Resistivity, magnetization, and microscopic ${}^{75}$As nuclear magnetic resonance (NMR) measurements in the antiferromagnetically ordered state of the iron-based superconductor parent material CaFe${}_2$As${}_2$ exhibit anomalous features that are consistent with the collective freezing of domain walls. Below $T^{*}\approx 10$ K, the resistivity exhibits a peak and downturn, the bulk magnetization exhibits a sharp increase, and ${}^{75}$As NMR measurements reveal the presence of slow fluctuations of the hyperfine field. These features in both the charge and spin response are strongly field dependent, are fully suppressed by $H^{*}\approx 15$ T, and suggest the presence of filamentary superconductivity nucleated at the antiphase domain walls in this material.

In a standard Kohn-Sham density functional calculation, the total energy of a crystal at zero temperature is evaluated for a perfect static lattice of nuclei and minimized with respect to the lattice constant. Sometimes a zero-point vibrational energy, whose anharmonicity expands the minimizing or equilibrium lattice constant, is included in the calculation or (as here) is used to correct the experimental reference value for the lattice constant to that for a static lattice. A simple model for this correction, based on the Debye and Dugdale-MacDonald approximations, requires as input only readily available parameters of the equation of state, plus the experimental Debye temperature. However, particularly because of the rough Dugdale-MacDonald estimation of Grüneisen parameters for diatomic solids, this simple model is found to overestimate the correction by about a factor of two for some solids in diamond and zinc-blende structures. Using the quasiharmonic phonon frequencies calculated from density functional perturbation theory gives a more accurate zero-point anharmonic expansion (ZPAE) correction. However, the error statistics for the lattice constants of various semilocal density functionals for the exchange–correlation energy are little changed by improving the ZPAE correction. The Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) for solids and the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-GGA, the latter of which is implemented self-consistently here in the band-structure program BAND and applied to a test set of 58 solids, remain the most accurate of the functionals tested, with MAREs below 0.7$\%$ for the lattice constants. The most positive and most negative revTPSS relative errors tend to occur for solids for which full nonlocality (missing from revTPSS) may be important.

We report systematic Cu and F NMR measurements of five-layered high-$T_c$ cuprates Ba${}_2$Ca${}_4$Cu${}_5$O${}_{10}$(F,O)${}_2$. It is revealed that antiferromagnetism (AFM) uniformly coexists with superconductivity (SC) in underdoped regions, and that the critical hole density $p_c$ for AFM is $\sim$0.11 in the five-layered compound. We present the layer-number dependence of AFM and SC phase diagrams in hole-doped cuprates, where $p_c$ for $n$-layered compounds $p_c\left(n\right)$ increases from $p_c\left(1\right)$ $\sim$ 0.02 in La${}_{2-x}$Sr${}_x$CuO${}_4$ or $p_c\left(2\right)$ $\sim$ 0.05 in YBa${}_2$Cu${}_3$O${}_{6+y}$ to $p_c\left(5\right)$ $\sim$ 0.11. The variation of $p_c\left(n\right)$ is attributed to interlayer magnetic coupling, which becomes stronger with increasing $n$. In addition, we focus on the ground-state phase diagram of CuO${}_2$ planes, where AFM metallic states in slightly doped Mott insulators change into the uniformly mixed phase of AFM and SC and into simple $d$-wave SC states. The maximum $T_c$ exists just outside the quantum critical hole density, at which AFM moments on a CuO${}_2$ plane collapse at the ground state, indicating an intimate relationship between AFM and SC. These characteristics of the ground state are accounted for by the Mott physics based on the $t$-$J$ model; the attractive interaction of high-$T_c$ SC, which raises $T_c$ as high as 160 K, is an in-plane superexchange interaction $J_{\text{in}}$ ($\sim 0.12$ eV), and the large $J_{\text{in}}$ binds electrons of opposite spins between neighboring sites. It is the Coulomb repulsive interaction $U$ ($>6$ eV) between Cu-3$d$ electrons that plays a central role in the physics behind high-$T_c$ phenomena.

We investigate the transduction of motion from a nanomechanical resonator to the cantilever/tip probe of an atomic force microscope. Our results show that amplitude-modulated high-frequency vibrations of nanomechanical resonators can be measured by means of a low-resonance frequency cantilever as a consequence of the demodulation introduced by the nonlinear forces involved in the system. The theoretical model presented in this paper enables the quantitative application of atomic force microscopy (AFM) for the characterization of a wide variety of devices. An analysis based on this model of previously reported experiments in carbon nanotube and graphene resonators demonstrates the ability of AFM to measure vibration amplitudes in the subnanometer range without significant perturbation of the resonators.

We performed the neutron powder diffraction (NPD) and synchrotron x-ray diffraction measurements on CeFeAsO${}_{1-x}$(D,H)${}_x$ ($x$ $=$ 0.0 − 0.48) as a representative of 1111-type family of iron-based superconductors $Ln$FeAsO${}_{1-x}$H${}_x$ ($Ln$ $=$ lanthanoid). Deuterated and hydrogenated samples (CeFeAsO${}_{1-x}$D${}_x$ and CeFeAsO${}_{1-x}$H${}_x$) were synthesized by the solid-state reaction of a metal oxide, arsenides, and a hydride and a deuteride source under an applied pressure of 2 GPa. No distinct differences were found between the structural and superconducting properties of the hydride and deuteride samples. Rietveld analyses of the NPD patterns demonstrated that deuterium exclusively substitutes on the oxygen sites in the 1111-type structures according to the nominal composition. Bulk superconductivity was observed over a wide $x$ region (0.1 < $x$ < 0.4) and the superconducting dome had a rather flat shape with a maximum $T_{\mathrm{c}}$ $=$ 47 K at around $x$ $=$ 0.25. It was concluded from density functional theory calculations and comparison with the superconducting dome of the fluorine-substituted system that the charge state of the hydrogen substituting the oxygen sites was −1. The relationship between the lattice parameter $a$ and $T_{\mathrm{c}}$ in our samples prepared from metal hydrides is almost the same as that reported previously for samples prepared from cerium hydroxide. These results strongly suggest that H${}^{-}$ ions exclusively occupy the oxygen sites in both samples, regardless of the hydrogen species in the starting material.

We measure transverse magnetically focused photocurrent signals in an InSb/InAlSb quantum well device. Using optical spin orientation by modulated circularly polarized light an electron spin-dependent signal is observed due to the spin-orbit interaction. Simulations of the focusing signal are performed using a classical billiard ball model, which includes both spin precession and a spin-dependent electron energy. The simulated data suggest that a signal dependent on the helicity of the incident light is expected for a Rashba parameter $\alpha >0.1\mathrm{eV}\AA$ and that a splitting of the focusing signal is not expected to be observed in linear polarized photocurrent and purely electrical measurements.

The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with $s$-wave pairing order. However, $T_{\mathrm{c}}$ is suppressed to zero at half-filling, where long-range charge-density-wave order also appears, degenerate with superconductivity. This paper presents determinant quantum Monte Carlo simulations of the attractive Hubbard model in the presence of a confining potential $V_{\mathrm{trap}}$ which makes the fermion density $\rho$ inhomogeneous across the lattice. Pair correlations are shown to be large at low temperatures in regions of the trapped system with incommensurate filling, and to exhibit a minimum as the local density $\rho \left(\mathit{i}\right)$ passes through one fermion per site. In this ring of $\rho \left(\mathit{i}\right)=1$, charge order is enhanced. A comparison is made between treating $V_{\mathrm{trap}}$ within the local-density approximation (LDA) and in an ab initio manner. It is argued that certain sharp features of the LDA result at integer filling do not survive the proximity of doped sites. The critical temperature of confined systems of fixed characteristic density is estimated.

The characteristic features of the Ca${}_{10}$(Pt${}_3$As${}_8$)[(Fe${}_{1-x}$Pt${}_x$)${}_2$As${}_2$]${}_5$ (the “10-3-8” phase) superconductor are triclinic symmetry, high anisotropy, and a clear separation of superconducting and antiferromagnetic regions in the $T$ versus doping ($x$) phase diagram, which enables the superconducting gap to be studied without complications due to the coexisting magnetic order. The London penetration depth, measured on the underdoped side of the superconducting “dome” ($x=$ 0.028, 0.041, 0.042, and 0.097), shows behavior remarkably similar to other Fe-based superconductors, exhibiting a robust power law, $\Delta \lambda \left(T\right)=A{T}^n$. The exponent $n$ decreases from 2.36 ($x=$ 0.097, close to the optimal doping) to 1.7 ($x=$ 0.028, a heavily underdoped composition), suggesting that the superconducting gap becomes more anisotropic at the dome edge. A similar trend is found in the lower anisotropy BaFe${}_2$As${}_2$ (“122”) -based superconductors, implying that it is an intrinsic property, unrelated to the coexistence of magnetic order and superconductivity or the anisotropy of the normal state.

We explore similarities between the quantum wells and quantum dots used as optical gain media in semiconductor lasers. We formulate a mapping procedure which allows a simpler, often analytical, description of quantum well lasers to study more complex lasers based on quantum dots. The key observation in relating the two classes of laser is that the influence of a finite capture time on the operation of quantum dot lasers can be approximated well by a suitable choice of the gain compression factor in quantum well lasers. Our findings are applied to the rate equations for both conventional (spin-unpolarized) and spin lasers in which spin-polarized carriers are injected optically or electrically. We distinguish two types of mapping that pertain to the steady-state and dynamical operation respectively and elucidate their limitations.

We study nanowires with proximity-induced $s$-wave superconducting pairing in an external magnetic field that rotates along the wire. Such a system is equivalent to nanowires with Rashba-type spin-orbit coupling, with strength proportional to the derivative of the field angle. For realistic parameters, we demonstrate that a set of permanent magnets can bring a nearby nanowire into the topologically nontrivial phase with localized Majorana modes at its ends. This occurs even for a magnetic field configuration with nodes along the wire and alternating sign of the effective Rashba coupling.

Natural 12CaO$·$7Al${}_2$O${}_3$ (C12A7) is a wide band gap insulator, but conductivity can be realized by introducing oxygen deficiency. Currently, there are two competing models explaining conductivity in oxygen-deficient C12A7, one involving the electron transfer via a “cage conduction band” inside the nominal band gap, the other involving electron hopping along framework lattice sites. To help resolve this debate, we probe insulating and conducting C12A7 with x-ray emission, x-ray absorption, and x-ray photoemission spectroscopy, which provide a full picture of both the valence and conduction band edges in these materials. These measurements suggest the existence of a narrow conduction band between the main conduction and valence bands common in both conducting and insulating C12A7 and support the theory that free electrons in oxygen-deficient C12A7 occupy the low-energy states of this narrow band. Our measurements are corroborated with density functional theory calculations.

A quantum particle can be localized in a disordered potential, the effect known as Anderson localization. In such a system, correlations of wave functions at very close energies may be described, due to Mott, in terms of a hybridization of localized states. We revisit this hybridization description and show that it may be used to obtain quantitatively exact expressions for some asymptotic features of correlation functions, if the tails of the wave functions and the hybridization matrix elements are assumed to have log-normal distributions typical for localization effects. Specifically, we consider three types of one-dimensional systems: a strictly one-dimensional wire and two quasi-one-dimensional wires with unitary and orthogonal symmetries. In each of these models, we consider two types of correlation functions: the correlations of the density of states at close energies and the dynamic response function at low frequencies. For each of those correlation functions, within our method, we calculate three asymptotic features: the behavior at the logarithmically large “Mott length scale,” the low-frequency limit at length scale between the localization length and the Mott length scale, and the leading correction in frequency to this limit. In the several cases, where exact results are available, our method reproduces them within the precision of the orders in frequency considered.

The oldest known magnetic material, magnetite, is of current interest for use in spintronics as a thin film. An open question is how thin can magnetite films be and still retain the robust ferrimagnetism required for many applications. We have grown 1-nm-thick magnetite crystals and characterized them in situ by electron and photoelectron microscopies including selected-area x-ray circular dichroism. Well-defined magnetic patterns are observed in individual nanocrystals up to at least 520 K, establishing the retention of ferrimagnetism in magnetite two unit cells thick.

A new methodology for micromagnetic simulations of magnetic nanocomposites is presented. The methodology is especially suitable for simulations of two-phase composites consisting of magnetically hard inclusions in a soft magnetic matrix phase. The proposed technique allows us to avoid unnecessary discretization of the “hard” inclusions (these are normally in a single-domain state) but enables arbitrary fine discretization of the “soft” phase. The method is applied to the determination of the equilibrium magnetization state of an iron-based nanocomposite from the Nanoperm (FeZrBCu) family of alloys and to the calculation of the corresponding small-angle neutron scattering (SANS) cross-section. The results of our simulations exhibit a remarkable agreement with nontrivial “clover-leaf” SANS cross-sections observed experimentally.

Utilizing large-scale Monte Carlo simulations, we investigate an unconventional two-component classical plasma in two dimensions which controls the behavior of the norms and overlaps of the quantum-mechanical wave functions of Ising-type quantum Hall states. The plasma differs fundamentally from that which is associated with the two-dimensional $XY$ model and Abelian fractional quantum Hall states. We find that this unconventional plasma undergoes a Berezinskii-Kosterlitz-Thouless phase transition from an insulator to a metal. The parameter values corresponding to Ising-type quantum Hall states lie on the metallic side of this transition. This result verifies the required properties of the unconventional plasma used to demonstrate that Ising-type quantum Hall states possess quasiparticles with non-Abelian braiding statistics.

Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\pi$ slips of the phase of the order parameter. However, in a finite-length wire, coherent quantum phase slips would manifest themselves simply as shifts of energy levels in the excitation spectrum of an electrical circuit incorporating this wire. The higher the phase slips' probability amplitude, the larger are the shifts. Phase slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slip amplitudes random functions of time, and therefore turn energy level shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a “slippery” wire. The slip-induced linewidths, despite being only of order $100\mathrm{kHz}$, were resolved from the flux-dependent dephasing of the fluxonium qubit.

The ground state of the two-dimensional electron systems in Bernal bilayer and ABC-stacked multilayer graphenes in the presence of a strong magnetic field is investigated with the Hartree-Fock approximation. Phase diagrams of the systems are obtained, focusing on charge density wave states including states with vortices of valley pseudospins (called a Skyrme crystal). The single-electron states in these stacked graphenes are given by two-component wave functions. That of the first excited Landau level has the same component as the lowest Landau level of the ordinary two-dimensional electrons. Because of this localized wave function, the Skyrme crystal has low energy in this first excited level up to four layers of graphene, when the interlayer distance is assumed to be infinitesimal. At the same time, bubble crystals are suppressed, so the phase diagram is different from that of a single-layer graphene.

We study the electronic instabilities of near 1/4 electron doped graphene using the singular-mode functional renormalization group, with a self-adaptive $k$ mesh to improve the treatment of the van Hove singularities, and variational Monte Carlo method. At 1/4 doping the system is a chiral spin-density wave state exhibiting the anomalous quantized Hall effect. When the doping deviates from 1/4, the $d_{x^2-y^2}+i{d}_{xy}$ Cooper pairing becomes the leading instability. Our results suggest that near 1/4 electron or hole doping (away from the neutral point) the graphene is either a Chern insulator or a topoligical superconductor.

Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois-conjugated Hamiltonians are typically non-Hermitian, we find that their ground-state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground-state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such nonunitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this, we rigorously prove that no local change of basis can transform the ground states of the Galois-conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasilocal Hamiltonians. A similar statement holds for many other nonunitary TQFTs. One consequence is that these nonunitary TQFTs do not describe physical realizations of topological phases. In particular, this implies that the “Gaffnian” wave function can not be the ground state of a gapped fractional quantum Hall state.

Topological insulator edges and spin-orbit-coupled quantum wires in proximity to $s$-wave superconductors can be tuned through a topological quantum phase transition by a Zeeman field. Here we show that a supercurrent flowing in the $s$-wave superconductor also drives such a transition. We propose to use this mechanism to generate and manipulate Majorana fermions that localize at domain walls between topological and nontopological regions of an edge or wire. In quantum wires, this method carries the added benefit that a supercurrent reduces the critical Zeeman field at which the topological phase appears.