The order parameter induced in the normal part of the superconductor-normal-superconductor proximity system in the magnetic field can form vortices, which are similar but not the same as vortices in bulk superconductors, or it can be modulated laminarly with the field-dependent decay length.

Using density functional theory calculations, many researchers have predicted that various tungsten nitride compounds ${\text{N}}_{1-x}{\text{W}}_x \left(x<\frac{1}{2}\right)$ will be “ultraincompressible” or “superhard,” i.e., as hard as or harder than diamond. Necessary conditions for such compounds are that they have large bulk and shear moduli, greater than approximately 200 GPa, and are elastically and vibrationally stable. Compounds with such desirable properties also must be energetically stable against decomposition into other compounds. This test for stability can only be found after the determination of the convex hull for ${\text{N}}_{1-x}{\text{W}}_x$, which connects the lowest enthalpy structures as a function of composition. Unfortunately, the experimental phase diagram of the N-W structure is uncertain, as it is difficult to break the ${\text{N}}_2$ bond to form compounds with tungsten. Experiment also indicates that there are a large number of partially filled sites in most N-W structures. This introduces computational difficulties since we cannot easily model randomly placed vacancies. In addition, van der Waals forces play a significant role in determining the structure of solid ${\text{N}}_2$ and the nitrogen-rich compounds. This makes it difficult to determine the relative energies of these compounds, as there is no universally accepted density functional incorporating van der Waals interactions. The exact shape and even composition of the convex hull is dependent upon the choice of density functional, even if we only chose between the local density approximation and a generalized gradient functional. Despite these difficulties, computations can determine much about the ground-state form of the convex hull. Here, we use high-throughput calculations to map out the hull and other low-energy structures for the N-W system. The lowest-energy structures all have vacancies, on the tungsten sites in hexagonal-based compounds, and on both the nitrogen and tungsten sites in cubic compounds. We find that most of the N-W structures proposed in the literature, both theoretical and experimental, are above the convex hull, in some cases by over $0.2 \mathrm{eV}/\mathrm{atom}$. One of the ground-state phases, N-W in the NbO structure, has relatively large bulk ($>300$ GPa) and ($>200$ GPa) shear moduli, and so is a candidate superhard material. This will require further investigation.

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3 + 1)-dimensional superconductors. Starting in 4 + 1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU{\left(2\right)}_2$ Kac-Moody current running along the defect line. The $SU{\left(2\right)}_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3 + 1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-antihedgehog pairs.

The disorder-induced metal-insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e., in the three conventional symmetry classes. Large-scale numerical simulations have been performed on systems with linear sizes up to $L=100$ in order to obtain eigenstates at the band center, $E=0$. The multifractal dimensions, exponents $D_q$ and ${\alpha }_q$, have been determined in the range of $-1\le q\le 2$. The finite-size scaling of the generalized multifractal exponents provide the critical exponents for the different symmetry classes in accordance with values known from the literature based on high-precision transfer matrix techniques. The multifractal exponents of the different symmetry classes provide further characterization of the Anderson transition, which was missing from the literature so far.

We discuss a protocol for growing states with topological order in interacting many-body systems using a sequence of flux quanta and particle insertion. We first consider a simple toy model, the superlattice Bose-Hubbard model, to explain all required ingredients. Our protocol is then applied to fractional quantum Hall systems in both, continuum and lattice. We investigate in particular how the fidelity, with which a topologically ordered state can be grown, scales with increasing particle number $N$. For small systems, exact diagonalization methods are used. To treat large systems with many particles, we introduce an effective model based on the composite fermion description of the fractional quantum Hall effect. This model also allows to take into account the effects of dispersive bands and edges in the system, which will be discussed in detail.

We propose a way to image dynamical properties of nonstationary electron systems using ultrafast resonant x-ray scattering. Employing a rigorous theoretical analysis within the framework of quantum electrodynamics, we demonstrate that a single scattering pattern from a nonstationary electron system encodes the instantaneous interatomic electron current in addition to the structural information usually obtained by resonant x-ray scattering from stationary systems. Thus, inelastic contributions that are indistinguishable from elastic processes induced by a broadband probe pulse, instead of being a concern, serve as an advantage for time-resolved resonant x-ray scattering. Thereby, we propose an approach combining elastic and inelastic resonant x-ray scattering for imaging dynamics of nonstationary electron systems in both real space and real time. In order to illustrate its power, we show how it can be applied to image the electron-hole current in an ionized diatomic molecule.

We synthesized single crystals of an itinerant ferromagnet ${\mathrm{LaCo}}_2{\mathrm{P}}_2$ with ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type structure and studied their magnetism by magnetization and ${}^{31}\mathrm{P}$ NMR measurements. We measured Knight shift $K$ and spin-lattice relaxation rate divided by temperature $1/T_{1}T$ with the applied fields parallel to the $a$ and $c$ axes, and estimated spin fluctuations in the $ab$ plane and $c$. In addition, we evaluated spin fluctuations from the result of magnetization data with a three-dimensional ferromagnetic model. There is little anisotropy in evaluated spin fluctuations in the $ab$ plane and $c$. Spin fluctuations of ${\mathrm{LaCo}}_2{\mathrm{P}}_2$ have a three-dimensional character and can be understood in the framework of the self-consistent renormalization theory of spin fluctuations.

A polarization-independent, nonthermal optical effect on the magnetization in bismuth iron garnet is found, in addition to the circular polarization-dependent inverse Faraday effect and the linear polarization-dependent photoinduced magnetic anisotropy. Its impulsive character is demonstrated by the field dependence of the amplitude of the resulting precession, which cannot be explained by a long-living photo or heat-induced anisotropy.

We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of $2k_F$ singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

Radiative heat transfer can be significantly enhanced via photon tunneling through a nanometer-scale gap to the point that it exceeds the blackbody limit. Here we report quantitative measurements of the near-field thermal radiation between doped-Si plates ($\text{width}=480\mu \text{m}$ and $\text{length}=1.34\mathrm{cm}$). A novel MEMS-based platform enables us to maintain doped-Si plates at nanoscale gap distances that cannot be achieved by other methods. The measured radiative heat transfer coefficient was found to be 2.91 times greater than the blackbody limit at a 400-nm vacuum gap.

Correlated materials have been studied extensively using photoemission spectroscopy. Their optical properties are instead much less explored. Here we present calculations of the optical absorption spectrum of vanadium dioxide $\left({\mathrm{VO}}_2\right)$ in the framework of the Bethe-Salpeter equation (BSE) of many-body perturbation theory. In order to deal with localized electrons we go beyond the standard BSE implementation and extend it to correlated insulators. We show that it is not enough to describe the spectra on the basis of independent electron-hole pairs, even when the electron and hole are separately well described by state-of-the-art one-body Green's functions. Crystal local-field effects are crucial to explain the experimental findings, even qualitatively, and excitonic effects strongly modify the spectra, especially at their onset. In this context, as highighted by the analysis of the BSE results, the quasi-one-dimensional nature of the vanadium-dimer chains plays a prominent role.

We use density functional plus $U$ methods to study the effects of a tensile or compressive substrate strain on the charge-ordered insulating phase of ${\mathrm{LuNiO}}_3$. The numerical results are analyzed in terms of a Landau energy function, with octahedral rotational distortions of the perovskite structure included as a perturbation. Less than $4\%$ tensile or compressive strain leads to a first-order transition from an insulating structure with large-amplitude breathing-mode distortions of the ${\mathrm{NiO}}_6$ octahedra to a metallic state in which breathing-mode distortions are absent but Jahn-Teller distortions in which two Ni-O bonds become long and the other four become short are present. Compressive strain produces uniform Jahn-Teller order with the long axis aligned perpendicular to the substrate plane, while tensile strain produces a staggered Jahn-Teller order in which the long bond lies in the plane and alternates between two nearly orthogonal in-plane directions, forming a checkerboard pattern. In the absence of the breathing-mode distortions and octahedral rotations, the tensile-strain-induced transition to the staggered Jahn-Teller state would be of second order.

We study the quantum anomalous thermal Hall effect in a topological superconductor, which possesses an integer bulk topological number and supports Majorana excitations on the surface. To realize the quantum thermal Hall effect, a finite gap at the surface is induced by applying an external magnetic field or by the proximity effects with magnetic materials or $s$-wave superconductors with complex pair potentials. Basing on the lattice model Hamiltonian for superconducting states in Cu-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, we compute the thermal Hall conductivity as a function of various parameters such as the chemical potential, the pair potential, and the spin-orbit coupling-induced band gap. It is argued that the bulk topological invariant corresponds to the quantization rule of the thermal Hall conductivity induced by complex $s$-wave pair potentials.

Spin-orbit interaction in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ leads to the realization of the $J_{\mathrm{eff}}=1/2$ state and also induces an insulating behavior. Using large-shift Raman spectroscopy, we found two high-energy excitations of the $d$-shell multiplet at 690 and 680 meV with $A_{1g}$ and $B_{1g}$ symmetry, respectively. As temperature decreases, the $A_{1g}$ and $B_{1g}$ peaks narrow, and the $A_{1g}$ peak shifts to higher energy while the energy of the $B_{1g}$ peak remains the same. When $25\%$ of Ir is substituted with Rh the $A_{1g}$ peak softens by $10\%$ but the $B_{1g}$ peak does not. We show that both pseudospin-flip and non-pseudo-spin-flip d-d electronic transitions are Raman active, but only the latter are observed. Our experiments and analysis place significant new constraints on the possible electronic structure of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

The thermodynamic properties of a strongly correlated system with a binary type of disorder are investigated using the combination of the coherent potential approximation and dynamical mean-field theory. The specific heat has a peak at low temperatures for the concentrations close to the filling of system. This peak is associated with the local moment formation due to Coulomb interaction. The linear coefficient to the specific heat is divergent and the system stays in the non-Fermi-liquid regime.

Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting reflection symmetry, which effectively puts the edge theories on an unoriented space-time, such as the Klein bottle. A key technical step taken in this paper is the use of the so-called cross-cap states, which encode entirely the unoriented nature of space-time, and can be obtained by rearranging the space-time geometry and exchanging the role of space and time coordinates. When the system is in a nontrivial SPT phase, we find that the corresponding cross-cap state is noninvariant under the action of the symmetries of the SPT phase, but acquires an anomalous phase. This anomalous phase, with a proper definition of a reference state, on which symmetry acts trivially, reproduces the known classification of (2+1)-dimensional bosonic and fermionic SPT phases protected by reflection symmetry, including in particular the ${\mathbb{Z}}_8$ classification of topological crystalline superconductors protected by reflection and time-reversal symmetries.

Topological quantum states cannot be created from product states with local quantum circuits of constant depth and are in this sense more entangled than topologically trivial states, but how entangled are they? Here we quantify the entanglement in one-dimensional topological states by showing that local quantum circuits of linear depth are necessary to generate them from product states. We establish this linear lower bound for both bosonic and fermionic one-dimensional topological phases and use symmetric circuits for phases with symmetry. We also show that the linear lower bound can be saturated by explicitly constructing circuits generating these topological states. The same results hold for local quantum circuits connecting topological states in different phases.

Silicon nano- and microparticles containing polarized ${}^{29}\mathrm{Si}$ spins are promising inexpensive and biocompatible medical imaging agents, particularly for magnetic resonance imaging (MRI). Maximizing out-of-equilibrium polarization (i.e., hyperpolarization) of the ${}^{29}\mathrm{Si}$ nuclear spins as efficiently as possible is critical for such an application. Here we identify and exploit a frequency-matched resonant transfer process between easily hyperpolarized bulk ${}^{31}\mathrm{P}$ and otherwise insensitive ${}^{29}\mathrm{Si}$ nuclear spins in natural silicon, boosting the ${}^{29}\mathrm{Si}$ signal to over 200 times its thermal equilibrium signal. This technique could be used in tandem with microwave-based hyperpolarization schemes for even higher efficiencies. Lastly, this hyperpolarization buildup process does not necessarily introduce an additional source of decoherence; after hyperpolarization the resonant transfer process can be switched off to recover the ultralong lifetimes of ${}^{29}\mathrm{Si}$ spins for in vivo imaging.

Charge transport in nanocrystalline SiC with and without embedded Si nanocrystals (Si NCs) prepared by annealing of $a-\mathrm{S}{\mathrm{i}}_{1-x}{\mathrm{C}}_x:\mathrm{H}$ precursors is studied using temperature-dependent current-voltage measurements supported by electron spin resonance and mass spectrometry data. Transport is Ohmic in all films at all temperatures and the temperature dependence of conductivity shows that the materials behave as disordered semiconductors, exhibiting extended-state transport at high temperature and variable-range hopping transport at low temperature. Grain-boundary-, surface-, and interface-dominated transport is systematically ruled out. Films are $n$ type, and films with Si NCs exhibit up to  ${10}^3$ times higher conductivity (up to $0.1\mathrm{S}\mathrm{c}{\mathrm{m}}^{-1}$) after exposure to a hydrogen plasma which passivates dangling bonds, particularly on Si NCs. A forming gas anneal does not have such an effect, indicating that atomic rather than molecular hydrogen is required. The conductivity of SiC films without Si NCs is largely unchanged by passivation and the Fermi level is not raised nearly as closely to the conduction band. This is attributed to a type I band offset between Si NCs and SiC that leads to extended-state conduction in films with Si NCs taking place in a Si network. This is confirmed by the dependence of the extended-state mobility on the volume fraction of excess Si. Variable-range hopping is relatively insensitive to the presence of excess Si and is hence considered to take place via shallow defect states throughout the volume of the films. The high conductivities are found to be a consequence of background doping by oxygen and nitrogen.