Determining the magnetic order of solids in high magnetic fields is technologically challenging. Here we probe the cascade of magnetic phase transitions in frustrated multiferroic CuFeO${}_2$ using nuclear forward scattering (NFS) in pulsed magnetic fields up to 30 T. Our results are in excellent agreement with detailed neutron diffraction experiments, currently limited to 15 T, while providing experimental confirmation of the proposed higher field phases for both $H\parallel c$ and $H\perp c$. We thus establish NFS as a valuable tool for spin structure studies in very high fields, both complementing and expanding on the applicability of existing techniques.

The interplay between stripe correlations, local structure, and superconductivity in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$ is studied with concomitant polarized x-ray absorption fine structure (XAFS) and x-ray diffraction measurements at high pressure. Long-range order of the CuO${}_6$ octahedral tilt pattern that pins charge-stripe order vanishes at a pressure-induced structural transition ($P=1.8$ GPa at $T=5$ K). Diffraction shows that static charge stripe and associated octahedral tilt correlations which survive in the high-pressure phase are effectively suppressed above 3.5 GPa. In contrast, XAFS analysis shows that instantaneous local correlations of the characteristic octahedral tilt pattern remain robust to at least 5 GPa. The decreasing local tilt angle is well correlated with a gradual increase in the superconducting transition temperature, suggesting that orientational pinning of charge correlations can survive the loss of static stripe order.

We report the observation of coherent oscillations associated with charge-density-wave (CDW) order in the underdoped cuprate superconductor YBa${}_2$Cu${}_3$O${}_{6+x}$ by time-resolved optical reflectivity. Oscillations with frequency $1.87$ THz onset at approximately 105 and 130 K for dopings of $x=0.67$ (ortho-VIII) and $x=0.75$ (ortho-III), respectively. Upon cooling below the superconducting critical temperature ($T_c$), the oscillation amplitude is enhanced, the phase shifts by $\pi$, and the frequency softens by $\delta \nu /\nu \approx 7\%$. A biquadratically coupled Landau-Ginzburg model qualitatively describes this behavior as arising from competition between superconducting and CDW orders.

In a one-dimensional spinless $p$-wave superconductor with coherence length $\xi$, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean-free path $l=\xi /2$. Here, we show that a multichannel spinless $p$-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number $N$. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean-free path $l=\xi /(N+1)$, parametrically smaller than the critical mean-free path in one dimension. Our result is valid in the limit that the wire width $W$ is much smaller than the superconducting coherence length $\xi$.

The dynamics of BCS (Bardeen-Cooper-Schrieffer) superconductors is fairly well understood due to the availability of a mean-field solution for the pairing Hamiltonian, a solution which gives the quantum state of a superconductor as a state of almost-free fermions interacting only with a condensate. As a result, transition probabilities may be computed, and expressed in terms of matrix elements of electron creation and annihilation operators between approximate eigenstates. These matrix elements are also called “coherence factors.” Mean-field theory is however not sufficient to describe all eigenstates of a superconductor, a deficiency which is hardly important in (or very close to) equilibrium, but one that becomes relevant in certain out-of-equilibrium situations. We report here on a computation of matrix elements (coherence factors) for the pairing Hamiltonian between any “two-arc” eigenstates in the thermodynamic limit.

We present a synchrotron grazing incidence x-ray diffraction analysis of the domain structure and polar symmetry of highly strained BiFeO${}_3$ (BFO) thin films grown on LaAlO${}_3$ substrate. We reveal the existence of periodic elastic nanodomains in the pure tetragonal-like BFO ultrathin films down to a thickness of 6 nm. A unique shear strain-accommodation mechanism is disclosed. We further demonstrate that the periodicity of the nanodomains increases with film thickness but deviates from the classical square root law in the ultrathin thickness regime (6–30 nm). Temperature-dependent experiments further reveal the disappearance of periodic modulation above ∼90 °C due to a $M_C$-$M_A$ structural phase transition.

The intrinsic stacking fault energy (SFE) of copper under volumetric, longitudinal, and shear strains is investigated using density functional theory (GGA-PBE). Calculations are performed using a copper slab model aligned perpendicular to the (111) intrinsic stacking fault plane. The calculated SFE for unstrained copper is γ $=$ 41 mJ/m${}^2$. Results show a strong dependence of γ on strain and distinct behavior for different types of strain: (a) volumetric and longitudinal in the direction perpendicular to the stacking fault, (b) longitudinal parallel to the stacking fault, and (c) shear parallel to the stacking fault. In the first case (a), the SFE decreases monotonically with strain with a slope $d$γ/$d$ε${|}_{\varepsilon =0}$ $=$ −0.44 J/m${}^2$ and −0.87 J/m${}^2$ for volumetric and longitudinal, respectively, and with $d^2$γ/$d$ε${}^2$ > 0. In contrast, for longitudinal strain parallel to the stacking fault (b), the SFE dependence exhibits $d^2$γ/$d$ε${}^2$ < 0 with a maximum at ε ≈ −0.015. For the case of shear parallel to the stacking fault (c), the SFE is nearly constant at small and moderately large strain, but drops rapidly at very large strain (by a factor of 1/3 for $\langle \overline{1}10\rangle \left\{111\right\}$ shear at ε $=$ ±0.1). For large $\langle 11\overline{2}\rangle \left\{111\right\}$ shear strains, the SFE can either increase or decrease at large strain depending on the sign of the strain. In volumetric or longitudinal (perpendicular to the stacking fault) tension and longitudinal strain in the boundary plane (and for some shear directions), the SFE can become negative, implying a limit on the stability of the fcc crystal structure. The strong dependence of the SFE on strain suggests deep implications for the mechanical properties, microstructural evolution, and dynamic plasticity of metals at high pressure, during severe plastic deformation, and in shock-loading conditions.

Ferroelectric PbTiO${}_3$  occupies a special place among ferroelectric materials owing to its unique status as a prototype displacive ferroelectric. However, while PbTiO${}_3$  undoubtedly provides one of the best examples of displacive phase transitions, several experimental and theoretical findings seem to suggest a certain degree of order-disorder mechanism associated with the phase transition. While multiple efforts have been undertaken to better understand the nature of the phase transition in this classic ferroelectric, the subject still remains controversial. Here we develop a force field from first principles to study soft mode dynamics in PbTiO${}_3$  from an atomistic viewpoint. Our computations indicate the presence of order-disorder mechanism in the vicinity of the phase transition in this classic displacive ferroelectric.

Femtosecond laser pulses are used to excite coherent optical phonons in single crystal Bi${}_2$Te${}_3$ thin films. Oscillations from low- and high-frequency A${}_{1\mathrm{g}}$ phonon modes are observed. A perturbation model based on molecular dynamics reveals various possibilities of phonon generation due to complex interactions among different phonon modes. In order to elucidate the process of phonon generation, measurements on thin films with thicknesses below the optical absorption depth are carried out, showing that a gradient force is necessary to excite the observed A${}_{1\mathrm{g}}$ phonon modes, which provides a refined picture of displacive excitation of coherent phonon.

We study the motion of several types of domain wall profiles in spin-orbit coupled magnetic nanowires and also the influence of spin-orbit interaction on the ferromagnetic resonance of uniform magnetic films. Whereas domain wall motion in systems without correlations between spin space and real space is not sensitive to the precise magnetization texture of the domain wall, spin-orbit interactions break the equivalence between such textures due to the coupling between the momentum and spin of the electrons. In particular, we extend previous studies by fully considering not only the fieldlike contribution from the spin-orbit torque, but also the recently derived Slonczewski-like spin-orbit torque. We show that the latter interaction affects both the domain wall velocity and the Walker breakdown threshold nontrivially, which suggests that it should be accounted for in experimental data analysis. We find that the presence of multiple spin-orbit torques may render the Walker breakdown universal in the sense that the threshold is completely independent on the material-dependent Gilbert damping $\alpha$, nonadiabaticity $\beta$, and the chirality $\sigma$ of the domain wall. We also find that domain wall motion against the current injection is sustained in the presence of multiple spin-orbit torques and that the wall profile will determine the qualitative influence of these different types of torques (e.g., fieldlike and Slonczewski-like). In addition, we consider a uniform ferromagnetic layer under a current bias, and find that the resonance frequency becomes asymmetric against the current direction in the presence of Slonczewski-like spin-orbit coupling. This is in contrast with those cases where such an interaction is absent, where the frequency is found to be symmetric with respect to the current direction. This finding shows that spin-orbit interactions may offer additional control over pumped and absorbed energy in a ferromagnetic resonance setup by manipulating the injected current direction.

We present a theoretical study of the two-dimensional spiral antiferromagnet ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$ in the presence of an external magnetic field. We employ a suitable nonlinear $\sigma$ model to calculate the $T=0$ phase diagram and the associated low-energy spin dynamics for arbitrary canted magnetic fields, in general agreement with experiment. In particular, when the field is applied parallel to the $c$ axis, a previously anticipated Dzyaloshinskii-type incommensurate-to-commensurate phase transition is actually mediated by an intermediate phase, in agreement with our earlier theoretical prediction confirmed by the recent observation of the so-called double-$k$ structure. The sudden $\pi /2$ rotations of the magnetic structures observed in experiment are accounted for by a weakly broken $U\left(1\right)$ symmetry of our model. Finally, our analysis suggests a nonzero weak-ferromagnetic component in the underlying Dzyaloshinskii-Moriya anisotropy, which is important for quantitative agreement with experiment.

The electronic structure and magnetic properties of FeGa${}_3$ and doped FeGa${}_3$ are studied using density functional calculations. An itinerant mechanism for ferromagnetism is found both for $n$-type doping with Ge and also for $p$-type doping. Boltzmann transport calculations of the thermopower are also reported.

In quasi-one-dimensional nanowires, superconductivity is destroyed by phase slip events. Phase slips can be caused by thermal activation over a free energy barrier (TAPS) or quantum tunneling through the barrier (QPS). Quantum phase slip is an example of macroscopic quantum tunneling. Here, we report the observation of QPS experimentally separated from interference of TAPS in aluminum nanowires. This separation between the low-temperature QPS and the high-temperature TAPS regions is made possible by a phase slip free superconducting region stabilized by the dissipative environment viz. the normal electrodes. Individual QPSs are detected by means of a single-shot voltage measurement protocol, in which they appear as stochastic switching events from the superconducting to the normal state.

Motivated by the search for an experimentally realizable high density and strongly interacting one-dimensional quantum liquid, we have performed quantum Monte Carlo simulations of bosonic helium-4 confined inside a nanopore with cylindrical symmetry. By implementing two numerical estimators of superfluidity corresponding to capillary flow and the rotating bucket experiment, we have simultaneously measured the finite size and temperature superfluid response of ${}^4$He to the longitudinal and rotational motion of the walls of a nanopore. Within the two-fluid model, the portion of the normal liquid dragged along with the boundaries is dependent on the type of motion, and the resulting anisotropic superfluid density plateaus far below unity at $T=0.5\text{K}$. The origin of the saturation is uncovered by computing the spatial distribution of superfluidity, with only the core of the nanopore exhibiting any evidence of phase coherence. The superfluid core displays a scaling behavior consistent with Luttinger liquid theory, thereby providing an experimental test for the emergence of a one-dimensional quantum liquid.

We report thermal expansion measurements on Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals with different thermal treatment, with samples chosen to represent four different ground states observed in this family. For all samples, thermal expansion is anisotropic with different signs of the in-plane and $c$-axis thermal expansion coefficients in the high temperature, tetragonal phase. The features in thermal expansion associated with the phase transitions are of opposite signs as well, pointing to a different response of transition temperatures to the in-plane and the $c$-axis stress. These features, and consequently the inferred pressure derivatives, are very large, clearly and substantially exceeding those in the Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ family. For all transitions the $c$-axis response is dominant.

We show that a periodic lattice of Abrikosov vortices in the type-II superconductor can support fermionic states with zero energy. Zero modes appear at the intersection of electronic Bloch bands with the Fermi level. In a chiral $p_x+i{p}_y$ wave superconductor the spectrum contains Majorana states at the center of an effective Brillouin zone. The Bloch bands formed by the overlapping vortex core states can transmit energy flow across the lattice. The hallmark of zero modes in electronic heat conductivity is discussed.

We investigate the thermoelectric properties of the electron-doped FeAs${}_2$ both experimentally and theoretically. Electrons are doped by partially substituting Se for As, which leads to a metallic behavior in the resistivity. A Seebeck coefficient of about $-$200 $\mu$V/K is reached at 300 K for 1% doping, and about $-$120 $\mu$V/K even at 5% doping. The origin of this large Seebeck coefficient, despite the metallic conductivity, is analyzed from a band structure point of view. The first-principles band calculation reveals the presence of a pudding-mold-type band just above the band gap, somewhat similar to Na${}_x$CoO${}_2$, but with a quasi-one-dimensional nature. We calculate the Seebeck coefficient using a tight-binding model that correctly reproduces this band structure, and this gives results roughly in agreement with the experiments. Moreover, a consideration of electron correlations beyond the generalized gradient approximation by the fluctuation exchange method gives even better agreement. The origin of this peculiar band shape is also discussed. Combined with previous studies, we now have good thermoelectric materials with quasi-one-, two-, and three-dimensional band structures that have partially flat portions. The present study reinforces the general efficiency of this peculiar band shape in thermoelectric materials.

A potential thermoelectric material CuAlO${}_2$ is theoretically studied. We first construct a model Hamiltonian of CuAlO${}_2$ based on the first principles band calculation, and calculate the Seebeck coefficient. Then, we compare the model with that of a well-known thermoelectric material Na${}_x$CoO${}_2$, and discuss the similarities and the differences. It is found that the two materials are similar from an electronic structure viewpoint in that they have a peculiar pudding-mold type band shape, which is advantageous for thermoelectric materials. There are, however, some differences, and we analyze the origin of the difference from a microscopic viewpoint. The band shape (a very flat band top but with an overall wide bandwidth) of CuAlO${}_2$ is found to be even more ideal than that of Na${}_x$CoO${}_2$, and we predict that once a significant amount of holes is doped in CuAlO${}_2$, thermoelectric properties (especially the power factor) even better than those of Na${}_x$CoO${}_2$ can be expected.

We discuss a topological classification of insulators and superconductors in the presence of both (nonspatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using the structure of bulk Dirac Hamiltonians of minimal matrix dimensions and explicit constructions of topological invariants, we provide the complete classification, which still has the same dimensional periodicities with the original Altland-Zirnbauer classification. The classification of reflection-symmetry-protected topological insulators and superconductors depends crucially on the way reflection symmetry operation is realized. When a boundary is introduced, which is reflected into itself, these nontrivial topological insulators and superconductors support gapless modes localized at the boundary.

We consider spaces of trial wave functions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground-state wave function, partitioned into two parts. In another, functions are defined by the way in which they vanish as several coordinates approach the same value, or by a projection-operator Hamiltonian that enforces those conditions. In a third way, functions are given by conformal blocks from a conformal field theory (CFT). These different spaces of functions are closely related. The use of CFT methods permits an algebraic formulation to be given for all of them. In some cases, we can prove that there is a ground state, a Hamiltonian, and a CFT such that, for any number of particles, all of these spaces are the same. For such cases, this resolves several questions and conjectures: it gives a finite-size bulk-edge correspondence, and we can use the analysis of functions to construct a projection-operator Hamiltonian that produces those functions as zero-energy states. For a model related to the $\mathcal{N}=1$ superconformal algebra, the corresponding Hamiltonian imposes vanishing properties involving only three particles; for this we determine all the wave functions explicitly. We do the same for a sequence of models involving the $M(3,p)$ Virasoro minimal models that has been considered previously, using results from the literature. We exhibit the Hamiltonians for the first few cases of these. The techniques we introduce can be applied in numerous examples other than those considered here.