In commonly employed models for two-dimensional (2D) topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to consider this feature, the occurrence of gapless states, a result of the band inversion process under protection of the symmetries. Similarly, the band inversion process might even be perceived as necessary to induce 2D topological phase transitions. To clarify these misleading perspectives, we propose a simple model with a flexible Chern number to demonstrate that the bulk gapless states emerge at the phase boundary of topological phase transitions, despite the absence of a band inversion process. Furthermore, the bulk gapless states do not need to occur at the special $k$ points protected by symmetries. Given the significance of these fundamental conceptual issues and their widespread influence, our clarification should generate strong general interests and significant impacts. Furthermore, the simplicity and flexibility of our general model with an arbitrary Chern number should prove useful in a wide range of future studies of topological states of matter.

The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the $p$ (hole doping) to $1+p$ jump measured in the Hall number $n_H$ at a doping $p^{*}$. Here we explore incommensurate collinear SDW as another possible explanation of this phenomenon, distinct from the incommensurate spiral SDW proposal. We examine the effect of different SDW strengths and wave vectors, and we find that the $n_H\sim p$ behavior is hardly reproduced at low doping. Furthermore, the calculated $n_H$ and Fermi surfaces give characteristic features that should be observed; thus, the lack of these features in experiment suggests that the incommensurate collinear SDW is unlikely to be a good candidate to explain the $n_H\sim p$ observed in the pseudogap regime.

A polarized light beam modifies the equilibrium tensors associated with any measurable property of a crystal. The light-induced linear magnetoelectric susceptibility and electric current density of bismuth ferrite (BFO) are investigated theoretically using their expansion in Wigner spherical functions. Under illumination, the interplay between magnetoelectric and photovoltaic properties yields the emergence in the paramagnetic and multiferroic phases of BFO of linear photomagnetoelectric tensor components changing sign in domains with opposite electric polarization or magnetization, and to magnetophotocurrents changing sense in opposite ferroelectric and magnetic domains.

We report picosecond acoustic measurements of longitudinal sound dispersion and attenuation in an amorphous ${\mathrm{SiO}}_2$ layer at temperatures from 20 to 300 K over frequencies ranging from about 40 to 200 GHz. The sample is a radio frequency cathodic sputtered silica layer grown on a sapphire substrate with an aluminum film transducer deposited on top. Acoustic attenuation is evaluated from the simultaneous analysis of three successive echoes using transfer matrix calculation. Results are found to follow rather well a model combining coupling to thermally activated relaxations of structural defects and interactions with thermal vibrations. This leads to a nontrivial variation of the attenuation coefficient with frequency and temperature. The number density of relaxing defects in the ${\mathrm{SiO}}_2$ layer is found to be slightly higher than that in bulk v-${\mathrm{SiO}}_2$. In contrast, similar anharmonic contribution to acoustic absorption is observed in both systems. The velocity variations are also measured and are compared to the dynamical velocity changes deduced from the sound attenuation.

We investigate the interplay between disorder and superconducting pairing for a one-dimensional $p$-wave superconductor subject to slowly varying incommensurate potentials with mobility edges. With amplitude increments of the incommensurate potentials, the system can undergo a transition from a topological phase to a topologically trivial localized phase. Interestingly, we find that there are four mobility edges in the spectrum when the strength of the incommensurate potential is below a critical threshold, and a novel topologically nontrivial localized phase emerges in a certain region. We reveal this energy-dependent metal-insulator transition by applying several numerical diagnostic techniques, including the inverse participation ratio, the density of states, and the Lyapunov exponent. Since the precise control of the background potential and the $p$-wave superfluid can be realized in the ultracold atomic systems, we believe that these novel mobility edges can be observed experimentally.

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice. We examine the excitation spectra as well as various thermodynamic quantities, such as the order parameter (magnetization), the uniform static susceptibility, the correlation length, the spin-spin correlations, and the specific heat, as well as the static and dynamic structure factors. We discuss the influence of the spin quantum number $S$ on the temperature dependence of these quantities. We compare our results for the pyrochlore ferromagnet with the corresponding ones for the simple-cubic lattice both having the same coordination number $z=6$. We find a significant suppression of magnetic ordering for the pyrochlore lattice due to its geometry with corner-sharing tetrahedra.

We consider ballistic SQUIDs with spin filtering inside half-metallic ferromagnetic arms. A singlet Cooper pair cannot pass through an arm in this case, so the Josephson current is entirely due to the Cooper pair splitting, with two electrons going to different interferometer arms. In order to elucidate the mechanisms of Josephson transport due to split Cooper pairs, we assume the arms to be single-channel wires in the short-junction limit. Different geometries of the system (determined by the length of the arms and the phases acquired by quasiparticles during splitting between the arms) lead to qualitatively different behavior of the SQUID characteristics (the Andreev levels, the current-phase relation, and the critical Josephson current) as a function of two control parameters, the external magnetic flux and misorientation of the two spin filters. The current-phase relation can change its amplitude and shape, in particular, turning to a $\pi$ junction form or acquiring additional zero crossings. The critical current can become a nonmonotonic function of the misorientation of the spin filters and the magnetic flux (on half of period). Periodicity with respect to the magnetic flux is doubled, in comparison to conventional SQUIDs.

We consider a buckled quantum spin Hall insulator (QSHI), such as silicene, proximity coupled to a conventional spin-singlet $s$-wave superconductor. Even limiting the discussion to the disorder-robust $s$-wave pairing symmetry, we find both odd-frequency ($\omega$) spin-singlet and spin-triplet pair amplitudes, both of which preserve time-reversal symmetry. Our results show that there are two unrelated mechanisms generating these different odd-$\omega$ pair amplitudes. The spin-singlet state is due to the strong interorbital processes present in the QSHI. It exists generically at the edges of the QSHI, but also in the bulk in the heavily doped regime if an electric field is applied. The spin-triplet state requires a finite gradient in the proximity-induced superconducting order along the edge, which we find is automatically generated at the atomic scale for armchair edges but not at zigzag edges. In combination these results make superconducting QSHIs a very exciting venue for investigating not only the existence of odd-$\omega$ superconductivity but also the interplay between different odd-$\omega$ states.

Single crystals of ${\mathrm{HfTe}}_3$ were successfully grown using a chemical transport reaction in an extremely narrow temperature range. Here, we report a comparative study of polycrystalline and single-crystal samples. The electrical resistivity $\rho \left(T\right)$ measured on polycrystalline samples shows a broad hump and clear drop at 80 and 1.7 K, which correspond to the formation of the charge density wave (CDW) and superconducting (SC) transition, respectively. For the single crystals, $\rho \left(T\right)$ shows a sharp change at $T_{\mathrm{CDW}}=93$ K, and the superconductivity is absent, in contrast to the polycrystalline samples. With the current flowing along the $a$ and $b$ directions, the coincidence of the linear temperature dependence of $\rho \left(T\right)/\rho \left(300\mathrm{K}\right)$ above $T_{\mathrm{CDW}}$ strongly implies that the electron-electron scattering mechanism dominates the transport properties in a quasi-one-dimensional chain. Furthermore, a metal-semiconductor-like transition is confirmed below $T_{\mathrm{CDW}}$ in ${\rho }_c$. The drop observed at 4.3 K in ${\rho }_b\left(T\right)$ for the single crystal with more defects (small residual resistivity ratio, large ${\rho }_0$, and weak drop) provides direct evidence of a disorder-related SC fluctuation in the CDW system. With temperature decreasing, the carrier density exhibits a similar and rapid decrease below $T_{\mathrm{CDW}}$ for flowing current in both the $a$ and $b$ directions, whereas an obvious enhancement of carrier mobility appears as $I\parallel b$. An analysis of x-ray photoelectron spectroscopy spectra suggests that the mixed-valence states of Hf and Te could be related to the CDW formation in the multichain system of ${\mathrm{HfTe}}_3$.

The present study investigates a way to design dikes which can filter the wavelengths of ocean surface waves. This offers the possibility to achieve a structure that can attenuate waves associated with storm swell, without affecting coastline in other conditions. Our approach is based on low-frequency resonances in metamaterials combined with Bragg frequencies for which waves cannot propagate in periodic lattices.

We have experimentally identified a different magnetic ground state for the kagome lattice, in the perfectly hexagonal ${\mathrm{Fe}}^{2+}$ ($3d^6,S=2$) compound ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$. A representational symmetry analysis of neutron diffraction data shows that below $T_N=3.5$ K, the spins on $\frac{2}{3}$ of the magnetic ions order into canted antiferromagnetic chains, separated by the remaining $\frac{1}{3}$ which are geometrically frustrated and show no long-range order down to at least $T=0.1$ K. Mössbauer spectroscopy confirms that there is no static order on the latter $\frac{1}{3}$ of the magnetic ions—i.e., they are in a liquidlike rather than a frozen state—down to at least 1.65 K. A heavily Mn-doped sample ${\mathrm{Fe}}_{1.45}{\mathrm{Mn}}_{2.55}{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$ has the same magnetic structure. Although the propagation vector $q=\left(0,\frac{1}{2},\frac{1}{2}\right)$ breaks hexagonal symmetry, we see no evidence for magnetostriction in the form of a lattice distortion within the resolution of our data. We discuss the relationship to partially frustrated magnetic order on the pyrochlore lattice of ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, and to theoretical models that predict symmetry breaking ground states for perfect kagome lattices.

The local dynamics of the lead-free relaxor $0.964{\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2}{\mathrm{TiO}}_3-0.036{\mathrm{BaTiO}}_3$ (NBT-3.6BT) have been investigated by a combination of quasielastic neutron-scattering (QENS) and ab initio molecular dynamics simulations. In a previous paper, we were able to show that the tetragonal platelets in the microstructure are crucial for understanding the dielectric properties of NBT-3.6BT [Pforr et al., Phys. Rev. B 94, 014105 (2016)]. To investigate their dynamics, ab initio molecular dynamics simulations were carried out using ${\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2}{\mathrm{TiO}}_3$ with 001 cation order as a simple model system for the tetragonal platelets in NBT-3.6BT. Similarly, 111-ordered ${\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2}{\mathrm{TiO}}_3$ was used as a model for the rhombohedral matrix. The measured single-crystal QENS spectra could be reproduced by a linear combination of calculated spectra. We find that the relaxational dynamics of NBT-3.6BT are concentrated in the tetragonal platelets. Chaotic stages, during which the local tilt order changes incessantly on the time scale of several picoseconds, cause the most significant contribution to the quasielastic intensity. They can be regarded as an excited state of tetragonal platelets, whose relaxation back into a quasistable state might explain the frequency dependence of the dielectric properties of NBT-3.6BT in the 100 GHz to THz range. This substantiates the assumption that the relaxor properties of NBT-3.6BT originate from the tetragonal platelets.

The critical behavior of a random-field $\mathbf{O}\left(N\right)$ model driven at a uniform velocity is investigated near three dimensions at zero temperature. From intuitive arguments, we predict that the large-scale behavior of the $D$-dimensional driven random-field $\mathbf{O}\left(N\right)$ model is identical to that of the $(D-1)$-dimensional pure $\mathbf{O}\left(N\right)$ model. This is an analog of the dimensional reduction property of equilibrium cases, which states that the critical exponents of $D$-dimensional random-field models are identical to those of $(D-2)$-dimensional pure models. However, the dimensional reduction property breaks down in low enough dimensions due to the presence of multiple metastable states. By employing the nonperturbative renormalization group approach, we calculate the critical exponents of the driven random-field $\mathbf{O}\left(N\right)$ model in the first order of $\epsilon =D-3$ and determine the range of $N$ in which the dimensional reduction breaks down.

Triplet-polaron quenching (TPQ) is a major cause of the efficiency loss at large current densities in phosphorescent organic light-emitting diodes. The nature of the interaction process is presently not well understood. In this paper, we study TPQ due to Förster-type triplet-polaron interactions in energetically disordered organic semiconductors with a Gaussian polaron density of states. A continuum theory, which neglects the spatial inhomogeneity and energetic disorder, is from a kinetic Monte Carlo approach shown to correctly predict that the effective steady-state TPQ rate coefficient $k_{\text{TPQ,eff}}$ depends only sensitively on the polaron diffusion in a rather narrow range of diffusion coefficients. However, in this regime, significant discrepancies between the two approaches are found, in particular for realistic values of the TPQ-Förster radius, around 3 nm, and for systems with strong energetic disorder. Both approaches show that $k_{\text{TPQ,eff}}$ is not constant but can depend on the polaron density and the electric field. Various methods for deducing the TPQ mechanism from experiment are discussed, including an approach which utilizes the shape of the time-dependent photoluminescence after pulsed illumination.

The interaction of phononic cavities modes in one-dimensional nanobeam-based structures is investigated theoretically. The overlapping of two closely spaced phononic cavity modes leads to the formation of symmetric and antisymmetric modes, which can be used for the modulation of the frequency and the quality factors of the propagating cavity modes. In addition, the efficient coupling of cavity modes with the modes of a phononic waveguide connecting the two phononic cavities has been demonstrated. We show that such coupling can be used for routing, controlling, and modulating the phononic cavity modes over large distances between cavities. This demonstration paves the way to engineering complex on-chip phonon networks utilizing mechanical waves to connect quantum systems as phononic or optomechanical cavities.

Spatial and time scales of spin-density fluctuations (SDFs) were analyzed in $3d$ ferromagnets using ab initio linear-response calculations of complete wave-vector and energy dependence of the dynamic spin susceptibility tensor. We demonstrate that SDFs are spread continuously over the entire Brillouin zone and while the majority of them reside within the $3d$ bandwidth, a significant amount comes from much higher energies. A validity of the adiabatic approximation in spin dynamics is discussed. The SDF spectrum is shown to have two main constituents: a minor low-energy spin-wave contribution and a much larger high-energy component from more localized excitations. Using the fluctuation-dissipation theorem, the on-site spin correlator and the related effective fluctuating moment were properly evaluated and their universal dependence on the $3d$ band population is further discussed.

We have investigated the magnetic properties of ${\mathrm{EuTi}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_3$ with $0\le x\le 1$ and established a detailed magnetic phase diagram. Substitution of ${\mathrm{Ti}}^{4+}$ with ${\mathrm{Al}}^{3+}$, which oxidizes magnetic ${\mathrm{Eu}}^{2+}$ $\left(J=7/2\right)$ into nonmagnetic ${\mathrm{Eu}}^{3+}$ $\left(J=0\right)$, turns the antiferromagnetic insulating ground state $\left(x=0\right)$ into the ferromagnetic (FM) insulating one $\left(0.10\le x\le 0.50\right)$. The ${\mathrm{Eu}}^{2+}/{\mathrm{Eu}}^{3+}$ mixed valence is indispensable for the FM behavior. In $0.10\le x\le 0.33$, the Curie temperature $T_{\mathrm{C}}$ has a plateau at $\sim 4$ K, and the FM correlation is most enhanced around $x=0.25$. In $0.33\le x\le 1,{\mathrm{Al}}^{3+}$ substitution suppresses the FM correlation due to the dilution of magnetic ${\mathrm{Eu}}^{2+}$ ions. Our present results would provide useful information for magnetoelectric phase control of ${\mathrm{EuTiO}}_3$-based compounds.

Using a membrane-driven diamond anvil cell and both ac magnetic susceptibility and electrical resistivity measurements, we have characterized the superconducting phase diagram of elemental barium to pressures as high as 65 GPa. We have determined the superconducting properties of the recently discovered Ba-VI crystal structure, which can only be accessed via the application of pressure at low temperature. We find that Ba-VI exhibits a maximum $T_c$ near 8 K, which is substantially higher than the maximum $T_c$ found when pressure is applied at room temperature. We discuss our results in terms of the implications for pressure-induced superconductivity in other elements exhibiting complex/modulated structures at high pressure. Finally, we highlight the potential of cryogenic compression to reveal additional richness in previously explored high-pressure phase diagrams.

$1T\text{−}{\mathrm{TaS}}_2$ is a layered transition-metal dichalcogenide with a very rich phase diagram. At $T=180$ K it undergoes a metal to Mott insulator transition. Mott insulators usually display antiferromagnetic ordering in the insulating phase but $1T\text{−}{\mathrm{TaS}}_2$ was never shown to order magnetically. In this paper we show that $1T\text{−}{\mathrm{TaS}}_2$ has a large paramagnetic contribution to the magnetic susceptibility but it does not show any sign of magnetic ordering or freezing down to 20 mK, as probed by muon spin relaxation, possibly indicating a quantum spin liquid ground state. Although $1T\text{−}{\mathrm{TaS}}_2$ exhibits a strong resistive behavior both in and out of plane at low temperatures we find a linear term in the heat capacity suggesting the existence of a Fermi surface, which has an anomalously strong magnetic field dependence.