the charge transfer between O and Mn ions is driven by the SC mechanism, which leads to the ferroelectricity accompanying O spin polarization.

The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin rotation symmetry and half-integer spin per unit cell does not admit a gapped symmetric ground state lacking fractionalized excitations. That is, the ground state must be gapless, spontaneously break a symmetry, or be a gapped spin liquid. Thus, such systems are natural spin-liquid candidates if no ordering is found. In this work, we give a much more general criterion that determines when an LSM-type theorem holds in a spin system. For example, we consider quantum magnets with arbitrary space-group symmetry and/or spin-orbit coupling. Our criterion is intimately connected to recent work on the general classification of topological phases with spatial symmetries and also allows for the computation of an “anomaly” associated with the existence of an LSM theorem. Moreover, our framework is also general enough to encompass recent works on “SPT-LSM” theorems where the system admits a gapped symmetric ground state without fractionalized excitations, but such a ground state must still be nontrivial in the sense of symmetry-protected topological phases.

Twisted bilayer graphene displays insulating and superconducting phases caused by exceptional flattening of its lowest energy bands. Superconductivity with highest $T_c$ appears near half filling of the valence band ($n\approx -2$). The data show that in the large part of the superconducting dome near $n=-2$, threefold lattice rotation symmetry is broken in the superconducting phase, i.e., a superconductor is also a nematic. We perform a comprehensive analysis of superconductivity in twisted-bilayer graphene within an itinerant approach and present a mechanism for nematic superconductivity. We take as an input the fact that at dopings, where superconductivity has been observed, the Fermi energy lies in the vicinity of twist-induced Van Hove singularities in the density of states. We argue that the low-energy physics can be properly described by patch models with either six or twelve Van Hove points. We obtain pairing interactions for the patch models in terms of parameters of the microscopic model for the flat bands, which contains both local and twist-induced nonlocal interactions. We show that the latter give rise to attraction in different superconducting channels. For six Van Hove points, there is just one attractive $d$-wave channel, and we find chiral $d\pm id$ superconducting order, which breaks time-reversal symmetry but leaves the lattice rotation symmetry intact. For twelve Van Hove points, we find two attractive channels, $g$ and $i$ waves, with almost equal coupling constants. We show that both order parameters are nonzero in the ground state and explicitly demonstrate that in this co-existence state the threefold lattice rotation symmetry is broken, i.e., the superconducting state is also a nematic. We find two possible nematic states, one is time-reversal symmetric, the other additionally breaks time-reversal symmetry. We apply our scenario to twisted bilayer graphene near $n=-2$ and argue that it is applicable also to other systems with two (or more) attractive channels with similar couplings as our reasoning for a nematic superconductivity is based on generic symmetry considerations.

We study the spontaneous formation of exciton-polariton vortices in an all-optical nonresonantly excited annular trap, which is formed by ring-shaped subpicosecond laser pulses. Since the light emitted by these vortices carries orbital angular momentum (OAM) corresponding to their topological charge, we apply a dedicated OAM spectroscopy technique to detect the OAM of the measurement signal with picosecond time resolution. This allows us to identify the formation of OAM modes and investigate the dynamics of the vortex formation process. We also study the power dependence of this process and how the ring diameter influences the formation of OAM modes.

We study theoretically the spin-wave emission from a moving domain wall in a ferromagnet. Introducing a deformation mode describing a modulation of the wall thickness in the collective coordinate description, we show that thickness variation couples to the spin wave linearly and induces spin-wave emission. The dominant emitted spin wave turns out to be polarized in the out-of wall plane ($\varphi$) direction. The emission contributes to the Gilbert damping parameter proportional to $\hslash {\omega }_{\varphi }/K$, the ratio of the angular frequency ${\omega }_{\varphi }$ of $\varphi$, and the easy-axis anisotropy energy $K$.

Selected magnetic domain patterns in Fe 12.8 at.% Si bulk crystals with different crystallographic surface orientation are tomographically imaged to reveal their three-dimensional structure. This alloy allows “freezing” of the domains as a precipitation pattern with subsequent imaging in a polarization microscope after cutting or successive polishing (Libovický method). The selected domain patterns are basic for materials with cubic crystal anisotropy and comprise spike, moth, fir tree, V-line, ant, chain, and echelon domains. Established domain models for these patterns are partially confirmed, but also surprising deviations and extensions of the models are found. Finally, the fundamental difference between magnetically hard- and soft-grain boundaries is revealed by combining domain tomography with surface domain observation by Kerr microscopy.

Superconducting materials with a nontrivial band structure are potential candidates for topological superconductivity. Here, by combining muon-spin rotation and relaxation ($\mu \mathrm{SR}$) methods with theoretical calculations, we investigate the superconducting and topological properties of the rocksalt-type compounds NbC and TaC (with $T_c=11.5$ and 10.3 K, respectively). At a macroscopic level, the magnetization and heat-capacity measurements under applied magnetic field provide an upper critical field of 1.93 and 0.65 T for NbC and TaC, respectively. The low-temperature superfluid density, determined by transverse-field $\mu \mathrm{SR}$ and electronic specific-heat data, suggest a fully gapped superconducting state in both NbC and TaC, with a zero-temperature gap ${\mathrm{\Delta }}_0=1.90$ and 1.45 meV, and a magnetic penetration depth ${\lambda }_0=141$ and 77 nm, respectively. Band-structure calculations suggest that the density of states at the Fermi level are dominated by the Nb $4d$ (or Ta $5d$) orbitals, which are strongly hybridized with the C $p$ orbitals to produce large cylinderlike Fermi surfaces, similar to those of high-$T_c$ iron-based superconductors. Without considering the spin-orbit coupling (SOC) effect, the first Brillouin zone contains three closed node lines in the bulk band structure, protected by time-reversal and space-inversion symmetry. When considering SOC, its effects in the NbC case appear rather modest. Therefore, the node lines may be preserved in NbC, hence proposing it as a potential topological superconductor.

Cobalt pyrochlore fluoride ${\mathrm{NaCaCo}}_2{\mathrm{F}}_7$ is a disordered frustrated magnet that is composed of ${\mathrm{Co}}^{2+}$ ions with an effective spin-$\frac{1}{2}$ magnetic moment and that exhibits spin freezing below $T_f\sim 2.4$ K. We perform ultrasound velocity measurements on a single crystal of the cubic ${\mathrm{NaCaCo}}_2{\mathrm{F}}_7$. The temperature dependence of the bulk modulus (the breathing elastic mode) exhibits Curie-type softening upon cooling below $\sim 20$ K down to $T_f$, which is suppressed by the magnetic field. This Curie-type softening should be a precursor to the enhancement of the strength of exchange disorder via the spin-lattice coupling, which causes the spin freezing. In contrast to the magnetic-field-suppressed Curie-type softening in the bulk modulus, the trigonal shear modulus exhibits softening with a characteristic minimum upon cooling, which is enhanced by the magnetic field at temperatures below $\sim 20$ K. This magnetic-field-enhanced elastic anomaly in the trigonal shear modulus suggests a coupling of the lattice to the dynamical spin-cluster state. For ${\mathrm{NaCaCo}}_2{\mathrm{F}}_7$, the observed elastic anomalies reveal an occurrence of magnetic-field-induced crossover from an isostructural lattice instability toward the spin freezing to a trigonal lattice instability arising from the emergent dynamical spin-cluster state.

We demonstrate sustained coherent emission of spin waves in NiFe films using rapid demagnetization from high repetition rate femtosecond laser pulse trains. As the pulse separation is shorter than the magnon decay time, magnons having a frequency equal to a multiple of the 1 GHz repetition rate are coherently amplified. Using scanning Brillouin light scattering (BLS) microscopy, we observe this coherent amplification as strong peaks spaced 1 GHz apart. The BLS counts vs laser power exhibit a stronger than parabolic dependence consistent with counts being proportional to the square of the magnetodynamic amplitude, and the demagnetization pulse strength being described by a Bloch law. Spatial spin wave mapping demonstrates how both localized and propagating spin waves can be excited, and how the propagation direction can be directly controlled. Our results demonstrate the versatility of frequency combs and BLS spectroscopy for rapid demagnetization studies, and enable a platform for photomagnonics where sustained coherent spin waves can be utilized.

We present an exact treatment of layered many-body electronic systems in the presence of interlayer coupling within the Schwinger functional derivative approach on the Keldysh contour. Our transparent approach allows us to clarify the definition of interlayer coupling by showing the independent roles hybridization and interactions play in generating new electronic and magnetic excitations. We find interlayer coupling to induce a variety of plasmons, magnons, and excitons, residing within a layer, traversing between layers, or propagating along the interface. Moreover, we predict interfacial excitations, including an electron-hole pairing pathway, facilitated by previously ignored layer nonconserving interactions. Finally, we briefly explore the consequence of interlayer coupling on a bilayer square lattice system.

The emergence of ferromagnetism in Rashba systems, where the evolving exchange interaction enters into competition with spin-orbit coupling, leads to a nontrivial spin-polarized electronic landscape with an intricate momentum-dependent spin structure, which is challenging to unveil. Here, we show a way to disentangle the contributions from the effective spin-orbit and exchange fields and thus to gain knowledge of the spin structure in ferromagnetic Rashba materials, which is required for spintronic applications. Our approach is based exclusively on spin-integrated photoemission measurements combined with a two-band modeling. As an example, we consider the mixed-valent material ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$ which, while being nonmagnetic in the bulk, reveals strong ferromagnetism at the iridium-silicide surface where both spin-orbit and exchange magnetic interactions coexist. The combined effect of these interactions causes a complex band dispersion of the surface state which can be observed in photoemission experiments. Our method allows us to comprehensively unravel the surface-state spin structure driven by spin-orbit coupling at the ferromagnetic surface. This approach opens up opportunities to characterize the spin structure of ferromagnetic Rashba materials, especially where dedicated spin-resolved measurements remain challenging.

In a semiconductor, collective excitations of spin textures usually decay rather fast due to D'yakonov-Perel' spin relaxation. The latter arises from spin-orbit coupling, which induces wave-vector $\left(\mathit{k}\right)$ -dependent spin rotations that, in conjunction with random disorder scattering, generate spin decoherence. However, symmetries occurring under certain conditions can prevent the relaxation of particular homogeneous and inhomogeneous spin textures. The inhomogeneous spin texture, referred to as a persistent spin helix, is especially appealing as it enables us to manipulate the spin orientation while retaining a long spin lifetime. Recently, it was predicted that such symmetries can be realized in zinc-blende two-dimensional electron gases if at least two growth-direction Miller indices agree in modulus, and the coefficients of the Rashba and $\mathit{k}$-linear Dresselhaus spin-orbit couplings are suitably matched [Kammermeier et al., Phys. Rev. Lett. 117, 236801 (2016)]. In the present paper, we systematically analyze the impact of the symmetry-breaking $\mathit{k}$-cubic Dresselhaus spin-orbit coupling, which generically coexists in these systems, on the stability of the emerging spin helices with respect to the growth direction. We find that, as an interplay between orientation and strength of the effective magnetic field induced by the $\mathit{k}$-cubic Dresselhaus terms, the spin relaxation is weakest for a low-symmetry growth direction that can be well approximated by a [225] lattice vector. These quantum wells yield a 30% spin-helix lifetime enhancement compared to [001]-oriented electron gases and, remarkably, require a negligible Rashba coefficient. The rotation axis of the corresponding spin helix is only slightly tilted out of the quantum-well plane. This makes the experimental study of the spin-helix dynamics readily accessible for conventional optical spin orientation measurements where spins are excited and detected along the quantum-well growth direction.

Results of a theoretical and experimental investigation of the spatiotemporal extent of optically generated elastic waves in thin, free-standing, semiconductor films are presented. Our study, focused on symmetric $S_1$ modes in the $10+$ GHz frequency range, indicates that diffraction-limited pulsed laser sources can produce narrow-band elastic excitations with in-plane group velocities sufficient for multi-micrometer-scale lateral propagation at room temperature in GaAs. The theory predicts that pumping GaAs with sub-ps, near-diffraction-limited, optical pulses excites cylindrically spreading $S_1$ vibration because of the Dirac conelike dispersion of the $S_1$ mode at small wave numbers. Theoretical predictions of Lamb wave propagation for optically excited 190-nm-thick GaAs suspended plates are found to agree with experimental data acquired using a near-infrared, ultrafast, pump-probe technique.

Using the framework of generalized hydrodynamics, we compute the low-frequency spin conductivity $\sigma \left(\omega \right)$ of XXZ spin chains with easy-plane anisotropy. We find that for almost all values of the anisotropy $-1<\mathrm{\Delta }<1$, the low-frequency conductivity scales anomalously with frequency, as $\sigma \left(\omega \right)\sim 1/\sqrt{\omega }$. We interpret this anomalous response as a consequence of quasiparticles undergoing Lévy flights. For special values of the anisotropy, the divergence is cut off at low frequencies, so $\sigma \left(\omega \right)$ has a finite dc limit. These results reveal a hitherto unknown mechanism for anomalous response in integrable systems and also provide a physical explanation of the discontinuous behavior of the spin Drude weight. We use our approach to recover that at the isotropic point $\mathrm{\Delta }=1$, $\sigma \left(\omega \right)\sim {\omega }^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.

Since cubic diamond was first recovered from explosively shocked graphite samples in 1961, the shock-induced graphite to diamond phase transformation has been of great scientific and technological interest. Recent real-time x-ray diffraction results on different types of pyrolytic graphite under shock compression have reported hexagonal diamond and cubic diamond formation at comparable stresses. To resolve and understand these differences, synchrotron x-ray diffraction measurements were used to examine, in real time, the plate impact shock response of two grades of highly oriented pyrolytic graphite and as-deposited pyrolytic graphite—at stresses below and above their respective phase transformation stresses. The present results show that at their respective transformation stresses, crystallites in as-deposited pyrolytic graphite are compressed $\sim 30\%$ more along the $c$ axis than crystallites in both highly oriented pyrolytic graphite types. This work establishes that the high-pressure phase of even ZYH-grade highly oriented pyrolytic graphite (a less oriented variety with mosaic spread $3.5^{\circ }\pm 1.5^{\circ }$), at $\sim 50$ GPa, is hexagonal diamond. In contrast, the high-pressure phase of as-deposited pyrolytic graphite (mosaic spread $\sim {45}^{\circ }$) in the present work, at $\sim 60$ GPa, is cubic diamond. Analysis of ambient x-ray diffraction data demonstrates that the crystallites in the highly oriented pyrolytic graphite samples have the hexagonal graphite crystal structure with three-dimensional long-range order. In contrast, the crystallites in the as-deposited pyrolytic graphite samples have a turbostratic carbon crystal structure which lacks rotational/translational order between parallel adjacent graphene layers. The ambient results suggest that the observed high-pressure crystal structure of shocked graphite depends strongly on the initial crystal structure—shock compression along the $c$ axis of hexagonal graphite (in highly oriented pyrolytic graphite) results in highly textured hexagonal diamond and shock compression of turbostratic carbon (in as-deposited pyrolytic graphite) results in nanograined cubic diamond. The present results reconcile previous disparate findings, establish the definitive role of the initial crystal structure, and provide a benchmark for theoretical simulations.

We report an optical homogeneous linewidth of 580 $\pm$ 20 Hz of ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_2{\mathrm{O}}_3$ ceramics at millikelvin temperatures, narrowest so far in rare-earth doped ceramics, as well as a slow spectral diffusion of $\sim 2$ kHz over a millisecond time scale. Detailed investigations of temperature and field dependence of optical coherence and spectral diffusions reveal the remaining weak dephasing mechanisms as coupling to elastic two-level systems and superhyperfine interactions of ${\mathrm{Er}}^{3+}$ with nuclear spins. The measured transient coherence properties can be understood in part from frozen ${\mathrm{Er}}^{3+}$ spins at dilution temperatures. In addition to informing possible refinement in material synthesis to further suppress dephasings, these spectroscopic results put ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_2{\mathrm{O}}_3$ ceramics as a promising candidate for quantum systems.

We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely, the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under local (on-site) basis transformations. In this case, the average entanglement entropy follows a Markovian dynamics, such that the entanglement property of the future state can be inferred from the entanglement property of the unitary operator of the underlying quantum dynamics. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schrödinger equation, such that various tools developed in quantum many-body physics can be applied. The framework enables us to investigate a variety of random quantum dynamics beyond Haar random circuits and Brownian circuits. We perform numerical simulations for these models and demonstrate the validity and prediction power of the entanglement feature approach.

Metallic superlattices where the magnetization vectors in the adjacent ferromagnetic layers are antiferromagnetically coupled by the interlayer exchange coupling through nonmagnetic spacer layers are systems available for the systematic study on antiferromagnetic (AF) spintronics. As a candidate of nonmagnetic spacer layer material exhibiting remarkable spin Hall effect, which is essential to achieve spin-orbit torque switching, we selected the Ir-doped Cu in this study. The AF coupling for the $\mathrm{Co}/\mathrm{C}{\mathrm{u}}_{95}\mathrm{I}{\mathrm{r}}_5/\mathrm{Co}$ was investigated, and was compared with those for the Co/Cu/Co and Co/Ir/Co. The maximum magnitude of AF-coupling strength was obtained to be $0.39\mathrm{mJ}/{\mathrm{m}}^2$ at the $\mathrm{C}{\mathrm{u}}_{95}\mathrm{I}{\mathrm{r}}_5$ thickness of about 0.75 nm. Furthermore, we found a large spin Hall angle of $\mathrm{C}{\mathrm{u}}_{95}\mathrm{I}{\mathrm{r}}_5$ in Co/$\mathrm{C}{\mathrm{u}}_{95}\mathrm{I}{\mathrm{r}}_5$ bilayers by carrying out spin Hall magnetoresistance and harmonic Hall voltage measurements, which are estimated to be 3–4%. Our experimental results clearly indicate that $\mathrm{C}{\mathrm{u}}_{95}\mathrm{I}{\mathrm{r}}_5$ is a nonmagnetic spacer layer allowing us to achieve moderately strong AF coupling and to generate appreciable spin-orbit torque via the spin Hall effect.