We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu${}_2$OSeO${}_3$. A magnetic-field-induced electric polarization ($\mathbf{P}$) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state ($T_c=59$ K). Both $\mathbf{P}$ and MC are explored in considerable detail as a function of temperature ($T$), applied field ${\mathbf{H}}_a$, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow us to map out the phase diagram of the system in the $H_a$-$T$ plane. Below the 3-up–1-down collinear ferrimagnetic phase, we find two additional magnetic phases. We demonstrate that these are related to the field-driven evolution of a long-period helical phase, which is stabilized by the chiral Dzyaloshinskii-Moriya term $D\mathbf{M}·(\nabla \times \mathbf{M})$ that is present in this noncentrosymmetric compound. We also present a phenomenological Landau-Ginzburg theory for the magnetic-field-induced electric polarization (ME${}_H$) effect, which is in excellent agreement with experimental data, and shows three main features: (i) the polarization $\mathbf{P}$ has a uniform as well as a long-wavelength spatial component that is given by the pitch of the magnetic helices, (ii) the uniform component of $\mathbf{P}$ points along the vector $(H^y{H}^z,H^z{H}^x,H^x{H}^y)$, and (iii) its strength is proportional to ${\eta }_{\parallel }^2-{\eta }_{\perp }^2/2$, where ${\eta }_{\parallel }$ is the longitudinal and ${\eta }_{\perp }$ is the transverse (and spiraling) component of the magnetic ordering. Hence, the field dependence of $\mathbf{P}$ provides a clear signature of the evolution of a conical helix under a magnetic field. A similar phenomenological theory is discussed for the MC.

We discuss $d$-wave topological (broken time-reversal symmetry) pairing structures in unpolarized and polarized Jain states. We demonstrate pairing in the Jain spin-singlet state by rewriting it in an explicit pairing form, in which we can recognize $d$-wave weak pairing of underlying quasiparticles—composite fermions. We find and describe the root configuration of the Jain spin-singlet state and its connection with neutral excitations of the Haldane-Rezayi state, and study the transition between these states via exact diagonalization. We find high overlaps with the Jain spin-singlet state upon a departure from the hollow-core model for which the Haldane-Rezayi state is the exact ground state. Due to a proven algebraic identity we are able to extend the analysis of topological $d$-wave pairing structures to polarized Jain states and integer quantum Hall states and discuss its consequences.

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero-temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling, which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis à la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than $1/2$ in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.

Ferroelectric domain-wall motions associated with local proton rearrangement and collective proton relay have been revealed in hydrogen-bonded organic ferroelectrics, Phz-H${}_2$ca [phenazine (Phz)-chloranilic-acid (H${}_2$ca)], through dielectric measurements and piezoresponse force microscopy. The domain wall (DW) and thus protons therein are found to be so mobile as to migrate spontaneously, and this feature can be accounted for by the characteristic proton dynamics emergent in this material. Our findings indicate that incomplete proton transfer is a key to a mobile ferroelectric DW in hydrogen-bonded ferroelectrics.

We investigate vortices in LiFeAs using scanning tunneling microscopy/spectroscopy. Zero-field tunneling spectra show two superconducting gaps without detectable spectral weight near the Fermi energy, evidencing fully gapped multiband superconductivity. We image vortices in a wide field range from 0.1 T to 11 T by mapping the tunneling conductance at the Fermi energy. A quasihexagonal vortex lattice at low field contains domain boundaries which consist of alternating vortices with unusual coordination numbers of 5 and 7. With increasing field, the domain boundaries become ill defined, resulting in a uniformly disordered vortex matter. Tunneling spectra taken at the vortex center are characterized by a sharp peak just below the Fermi energy, apparently violating particle-hole symmetry. The image of each vortex shows energy-dependent 4-fold anisotropy which may be associated with the anisotropy of the Fermi surface. The vortex radius shrinks with decreasing temperature and becomes smaller than the coherence length estimated from the upper critical field. This is direct evidence of the Kramer-Pesch effect expected in a clean superconductor.

Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic and strongly driven multilevel system, realized as a superconducting transmon-type circuit. We measure the contribution of the second excited state to the two-level geometric phase and find good agreement with theory treating higher energy levels perturbatively. By changing the evolution time, we confirm the independence of the geometric phase of time and explore the validity of the adiabatic approximation at the transition to the nonadiabatic regime.

Electronic scattering at individual defect sites is presumably sensitive to defect chemistry. Here, we combine advances in carbon nanotube device fabrication and scanning probe characterization to investigate this correspondence. Specifically, we apply scanning gate spectroscopy (SGS) to the study of defects introduced into single walled carbon nanotubes by point functionalization in water, sulfuric acid, or hydrochloric acid. SGS measures the energy-dependent transmission functions of defect sites, and by working in the dilute limit of individual, isolated defects we empirically distinguish the three chemical types. A preliminary analysis proposes a scattering model in order to motivate further theoretical investigations of this one-dimensional scattering system.

We have carried out tilt magnetic field ($B$) studies of the $\nu =12/5$ fractional quantum Hall state in an ultrahigh-quality GaAs quantum well specimen. Its diagonal magnetoresistance $R_{xx}$ shows a nonmonotonic dependence on tilt angle (θ). It first increases sharply with increasing θ, reaches a maximal value of ∼70 Ω at θ ≈ 14°, and then decreases at higher tilt angles. Correlated with this dependence of $R_{xx}$ on θ, the 12/5 activation energy (${\Delta }_{12/5}$) also shows a nonmonotonic tilt dependence. ${\Delta }_{12/5}$ first decreases with increasing θ. Around $\theta ={14}^{\circ }$, ${\Delta }_{12/5}$ disappears as $R_{xx}$ becomes nonactivated. With further increasing tilt angles, ${\Delta }_{12/5}$ reemerges and increases with θ. This tilt $B$ dependence at $\nu =12/5$ is strikingly different from that of the well-documented 5/2 state and calls for more investigations on the nature of its ground state.

We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick (SK) model, we present a detailed derivation of the density $\rho \left(\Delta M\right)$ of the magnetization jumps $\Delta M$. It is obtained by introducing a multicomponent generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that $\rho \left(\Delta M\right)\sim \Delta M^{-\tau }$ with an avalanche exponent $\tau =1$ for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size $1\ll \Delta M<N^{1/2}$, being provoked by changes of the external field by $\delta H=O\left(N^{-1/2}\right)$ where $N$ is the total number of spins. Our general formula also suggests that the density of overlap $q$ between initial and final states in an avalanche is $\rho \left(q\right)\sim 1/(1-q)$. These results show interesting similarities with numerical simulations for the out-of-equilibrium dynamics of the SK model. For finite-range models, using droplet arguments, we obtain the prediction $\tau =(d_{\mathrm{f}}+\theta )/d_{\mathrm{m}}$ where $d_{\mathrm{f}},d_{\mathrm{m}}$, and $\theta$ are the fractal dimension, magnetization exponent, and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.

We report $\beta$-NMR investigations of polarized ${}^8$Li implanted in thin Pb and Ag/Nb films. At the critical superconducting temperature, we observe a singular peak in the spin relaxation rate in small longitudinal magnetic fields, which is attributed to unexpected slow fluctuations in the superconducting order parameter. The peak is several orders of magnitude larger than the prediction based on the enhancement of the dynamic electron spin susceptibility by superconducting fluctuations. The observed peak in $\frac{1}{T_1}$ is rapidly suppressed in a small magnetic field, indicating that it is due to remarkably slow diamagnetic fluctuations which are undetectable with conventional NMR.

Applications of existing precise electronic-structure methods based on density functional theory are typically limited to the treatment of about 1000 inequivalent atoms, which leaves unresolved many open questions in material science, e.g., on complex defects, interfaces, dislocations, and nanostructures. KKRnano is a new massively parallel linear scaling all-electron density functional algorithm in the framework of the Korringa-Kohn-Rostoker (KKR) Green's-function method. We conceptualized, developed, and optimized KKRnano for large-scale applications of many thousands of atoms without compromising on the precision of a full-potential all-electron method, i.e., it is a method without any shape approximation of the charge density or potential. A key element of the new method is the iterative solution of the sparse linear Dyson equation, which we parallelized atom by atom, across energy points in the complex plane and for each spin degree of freedom using the message passing interface standard, followed by a lower-level OpenMP parallelization. This hybrid four-level parallelization allows for an efficient use of up to $100000$ processors on the latest generation of supercomputers. The iterative solution of the Dyson equation is significantly accelerated, employing preconditioning techniques making use of coarse-graining principles expressed in a block-circulant preconditioner. In this paper, we will describe the important elements of this new algorithm, focusing on the parallelization and preconditioning and showing scaling results for NiPd alloys up to 8192 atoms and $65536$ processors. At the end, we present an order-$N$ algorithm for large-scale simulations of metallic systems, making use of the nearsighted principle of the KKR Green's-function approach by introducing a truncation of the electron scattering to a local cluster of atoms, the size of which is determined by the requested accuracy. By exploiting this algorithm, we show linear scaling calculations of more than $16000$ NiPd atoms.

We report specific-heat studies on high-quality Ba-doped phenanthrene, one of the organic superconductors with fused benzene rings, with 100$\%$ shielding fraction. The specific-heat data indicate that Ba-doped phenanthrene is a single-gap $s$-wave superconductor with moderate coupling, and this sets constraints on theoretical models for the understanding of superconductivity in these hydrocarbon superconductors.

Motivated by Sr${}_2$RuO${}_4$, the magnetic properties of edge states in a two-band spin-triplet superconductor with electronlike and holelike Fermi surfaces are investigated assuming chiral $p$-wave pairing symmetry. The two bands correspond to the $\alpha$-$\beta$ bands of Sr${}_2$RuO${}_4$ and are modeled within a tight-binding model including interorbital hybridization and spin-orbit coupling effects. Including superconductivity, the quasiparticle spectrum is determined by means of a self-consistent Bogoliubov–de Gennes calculation. While a full quasiparticle excitation gap appears in the bulk, gapless states form at the edges that produce spontaneous spin and/or charge currents. The spin current is the result of the specific band structure, while the charge current originates from the superconducting condensate. Together they induce a small spin polarization at the edge. Furthermore, onsite Coulomb repulsion is included to show that the edge states are unstable against the formation of a Stoner-type spin polarization of the edge states. Through spin-orbit coupling, the current- and the correlation-induced magnetism are coupled to the orientation of the chirality of the superconducting condensate. We speculate that this type of phenomenon could yield a compensation of the magnetic fields induced by currents and also explain the negative result in the recent experimental search for chiral edge currents.

We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastingsâ 1D area law and which is tight to within a polynomial factor. For particles of dimension $d$, spectral gap $\epsilon >0$, and interaction strength at most $J$, our entropy bound is $S_{1D}\le \mathcal{O}\left(1\right)·X^3{\log }^{8}X$, where $X\stackrel{\mathrm{def}}{=}\left(J\log d\right)/\epsilon$. Our proof is completely combinatorial, combining the detectability lemma with basic tools from approximation theory. In higher dimensions, when the bipartitioning area is $\left|\partial L\right|$, we use additional local structure in the proof and show that $S\le \mathcal{O}\left(1\right)·{\left|\partial L\right|}^2{\log }^6\left|\partial L\right|·X^3{\log }^{8}X$. This is at the cusp of being nontrivial in the 2D case, in the sense that any further improvement would yield a subvolume law.

We report the excitation of spin waves in ferromagnetic semiconductor (Ga,Mn)As films by picosecond strain pulses. The strain pulse with a broad acoustic spectrum excites a number of magnon modes, which contribute to the precession of magnetization. The spectrum of the excited spin waves shows two well-resolved peaks with intensities dependent on the applied magnetic field. For a certain range of magnetic fields only the low-frequency spin wave is detected. We present the theoretical analysis and compare it with the experimental results, addressing the spatial overlap of the magnon and phonon eigenfunctions. Depending on the boundary conditions and the spectrum of the spin waves the spatial matching of the spin wave and resonance phonon eigenfunctions may provide high excitation efficiency for only one magnon mode, while other modes are not excited.

We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field.

Evidence of two-dimensional (2D) quantum critical fluctuations is observed in the superfluid density $n_s$($T$) ∝ λ${}^{-2}$($T$) of extremely underdoped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ (Bi-2212) films, indicating that, in general, quantum fluctuations play a dominant role in underdoped cuprates. Two-dimensional (2D) fluctuations are expressed by the linear scaling $T_c$ ∝ $n_s$(0). 2D scaling in Bi-2212 contrasts with three-dimensional scaling that is seen in the much less anisotropic YBa${}_2$Cu${}_3$O${}_{7-\delta }$. Quantum critical fluctuations could also account for the absence of thermal critical behavior in λ${}^{-2}$($T$) of strongly underdoped Bi-2212 samples, $T_c<48$ K.

We predict the existence of an intriguing “disorder by order” phenomenon in graphene transport where higher quality (and thus more ordered) samples, while having higher mobility at high carrier density, will manifest more strongly insulating (and thus effectively more disordered) behavior as the carrier density is lowered compared with lower quality samples (with higher disorder) which exhibit an approximate resistivity saturation phenomenon at low carrier density near the Dirac point. This predicted behavior simulating a metal-insulator transition, which we believe to have recently been observed in an experiment at Manchester University [L. A. Ponomarenko et al., Nat. Phys. 7, 958 (2011)], arises from the suppression of Coulomb disorder induced inhomogeneous puddles near the charge neutrality point in high quality graphene samples.

Using in situ low-energy electron microscopy and density functional theory, we studied the growth structure and work function of bilayer graphene on Pd(111). Low-energy electron diffraction analysis established that the two graphene layers have multiple rotational orientations relative to each other and the substrate plane. We observed heterogeneous nucleation and simultaneous growth of multiple, faceted layers prior to the completion of second layer. We propose that the faceted shapes are due to the zigzag-terminated edges bounding graphene layers growing under the larger overlying layers. We also found that the work functions of bilayer graphene domains are higher than those of monolayer graphene, and depend sensitively on the orientations of both layers with respect to the substrate. Based on first-principles simulations, we attribute this behavior to oppositely oriented electrostatic dipoles at the graphene/Pd and graphene/graphene interfaces, the strengths of which depend on the orientations of the two graphene layers.

We report a direct measurement of the low-frequency noise spectrum in a superconducting flux qubit. Our method uses the noise sensitivity of a free-induction Ramsey interference experiment, comprising free evolution in the presence of noise for a fixed period of time followed by single-shot qubit-state measurement. Repeating this procedure enables Fourier-transform noise spectroscopy with access to frequencies up to the achievable repetition rate, a regime relevant to dephasing in ensemble-averaged time-domain measurements such as Ramsey interferometry. Rotating the qubit's quantization axis allows us to measure two types of noise: effective flux noise and effective critical-current or charge noise. For both noise sources, we observe that the very same $1/f$-type power laws measured at considerably higher frequencies ($0.2-20$ MHz) are consistent with the noise in the $0.01-100$-Hz range measured here. We find no evidence of temperature dependence of the noises over $65-200$ mK, and also no evidence of time-domain correlations between the two noises. These methods and results are pertinent to the dephasing of all superconducting qubits.