We develop a theory for the maximum achievable mobility in modulation-doped 2D GaAs-AlGaAs semiconductor structures by considering the momentum scattering of the 2D carriers by the remote ionized dopants, which must invariably be present in order to create the 2D electron gas at the GaAs-AlGaAs interface. The minimal model, assuming first-order Born scattering by random quenched remote dopant ions as the only scattering mechanism, gives a mobility much lower (by a factor of 3 or more) than that observed experimentally in many ultrahigh-mobility modulation-doped 2D systems, establishing convincingly that the model of uncorrelated scattering by independent random remote quenched dopant ions is often unable to describe the physical system quantitively. We theoretically establish that the consideration of spatial correlations in the remote dopant distribution can enhance the mobility by (up to) several orders of magnitudes in experimental samples. The precise calculation of the carrier mobility in ultrapure modulation-doped 2D semiconductor structures thus depends crucially on the unknown spatial correlations among the dopant ions in the doping layer which may manifest sample to sample variations even for nominally identical sample parameters (i.e., density, well width, etc.), depending on the details of the modulation-doping growth conditions.

Using the recently derived representation for the polarization tensor in (2+1)-dimensional space-time allowing an analytic continuation to the entire plane of complex frequencies, we obtain simple analytic expressions for the reflection coefficients of graphene at nonzero Matsubara frequencies. In the framework of the Lifshitz theory, these coefficients are shown to lead to nearly exact results for the Casimir free energy and pressure between two graphene sheets. The constituent parts of large thermal effect, arising in the Casimir interaction at short separations due to an explicit parametric dependence of the polarization tensor on the temperature and an implicit dependence through a summation over the Matsubara frequencies, are calculated. It is demonstrated that an explicit thermal effect exceeds an implicit one at shorter separations, both effects are similar in magnitudes at moderate separations, and that an implicit effect becomes a larger one with further increase of separation. Possible applications of the developed formalism, other than the Casimir effect, are discussed.

Icosahedral short-range order (ISRO) has been widely accepted to be dominant in Cu-Zr metallic glasses (MGs). However, the diffusion mechanism and correlation of ISRO and medium-range order (MRO) to diffusion in MGs remain largely unexplored. Here, we perform a long time annealing up to 1.8 μs in molecular dynamics simulations to study the diffusion mechanism and the relationship between atomic structures and the diffusion path in a $\mathrm{C}{\mathrm{u}}_{64.5}\mathrm{Z}{\mathrm{r}}_{35.5}$ MG. It is found that most of the diffusing events performed by the diffusing atoms are outside ISRO and the Bergman-type MRO. The long-range diffusion in MGs is highly heterogeneous, via collective diffusing events through the liquidlike channels in the glass. Our results clearly demonstrate a strong correlation between the atomic structures and transport in MGs.

The intergrowth crystal of $n$-tetracosane/urea presents a misfit parameter, defined by the ratio $\gamma =c_h/c_g(c_{\mathrm{host}}/c_{\mathrm{guest}})$, that is very close to a commensurate value $(\gamma \cong 1/3)$. High-resolution diffraction studies presented here reveal an aperiodic misfit parameter of $\gamma =0.3369$, which is found to be constant at all temperatures studied. A complex sequence of structural phases is reported. The high temperature phase (phase I) exists in the four-dimensional superspace group $P{6}_{1}22\left(00\gamma \right)$. At $T_{c1}=179\left(1\right)\mathrm{K}$, a ferroelastic phase transition increases the dimension of the crystallographic superspace. This orthorhombic phase (phase II) is characterized by the five-dimensional (5D) superspace group $C{222}_1\left(00\gamma \right)\left(10\delta \right)$ with a modulation vector ${{\mathit{a}}_{\mathit{o}}}^{*}+{{\mathit{c}}_{\mathit{m}}}^{*}={{\mathit{a}}_{\mathit{o}}}^{*}+\delta ·{{\mathit{c}}_{\mathit{h}}}^{*}$, in which the supplementary misfit parameter is $\delta =0.025\left(1\right)$ in host reciprocal units. This corresponds to the appearance of a modulation of very long period (about $440\pm 16\AA$). At $T_{c2}=163.0\left(5\right)\mathrm{K}$, a 5D to 5D phase transition leads to the crystallographic superspace group $P{2}_1{2}_1{2}_1\left(00\gamma \right)\left(00\delta \right)$ with a very similar value of δ. This phase transition reveals a significant hysteresis effect.

The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the approximation of an effective core radius, inside which ad hoc regularizations are implemented, such approximations lead to a compromise in the accuracy of the calculations. In this work an anisotropic nonsingular elastic representation of dislocation fields is developed to accurately represent the near-core stresses of dislocations in $\alpha$-iron. The regularized stress field is enabled through the use of a nonsingular Green's tensor function of Helmholtz-type gradient anisotropic elasticity, which requires only a single characteristic length parameter in addition to the material's elastic constants. Using a magnetic bond-order potential to model atomic interactions in iron, molecular statics calculations are performed, and an optimization procedure is developed to extract the required length parameter. Results show the method can accurately replicate the magnitude and decay of the near-core dislocation stresses even for atoms belonging to the core itself. Comparisons with the singular isotropic and anisotropic theories show the nonsingular anisotropic theory leads to a substantially more accurate representation of the stresses of both screw and edge dislocations near the core, in some cases showing improvements in accuracy of up to an order of magnitude. The spatial extent of the region in which the singular and nonsingular stress differ substantially is also discussed. The general procedure we describe may in principle be applied to accurately model the near-core dislocation stresses of any arbitrarily shaped dislocation in anisotropic cubic media.

The theory of spin fluctuations is developed for an ensemble of localized electrons, taking into account both the hyperfine interaction of electron and nuclear spins and electron hopping between the sites. The analytical expression for the spin noise spectrum is derived for an arbitrary relation between the electron spin precession frequency in a field of nuclear fluctuations and the hopping rate. An increase in the hopping rate results in a drastic change in the spin noise spectrum. The effect of an external magnetic field is briefly addressed.

We develop an analytical approximate method for determining the Bohr radii of Wannier-Mott excitons in thin quantum wells under the influence of magnetic field perpendicular to the quantum well plane. Our hybrid variational-perturbative method allows us to obtain simple closed formulas for exciton binding energies and optical transition rates. We confirm the reliability of our method through exciton-polariton experiments realized in a GaAs/AlAs microcavity with an 8 nm ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum well and magnetic field strengths as high as 14 T.

Optical metasurfaces have become a new paradigm for creating flat optical devices. While being typically an order of magnitude thinner than the wavelength of light, metasurfaces allow control of the phase of propagating light waves across the full $2\pi$ range and therefore enable the realization of optical elements such as lenses, waveplates, and beam converters. Currently one of the limiting factors of functional metasurfaces is their small range of operational angles. Here we demonstrate both theoretically and experimentally that the angular range can be broadened by increasing the rotational symmetry of metasurfaces. We develop an analytical model based on the discrete dipole approximation that quantitatively describes the response of metasurfaces under oblique excitation. It shows that the effective optical symmetry is doubled for structures with odd rotational symmetry, increasing the angular range correspondingly. We apply and experimentally verify our model for metasurfaces consisting of identical meta-atoms, arranged into square lattices, hexagonal lattices, and on the vertices of a Penrose tiling. The results demonstrate the increasing angular performance with increasing rotational symmetry.

Different from the two-dimensional (2D) topological insulator, the 2D topological crystalline insulator (TCI) phase disappears when the mirror symmetry is broken, e.g., upon placing on a substrate. Here, based on a new family of 2D TCIs—SnTe and PbTe monolayers—we theoretically predict the realization of the quantum anomalous Hall effect with a Chern number $\mathcal{C}=2$ even when the mirror symmetry is broken. Remarkably, we also demonstrate that the considered materials retain their large-gap topological properties in quantum well structures obtained by sandwiching the monolayers between NaCl layers. Our results demonstrate that the TCIs can serve as a seed for observing robust topologically nontrivial phases.

We demonstrate that graphene-based photonic superlattices provide a versatile platform for electrical and all-optical control of photonic beams with deep-subwavelength accuracy. Specifically, by inserting graphene sheets into periodic metallodielectric structures, one can design optical superlattices that possess photonic Dirac points (DPs) at frequencies at which the spatial average of the permittivity of the superlattice $\overline{\varepsilon }$ vanishes. Similar to the well-known zero-$\overline{n}$ band gaps, we show that these zero-$\overline{\varepsilon }$ DPs are highly robust against structural disorder. We also show that, by tuning the graphene permittivity via the optical Kerr effect or electrical doping, one can induce a spectral variation of the DP exceeding 30 nm, at mid-IR and THz frequencies. The implications of this wide tunability for the photonic Zitterbewegung effect in a vicinity of the DP are also explored.

We present magnetization isotherms in pulsed magnetic fields up to 62 T, supported by first-principles calculations, demonstrating a huge uniaxial magnetocrystalline anisotropy energy—approximately 20 $\text{MJ}/{\mathrm{m}}^3$—in ${\mathrm{UMn}}_2{\mathrm{Ge}}_2$. This large anisotropy results from the extremely strong spin-orbit coupling affecting the uranium $5f$ electrons, which in the calculations exhibit a substantial orbital moment exceeding $2{\mu }_B$. We also find from theoretical calculations that a number of isostructural Mn actinide compounds are expected to have similarly large anisotropy.

We develop a theory of spin excitations in a field-induced spin-nematic state, and use it to show how a spin-nematic order can be indentified using inelastic neutron scattering. We concentrate on two-dimensional frustrated ferromagnets, for which a two-sublattice, bond-centered spin-nematic state is predicted to exist over a wide range of parameters. First, to clarify the nature of spin-excitations, we introduce a soluble spin-1 model, and use this to derive a continuum field theory, applicable to any two-sublattice spin-nematic state. We then parameterize this field theory, using diagrammatic calculations for a realistic microscopic model of a spin-$\frac{1}{2}$ frustrated ferromagnet, and show how it can be used to make predictions for inelastic neutron scattering. As an example, we show quantitative predictions for inelastic scattering of neutrons from ${\mathrm{BaCdVO}(\mathrm{PO}}_4{)}_2$, a promising candidate to realize a spin-nematic state at an achievable $h\sim 4$ T. We show that in this material it is realistic to expect a ghostly Goldstone mode, signalling spin-nematic order, to be visible in experiment.

Nambu-Goldstone modes associated with (topological) defects such as vortices and domain walls in (super)fluids are known to possess quadratic/noninteger dispersion relations in finite/infinite-size systems. Here, we report interpolating formulas connecting the dispersion relations in finite- and infinite-size systems for Kelvin modes along a quantum vortex and ripplons on a domain wall in superfluids. Our method can provide not only the dispersion relations but also the explicit forms of quasiparticle wave functions $(u,v)$. We find a complete agreement between the analytical formulas and numerical simulations. All these formulas are derived in a fully analytical way, and hence not empirical ones. We also discuss common structures in the derivation of these formulas and speculate on the general procedure.

A conformal transformation of a uniform triangular pinning array produces a structure called a conformal crystal which preserves the sixfold ordering of the original lattice but contains a gradient in the pinning density. Here we use numerical simulations to show that vortices in type-II superconductors driven with an ac drive over gradient pinning arrays produce the most pronounced ratchet effect over a wide range of parameters for a conformal array, while square gradient or random gradient arrays with equivalent pinning densities give reduced ratchet effects. In the conformal array, the larger spacing of the pinning sites in the direction transverse to the ac drive permits easy funneling of interstitial vortices for one driving direction, producing the enhanced ratchet effect. In the square array, the transverse spacing between pinning sites is uniform, giving no asymmetry in the funneling of the vortices as the driving direction switches, while in the random array, there are numerous easy-flow channels present for either direction of drive. We find multiple ratchet reversals in the conformal arrays as a function of vortex density and ac amplitude, and correlate the features with a reversal in the vortex ordering, which is greater for motion in the ratchet direction. The enhanced conformal pinning ratchet effect can also be realized for colloidal particles moving over a conformal array, indicating the general usefulness of conformal structures for controlling the motion of particles.

We report electron doping effects by Ni in ${\text{K}}_x{\text{Fe}}_{2-\delta -y}{\text{Ni}}_y{\text{Se}}_2(0.06\le y\le 1.44)$ single-crystal alloys. A rich ground-state phase diagram is observed. A small amount of Ni ($\sim 4$%) suppressed superconductivity below 1.8 K, inducing insulating spin-glass magnetic ground state for higher Ni content. With further Ni substitution, metallic resistivity is restored. For high Ni concentration in the lattice the unit cell symmetry is high symmetry $I4/mmm$ with no phase separation whereas both $I4/m+I4/mmm$ space groups were detected in the phase separated crystals when concentration of Ni $<$ Fe. The absence of superconductivity coincides with the absence of crystalline Fe vacancy order.

It has been shown that the bosonic symmetry-protected-trivial (SPT) phases with pure gauge anomalous boundary can all be realized via nonlinear $\sigma$ models $\left(\mathrm{NL}\sigma \mathrm{Ms}\right)$ of the symmetry group $G$ with various topological terms. Those SPT phases (called the pure SPT phases) can be classified by group cohomology ${\mathcal{H}}^d(G,\mathbb{R}/\mathbb{Z})$. But there are also SPT phases with mixed gauge-gravity anomalous boundary (which will be called the mixed SPT phases). Some of the mixed SPT states were also referred as the beyond-group-cohomology SPT states. In this paper, we show that those beyond-group-cohomology SPT states are actually within another type of group cohomology classification. More precisely, we show that both the pure and the mixed SPT phases can be realized by $G\times SO\left(\infty \right) \mathrm{NL}\sigma \mathrm{Ms}$ with various topological terms. Through the group cohomology ${\mathcal{H}}^d[G\times SO\left(\infty \right),\mathbb{R}/\mathbb{Z}]$, we find that the set of our constructed SPT phases in $d$-dimensional space-time are described by $E^d\left(G\right)⋊{\oplus }_{k=1}^{d-1}{\mathcal{H}}^k(G,{\text{iTO}}_L^{d-k})\oplus {\mathcal{H}}^d(G,\mathbb{R}/\mathbb{Z})$ where $G$ may contain time reversal. Here ${\text{iTO}}_L^d$ is the set of the topologically ordered phases in $d$-dimensional space-time that have no topological excitations, and one has ${\text{iTO}}_L^1={\text{iTO}}_L^2={\text{iTO}}_L^4={\text{iTO}}_L^6=0,{\text{iTO}}_L^3=\mathbb{Z},{\text{iTO}}_L^5={\mathbb{Z}}_2,{\text{iTO}}_L^7=2\mathbb{Z}$. For $G=U\left(1\right)⋊Z_2^T$ (charge conservation and time-reversal symmetry), we find that the mixed SPT phases beyond ${\mathcal{H}}^d[U\left(1\right)⋊Z_2^T,\mathbb{R}/\mathbb{Z}]$ are described by ${\mathbb{Z}}_2$ in 3 + 1D, $\mathbb{Z}$ in 4 + 1D, $3{\mathbb{Z}}_2$ in 5 + 1D, and $4{\mathbb{Z}}_2$ in 6 + 1D. Our construction also gives us the topological invariants that fully characterize the corresponding SPT and iTO phases. Through several examples, we show how the universal physical properties of SPT phases can be obtained from those topological invariants.

Upon decreasing temperature $(T_c\sim 81$ K) tetrathiafulvalene-chloranil (TTF-CA) undergoes a discontinuous phase transition from a neutral regular stack to an ionic dimerized stack. The same system may undergo a phase transition upon photoexcitation. We discuss the early time $(<3$ ps) dynamics following ultrafast $(<20$ fs) excitation of TTF-CA crystals either near or far from the neutral-ionic transition $(T\sim 90$ and 260 K, respectively). Adopting a modified Hubbard model with linear coupling of electrons to a zone-center lattice (dimerization) phonon and to a molecular vibration, both assumed to be harmonic, we are able to quantitatively reproduce coherent oscillations recently reported for this system [H. Uemura and H. Okamoto, Phys. Rev. Lett. 105, 258302 (2010); T. Miyamoto, H. Uemura, and H. Okamoto, J. Phys. Soc. Jpn. 81, 073703 (2012)]. We demonstrate that the microscopic model with parameters optimized for ground state properties of TTF-CA also applies to the coherent dynamics following photoexcitation. The modulation of the frequency of coherent molecular oscillations at the frequency of the lattice phonon emerges naturally as due to strong anharmonic coupling between the two harmonic vibrational degrees of freedom through coupling to delocalized electrons. Detailed comparison with experiment validates the model and sheds light on other aspects of photoinduced dynamics, including the almost instantaneous transfer of several electrons upon absorption of a single photon, as due to a cooperative effect of electronic correlations and molecular vibrations.

First-principles molecular dynamics simulations within the density functional theory framework were performed to generate amorphous models of the ${\mathrm{Ga}}_4{\mathrm{Sb}}_6{\mathrm{Te}}_3$ phase change alloy by quenching from the melt. We find that Ga-Sb and Ga-Te are the most abundant bonds with only a minor amount of Sb-Te bonds participating to the alloy network. Ga and four-coordinated Sb atoms present a tetrahedral-like geometry, whereas three-coordinated Sb atoms are in a pyramidal configuration. The tetrahedral-like geometries are similar to those of the crystalline phase of the two binary compounds GaTe and GaSb. A sizable fraction of Sb-Sb bonds is also present, indicating a partial nanoscale segregation of Sb. Despite the fact that the composition ${\mathrm{Ga}}_4{\mathrm{Sb}}_6{\mathrm{Te}}_3$ lies on the pseudobinary $\mathrm{Ga}\mathrm{Sb}-{\mathrm{Sb}}_2{\mathrm{Te}}_3$ tie line, the amorphous network can be seen as a mixture of the two binary compounds GaTe and GaSb with intertwined elemental Sb.