We show that biaxial strain induces alternating tetragonal superconducting and orthorhombic nematic domains in Co-substituted ${\mathrm{CaFe}}_2{\mathrm{As}}_2$. We use atomic force, magnetic force, and scanning tunneling microscopy to identify the domains and characterize their properties, finding in particular that tetragonal superconducting domains are very elongated, more than several tens of micrometers long and about 30 nm wide; have the same $T_c$ as unstrained samples; and hold vortices in a magnetic field. Thus, biaxial strain produces a phase-separated state, where each phase is equivalent to what is found on either side of the first-order phase transition between antiferromagnetic orthorhombic and superconducting tetragonal phases found in unstrained samples when changing Co concentration. Having such alternating superconducting domains separated by normal conducting domains with sizes of the order of the coherence length opens opportunities to build Josephson junction networks or vortex pinning arrays and suggests that first-order quantum phase transitions lead to nanometric-size phase separation under the influence of strain.

Topological phases typically encode topology at the level of the single-particle band structure. But a remarkable class of models shows that quantum anomalous Hall effects can be driven exclusively by interactions, while the parent noninteracting band structure is topologically trivial. Unfortunately, these models have so far relied on interactions that do not spatially decay and are therefore unphysical. We study a model of spinless fermions on a decorated honeycomb lattice. Using complementary methods, mean-field theory and exact diagonalization, we find a robust quantum anomalous Hall phase arising from spatially decaying interactions. Our finding indicates that the quantum anomalous Hall effect driven entirely by interactions is a surprisingly robust and realistic phenomenon.

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe nonequilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations.

We report small-angle neutron scattering studies of the lacunar spinel ${\mathrm{GaV}}_4{\mathrm{S}}_8$, which reveal the long-wavelength magnetic phases to be cycloidally modulated. Upon cooling, these modulated phases, including a recently proposed Néel-type skyrmion phase, transform into a simple ferromagnetic state. These results indicate the modulated phases in ${\mathrm{GaV}}_4{\mathrm{S}}_8$ gain their stability from thermal fluctuations, while at lower temperatures the ferromagnetic state emerges in accord with the strong easy-axis magnetic anisotropy. Crucially, our study provides microscopic evidence that the skyrmions in ${\mathrm{GaV}}_4{\mathrm{S}}_8$ indeed display a Néel-type helicity. More generally, our approach can be applied to evidence the helicity of any bulk skyrmion phase.

A spin fractionalizes into matter and gauge fermions in Kitaev's spin liquid on the honeycomb lattice. This follows from a Jordan-Wigner mapping to fermions, allowing for the construction of a minimal entropy ground-state wave function on the cylinder. We use this to calculate the entanglement entropy by choosing several distinct partitionings. First, by partitioning an infinite cylinder into two, the $-ln2$ topological entanglement entropy is reconfirmed. Second, the reduced density matrix of the gauge sector on the full cylinder is obtained after tracing out the matter degrees of freedom. This allows for evaluating the gauge entanglement Hamiltonian, which contains infinitely long-range correlations along the symmetry axis of the cylinder. The matter-gauge entanglement entropy is $(N_y-1)ln2$, with $N_y$ the circumference of the cylinder. Third, the rules for calculating the gauge sector entanglement of any partition are determined. Rather small correctly chosen gauge partitions can still account for the topological entanglement entropy in spite of long-range correlations in the gauge entanglement Hamiltonian.

Superconductivity can be understood in terms of a phase transition from an uncorrelated electron gas to a condensate of Cooper pairs in which the relative phases of the constituent electrons are coherent over macroscopic length scales. The degree of correlation is quantified by a complex-valued order parameter, whose amplitude is proportional to the strength of the pairing potential in the condensate. Supercurrent-carrying states are associated with nonzero values of the spatial gradient of the phase. The pairing potential and several physical observables of the Cooper condensate can be manipulated by means of temperature, current bias, dishomogeneities in the chemical composition, or application of a magnetic field. Here we show evidence of complete suppression of the energy gap in the local density of quasiparticle states (DOS) of a superconducting nanowire upon establishing a phase difference equal to $\pi$ over a length scale comparable to the superconducting coherence length. These observations are consistent with a complete collapse of the pairing potential in the center of the wire, in accordance with theoretical modeling based on the quasiclassical theory of superconductivity in diffusive systems. Our spectroscopic data, fully exploring the phase-biased states of the condensate, highlight the profound effect that extreme phase gradients exert on the amplitude of the pairing potential. Moreover, the sharp magnetic response (up to 27 mV/${\mathrm{\Phi }}_0$) observed near the onset of the superconducting gap collapse regime is exploited to realize magnetic flux detectors with noise-equivalent resolution as low as 260 $\mathrm{n}{\mathrm{\Phi }}_0/\sqrt{\text{Hz}}$.

We have performed an in situ angle-resolved photoemission spectroscopy study of undoped one-monolayer (1-ML) FeSe film on ${\mathrm{SrTiO}}_3$ to elucidate the nature of the parent phase of high-temperature superconductivity. Accurate tuning of carrier concentration at zero doping by low-temperature postgrowth annealing of the film enabled us to observe a linearly dispersive Dirac-cone band and a pointlike Fermi surface on the $\mathrm{\Gamma }M$ mirror reflection plane arising from the nematic order. Intriguingly, the low-energy excitations of this material are solely characterized by the Dirac-cone band, since no other bands cross the Fermi level unlike its multilayer counterpart. The present result strongly suggests that undoped 1-ML FeSe is a two-dimensional Dirac semimetal with a mirror-symmetry-protected Dirac-cone band.

Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin $j=\frac{3}{2}$ quasiparticles, which are fundamentally different from those in ordinary metals with spin $j=\frac{1}{2}$. For both local and nonlocal pairing channels in $j=\frac{3}{2}$ materials we develop a general approach to analyzing pairing instabilities, thereby providing the computational tools needed to investigate the physics of these systems beyond phenomenological considerations. Furthermore, applying our method to a generic density-density interaction, we establish that: (i) The pairing strengths in the different symmetry channels uniquely encode the $j=\frac{3}{2}$ nature of the Fermi surface band structure—a manifestation of the fundamental difference with ordinary metals. (ii) The leading odd-parity pairing instabilities are different for electron doping and hole doping. Finally, we argue that polar phonons, i.e., Coulomb interactions mediated by the long-ranged electric polarization of the optical phonon modes, provide a coupling strength large enough to account for a Kelvin-range transition temperature in the $s$-wave channel, and are likely to play an important role in the overall attraction in non-$s$-wave channels. Moreover, the explicit calculation of the coupling strengths allows us to conclude that the two largest non-$s$-wave contributions occur in nonlocal channels, in contrast with what has been commonly assumed.

We present measurements of Josephson junctions containing three magnetic layers with noncollinear magnetizations. The junctions are of the form $S/F^{\prime }/N/F/N/F^{″}/S$, where $S$ is superconducting Nb, $F^{\prime }$ is either a thin Ni or Permalloy layer with in-plane magnetization, $N$ is the normal metal Cu, $F$ is a synthetic antiferromagnet with magnetization perpendicular to the plane, composed of Pd/Co multilayers on either side of a thin Ru spacer, and $F^{″}$ is a thin Ni layer with in-plane magnetization. The supercurrent in these junctions decays more slowly as a function of the $F$-layer thickness than for similar spin-singlet junctions not containing the $F^{\prime }$ and $F^{″}$ layers. The slower decay is the prime signature that the supercurrent in the central part of these junctions is carried by spin-triplet pairs. The junctions containing $F^{\prime }=$ Permalloy are suitable for future experiments where either the amplitude of the critical current or the ground-state phase difference across the junction is controlled by changing the relative orientations of the magnetizations of the $F^{\prime }$ and $F^{″}$ layers.

We present a theoretical and experimental investigation of exciton recombination dynamics and the related polarization of emission in highly in-plane asymmetric nanostructures. Considering general asymmetry- and size-driven effects, we illustrate them with a detailed analysis of InAs/AlGaInAs/InP elongated quantum dots. These offer widely varied confinement characteristics tuned by size and geometry that are tailored during the growth process, which leads to emission in the application-relevant spectral range of 1.25–1.65 $\mu \mathrm{m}$. By exploring the interplay of the very shallow hole confining potential and widely varying structural asymmetry, we show that a transition from the strong through intermediate to even weak confinement regime is possible in nanostructures of this kind. This has a significant impact on exciton recombination dynamics and the polarization of emission, which are shown to depend not only on the details of the calculated excitonic states but also on excitation conditions in the photoluminescence experiments. We estimate the impact of the latter and propose a way to determine the intrinsic polarization-dependent exciton light-matter coupling based on kinetic characteristics.

We discuss pairing signatures in mesoscopic nanowires with a variable attractive pairing interaction. Depending on the wire length, density, and interaction strength, these systems realize a simultaneous bulk-to-mesoscopic and BCS-BEC crossover, which we describe in terms of the parity parameter that quantifies the odd-even energy difference and generalizes the bulk Cooper pair binding energy to mesoscopic systems. We show that the parity parameter can be extracted from recent measurements of conductance oscillations in ${\mathrm{SrTiO}}_3$ nanowires by Cheng et al. [Nature (London) 521, 196 (2015)], where it marks the critical magnetic field that separates pair and single-particle currents. Our results place the experiment in the fluctuation-dominated mesoscopic regime on the BCS side of the crossover.

The presence of charge and spin stripe order in the ${\mathrm{La}}_2{\mathrm{CuO}}_4$-based family of superconductors continues to lead to new insight on the unusual ground-state properties of high-$T_c$ cuprates. Soon after the discovery of charge stripe order at $T_{\mathrm{charge}}\simeq 65$ K in ${\mathrm{Nd}}^{3+}$ co-doped ${\mathrm{La}}_{1.48}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4(T_c\simeq 6$ K) [Tranquada et al., Nature (London) 375, 561 (1995)], Hunt et al. demonstrated that ${\mathrm{La}}_{1.48}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4$ and superconducting ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x\sim 1/8(T_c\simeq 30$ K) share nearly identical NMR anomalies near $T_{\mathrm{charge}}$ of the former [Phys. Rev. Lett. 82, 4300 (1999)]. Their inevitable conclusion that ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_4$ also undergoes charge order at a comparable temperature became controversial, because diffraction measurements at the time were unable to detect Bragg peaks associated with charge order. Recent advances in x-ray diffraction techniques finally led to definitive confirmations of the charge order Bragg peaks in ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_4$ with an onset at as high as $T_{\mathrm{charge}}\simeq 80$ K. Meanwhile, improved instrumental technology has enabled routine NMR measurements that were not feasible two decades ago. Motivated by these new developments, we revisit the charge order transition of a ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_4$ single crystal based on ${}^{63}\mathrm{Cu}$ NMR techniques. We demonstrate that ${}^{63}\mathrm{Cu}$ NMR properties of the nuclear spin $I_z=-\frac{1}{2}$ to $+\frac{1}{2}$ central transition below $T_{\mathrm{charge}}$ exhibit unprecedentedly strong dependence on the measurement time scale set by the separation time $\tau$ between the ${90}^{\circ }$ and ${180}^{\circ }$ radio-frequency pulses; a new kind of anomalous, very broad winglike ${}^{63}\mathrm{Cu}$ NMR signals gradually emerge below $T_{\mathrm{charge}}$ only for extremely short $\tau \lesssim 4\mu \mathrm{s}$, while the spectral weight $I_{\mathrm{Normal}}$ of the normal NMR signals is progressively wiped out. The NMR linewidth and relaxation rates depend strongly on $\tau$ below $T_{\mathrm{charge}}$, and their enhancement in the charge ordered state indicates that charge order turns on strong but inhomogeneous growth of Cu spin-spin correlations.

As most perovskites, ${\mathrm{SrRuO}}_3$ exhibits structural phase transitions associated with rotations of the ${\mathrm{RuO}}_6$ octahedra. The application of moderate magnetic fields in the ferromagnetically ordered state allows one to control these structural distortions, although the ferromagnetic order occurs at six times lower temperature than the structural distortion. Our neutron-diffraction and macroscopic measurements unambiguously show that magnetic fields rearrange structural domains, and that for the field along a cubic ${\left[110\right]}_c$ direction, a fully detwinned crystal is obtained. Subsequent heating above $T_C$ into the paramagnetic phase causes a magnetic shape-memory effect, where the initial structural domains recover.

We report a spin injection and detection mechanism via the anomalous Hall effect in a ferromagnetic metal. The anomalous spin Hall effect (ASHE) refers to the transverse spin current generated within the ferromagnet. We utilize the ASHE and its reciprocal effect to electrically inject and detect magnons in a magnetic insulator (yttrium iron garnet) in a nonlocal geometry. Our experiments reveal that permalloy has a comparable spin injection and detection efficiency to that of platinum, owing to the ASHE. We also demonstrate the tunability of the ASHE via the orientation of the permalloy magnetization, thus creating possibilities for spintronic applications.

We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field-induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wave-packet dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wave-packet dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. We show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.

Two-electron charged self-assembled quantum dot molecules exhibit a decoherence-avoiding singlet-triplet qubit subspace and an efficient spin-photon interface. We demonstrate quantum entanglement between emitted photons and the spin qubit after the emission event. We measure the overlap with a fully entangled state to be $69.5\pm 2.7\%$, exceeding the threshold of $50\%$ required to prove the nonseparability of the density matrix of the system. The photonic qubit is encoded in two photon states with an energy difference larger than the timing resolution of existing detectors. We devise a heterodyne detection method, enabling the projective measurements of such photonic color qubits along any direction on the Bloch sphere.

We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree) from the central site (“root”) to the boundary (“leaves”). We show that the eigenfunction moments $P_q={N\langle \left|\psi \right|}^{2q}\left(i\right)\rangle$ exhibit a multifractal scaling $P_q\propto N^{-{\tau }_q}$ with the volume (number of sites) $N$ at $N\to \infty$. The multifractality spectrum ${\tau }_q$ depends on the strength of disorder and on the parameter $s$ characterizing the position of the observation point $i$ on the lattice. Specifically, $s=r/R$, where $r$ is the distance from the observation point to the root, and $R$ is the “radius” of the lattice. We demonstrate that the exponents ${\tau }_q$ depend linearly on $s$ and determine the evolution of the spectrum with increasing disorder, from delocalized to the localized phase. Analytical results are obtained for the $n$-orbital model with $n\gg 1$ that can be mapped onto a supersymmetric $\sigma$ model. These results are supported by numerical simulations (exact diagonalization) of the conventional ($n=1$) Anderson tight-binding model.

We report the results of the numerical study of the nondissipative quantum Josephson junction chain with the focus on the statistics of many-body wave functions and local energy spectra. The disorder in this chain is due to the random offset charges. This chain is one of the simplest physical systems to study many-body localization. We show that the system may exhibit three distinct regimes: insulating, characterized by the full localization of many-body wave functions, a fully delocalized (metallic) one characterized by the wave functions that take all the available phase volume, and the intermediate regime in which the volume taken by the wave function scales as a nontrivial power of the full Hilbert-space volume. In the intermediate nonergodic regime the Thouless conductance (generalized to the many-body problem) does not change as a function of the chain length indicating a failure of the conventional single-parameter scaling theory of localization transition. The local spectra in this regime display the fractal structure in the energy space which is related with the fractal structure of wave functions in the Hilbert space. A simple theory of fractality of local spectra is proposed, and a scaling relationship between fractal dimensions in the Hilbert and energy spaces is suggested and numerically tested.

We present high-field electron spin resonance (ESR) studies of the honeycomb-lattice material $\alpha \text{−}{\mathrm{RuCl}}_3$, a prime candidate to exhibit Kitaev physics. Two modes of antiferromagnetic resonance were detected in the zigzag ordered phase, with magnetic field applied in the $ab$ plane. A very rich excitation spectrum was observed in the field-induced quantum paramagnetic phase. The obtained data are compared with the results of recent numerical calculations, strongly suggesting a very unconventional multiparticle character of the spin dynamics in $\alpha \text{−}{\mathrm{RuCl}}_3$. The frequency-field diagram of the lowest-energy ESR mode is found consistent with the behavior of the field-induced energy gap, revealed by thermodynamic measurements.

${\mathrm{MoTe}}_2$ has recently been shown to realize in its low-temperature phase the type-II Weyl semimetal (WSM). We investigated by time- and angle- resolved photoelectron spectroscopy (tr-ARPES) the possible influence of the Weyl points on the electron dynamics above the Fermi level $E_F$, by comparing the ultrafast response of ${\mathrm{MoTe}}_2$ in the trivial and topological phases. In the low-temperature WSM phase, we report an enhanced relaxation rate of electrons optically excited to the conduction band, which we interpret as a fingerprint of the local gap closure when Weyl points form. By contrast, we find that the electron dynamics of the related compound ${\mathrm{WTe}}_2$ is slower and temperature independent, consistent with a topologically trivial nature of this material. Our results shows that tr-ARPES is sensitive to the small modifications of the unoccupied band structure accompanying the structural and topological phase transition of ${\mathrm{MoTe}}_2$.