The elasticity at high pressure of solid hydrogen in hexagonal close-packed (hcp) phase I has been examined experimentally by laser acoustics technique in a diamond anvil cell, up to 55 GPa at 296 K, and theoretically using pair and three-body semiempirical potentials, up to 160 GPa. In the experiments on ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, the compressional sound velocity has been measured; the Poisson's ratio has been determined by combining these data with the previously reported equation of state. At room temperature, the difference between the adiabatic and isothermal processes vanishes above 25 GPa but cannot be neglected at lower pressure. Theoretically, all five elastic constants of hcp hydrogen have been calculated, and various derived elastic quantities are presented. The elastic anisotropy of hcp hydrogen was found to be significant, with $\mathrm{\Delta }P\approx 1.2,\mathrm{\Delta }{S}_1\approx 1.7$, and $\mathrm{\Delta }{S}_2\approx 1$. Calculations suggest the Poisson's ratio to decrease with pressure reaching a minimum value of 0.28 at 145 GPa. In the experiment, the Poisson's ratio is also found to decrease with pressure. Theoretical calculations show that the inclusion of zero-point vibrations on the elastic properties of ${\mathrm{H}}_2$ does not result in any drastic changes of the behavior of the elastic quantities.

Based on simultaneous force and conductance simulations, a proof of concept for a potential method of molecular detection is presented. Using density functional theory calculations, a metallic tip has been approached to different small inorganic molecules such as CO, ${\mathrm{CO}}_2$, ${\mathrm{H}}_2\mathrm{O}$, NO, ${\mathrm{N}}_2$, or ${\mathrm{O}}_2$. The molecules have been previously chemisorbed on a defect formed by two Mo atoms occupying a S divacancy on a ${\mathrm{MoS}}_2$ monolayer where they are strongly bonded to the topmost substitutional molybdenum. At that site, the fixed molecules can be imaged by a conductive atomic-force-microscopy tip. Due to the differences in atomic composition and electronic configurations, each molecule yields specific conductance/force curves during the tip approach. A molecule-tip contact is established at the force minimum, followed by the formation of a characteristic plateau in the conductance in most of the cases. Focusing our attention on the position and values of such force minimum and conductance maximum, we can conclude that both characteristic properties can give a clear signature of each molecule, proposing a different method of detecting molecules adsorbed on highly reactive sites.

We investigated the local structure deformation induced by x-ray irradiation in an organic molecular conductor $\kappa -{\left(\mathrm{BEDT}-\mathrm{TTF}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Br}$ using density-functional-theory (DFT-) based first-principles calculations. Our results demonstrate that the structure change due to x-ray excitation can be predicted by introducing a core hole at specific light atoms of the anion molecules with an infinite lifetime. The formation of a bond-shifted structure triggered by a double excitation was expected as a possible irreversible molecular defect leading to permanent irradiation damage. The calculated change in molecular vibration spectra after irradiation was consistent with the experimental results, and some different vibration modes by further irradiation were also predicted. The calculated local density of states indicates that the bond-shifted structure in the anion layer causes local potential modulation to the carriers (holes) in the cation layer. The introduced potential disorder for the carriers could increase the resistivity due to a localization effect that has been observed experimentally so far.

We present a theoretical analysis of the electron spin echo envelope modulation (ESEEM) spectra of polarons in semiconducting $\pi$-conjugated polymers. We show that the contact hyperfine coupling and the dipolar interaction between the polaron and the proton spins give rise to different features in the ESEEM spectra. Our theory enables direct selective probe of different groups of nuclear spins, which affect the polaron spin dynamics. Namely, we demonstrate how the signal from the distant protons (coupled to the polaron spin via dipolar interactions) can be distinguished from the signal coming from the protons residing on the polaron site (coupled to the polaron spin via contact hyperfine interaction). We propose a method for directly probing the contact hyperfine interaction, that would enable detailed study of the polaron orbital state and its immediate environment. We also analyze the decay of the spin echo modulation, and its connection to the polaron transport.

We apply the first-order reversal curve (FORC) method, adapted from studies of ferromagnetic materials, to the magnetostructural phase transition of ${\mathrm{Fe}}_{1+y}\mathrm{Te}$. FORC measurements reveal two features in the hysteretic phase transition, even in samples where traditional temperature measurements display only a single transition. For ${\mathrm{Fe}}_{1.13}\mathrm{Te}$, the influence of magnetic field suggests that the main feature is primarily structural while a smaller, slightly higher-temperature transition is magnetic in origin. By contrast, ${\mathrm{Fe}}_{1.03}\mathrm{Te}$ has a single transition which shows a uniform response to magnetic field, indicating a stronger coupling of the magnetic and structural phase transitions. We also introduce uniaxial stress, which spreads the distribution width without changing the underlying energy barrier of the transformation. The work shows how FORC can help disentangle the roles of the magnetic and structural phase transitions in FeTe.

We discuss the stability of highly degenerate zero-energy states that appear at the surface of a nodal superconductor preserving time-reversal symmetry. The existence of such surface states is a direct consequence of the nontrivial topological numbers defined in the restricted Brillouin zones in the clean limit. In experiments, however, potential disorder is inevitable near the surface of a real superconductor, which may lift the high degeneracy at zero energy. We show that an index defined in terms of the chiral eigenvalues of the zero-energy states can be used to measure the degree of degeneracy at zero energy in the presence of potential disorder. We also discuss the relationship between the index and the topological numbers.

We study the ultrafast Kerr effect and high-harmonic generation in superconductors by formulating a model for a time-varying electromagnetic pulse normally incident on a thin-film superconductor. It is found that superconductors exhibit exceptionally large ${\chi }^{\left(3\right)}$ due to the progressive destruction of Cooper pairs, and display high-harmonic generation at low incident intensities, and the highest nonlinear susceptibility of all known materials in the THz regime. Our theory opens up avenues for accessible analytical and numerical studies of the ultrafast dynamics of superconductors.

Understanding the mechanism of Cooper pairing amounts to determining the effective interaction that operates at low energies. Efforts to achieve such a goal for superconducting materials, especially strongly correlated ones, from both bottom-up and top-down approaches, have been plagued by having to use uncontrolled approximations. Here, we perform large-scale, numerically exact, sign-problem-free zero-temperature quantum Monte Carlo simulations on an effective theory based on “hot spots” plus fluctuating collective modes. Because hot spots are clearly identified by angle-resolved photoemission spectroscopy for electron-doped cuprates, we focus our attention on such materials. Our goal is to determine the minimum effective action that can describe the observed superconductivity and charge-density wave. The results suggest that antiferromagnetic fluctuation alone is not sufficient—the effective action needs to be amended with nematic fluctuations. We believe that our results address the pairing mechanism of high-$T_c$ superconductivity in electron-doped cuprates, and they shed light on the pairing mechanism of hole-doped cuprates.

The spin relaxation in chromium spinel oxides $A{\mathrm{Cr}}_2{\mathrm{O}}_4$ ($A=$ Mg, Zn, Cd) is investigated in the paramagnetic regime by electron spin resonance (ESR). The temperature dependence of the ESR linewidth indicates an unconventional spin-relaxation behavior, similar to spin-spin relaxation in the two-dimensional (2D) chromium-oxide triangular lattice antiferromagnets. The data can be described in terms of a generalized Berezinskii-Kosterlitz-Thouless (BKT) type scenario for 2D systems with additional internal symmetries. Based on the characteristic exponents obtained from the evaluation of the ESR linewidth, short-range order with a hidden internal symmetry is suggested.

We experimentally investigated the hypersonic attenuation process of a longitudinal mode (L-mode) sound wave in ${\mathrm{TeO}}_2$ from room temperature to a lower temperature using Brillouin scattering and impulsive stimulated thermal scattering (ISTS) measurements. For precise measurement of the Brillouin linewidth at low temperatures, whereby the mean free path of the phonon becomes longer than the sample length, it is indispensable that the phonon should propagate along the phonon-resonance direction. To figure out the suitable direction, we defined two indices characterizing a degree of phonon divergence and a purity of propagation direction. The best direction that we found from these indices is [110] direction in ${\mathrm{TeO}}_2$, and it was used to discuss the temperature and frequency dependences of Brillouin spectra. We extracted the temperature dependence of the attenuation rate of $T^4$ from the modulated Brillouin spectra due to the phonon resonance below Debye temperature. The frequency dependence ${\omega }^1$ of the hypersonic attenuation was also estimated from the polarization dependence of the Brillouin linewidth. Theoretically, it predicted that the L-mode phonon attenuation at low temperatures in ${\mathrm{TeO}}_2$ is a result of Herring's process, which shows the attenuation behavior of ${\omega }^2{T}^3$. The ${\omega }^1{T}^4$ dependence is not allowed in Herring's process but is allowed by the $L+L\to L$ process, which has been considered to be forbidden so far. We evaluated the thermal phonon lifetime using ISTS and established that it was finite even at 20 K, thereby allowing the $L+L\to L$ process. Therefore, we conclude that the $L+L\to L$ process dominates the attenuation of an L-mode phonon in ${\mathrm{TeO}}_2$ in the low-temperature region.

The dynamic response of dipole skyrmions in Fe/Gd multilayer films is investigated by ferromagnetic resonance measurements and compared to micromagnetic simulations. We detail thickness- and temperature-dependent studies of the observed modes as well as the effects of magnetic field history on the resonant spectra. Correlation between the modes and the magnetic phase maps constructed from real-space imaging and scattering patterns allows us to conclude that the resonant modes arise from local topological features such as dipole skyrmions but do not depend on the collective response of a close-packed lattice of these chiral textures. Using micromagnetic modeling, we are able to quantitatively reproduce our experimental observations which suggests the existence of localized spin-wave modes that are dependent on the helicity of the dipole skyrmion. We identify four localized spin-wave excitations for the skyrmions that are excited under either in-plane or out-of-plane rf fields. Lastly we show that dipole skyrmions and nonchiral bubble domains exhibit qualitatively different localized spin-wave modes.

The collective spin-wave excitations in the antiferromagnetic state of $\gamma \text{−}{\mathrm{Fe}}_{0.7}{\mathrm{Mn}}_{0.3}$ were investigated using the inelastic neutron-scattering technique. The spin excitations remain isotropic up to high excitation energy, $\hslash \omega =78$ meV. The excitations gradually become broad and damped above 40 meV. The damping parameter $\gamma$ reaches 110(16) meV at $\hslash \omega =78$ meV, which is much larger than that for other metallic compounds, e.g., ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ (24 meV), ${\mathrm{La}}_{2-2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_2{\mathrm{O}}_7$ (52–72 meV), and ${\mathrm{Mn}}_{90}{\mathrm{Cu}}_{10}$ (88 meV). In addition, the spin-wave dispersion shows a deviation from the relation ${\left(\hslash \omega \right)}^2=c^2{q}^2+{\mathrm{\Delta }}^2$ above 40 meV. The group velocity above this energy increases to 470(40) meVÅ, which is higher than that at the low energies, $c=226\left(5\right)$ meVÅ. These results could suggest that the spin-wave excitations merge with the continuum of the individual particle-hole excitations at 40 meV.

The order parameter of bulk two-dimensional superconductors is classified as nodal if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Nonmagnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between normal-metal and unconventional superconductors by solving the quasiclassical Eilenberger equation self-consistently, including the presence of nonmagnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge $e$, and (ii) for finite bias, the current-voltage characteristics follows that of a normal-state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only $p_x$-wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency $s$-wave Cooper pairs near the interface. Due to their anisotropic dependence on the wave vector, impurity scattering is an effective pair-breaking mechanism for the remaining nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.

A time-reversal (TR) invariant topological superconductor is characterized by a Kramers pair of Majorana zero-energy modes on boundaries and in a core of a TR invariant vortex. A vortex defect that preserves TR symmetry has remained primarily of theoretical interest, since typically a magnetic field, which explicitly breaks TR, needs to be applied to create vortices in superconductors. In this paper, we show that an odd-parity topological superconductor with a nematic pairing order parameter can host a nematic vortex that preserves TR symmetry and binds a Majorana Kramers pair. Such a nematic superconductor could be realized in metal-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, as suggested by recent experiments. We provide an analytic solution for the zero modes in a continuous nematic vortex. In lattice, crystalline anisotropy can pin the two-component order parameter along high-symmetry directions. We show that a discrete nematic vortex, which forms when three nematic domains meet, also supports a TR pair of Majorana modes. Finally, we discuss possible experiments to probe the zero modes.

We study two Weyl semimetal generalizations in five dimensions (5D) which have Yang monopoles and linked Weyl surfaces in the Brillouin zone, respectively, and carry the second Chern number as a topological number. In particular, we show a Yang monopole naturally reduces to a Hopf link of two Weyl surfaces when the $\mathbf{TP}$ (time reversal combined with space inversion) symmetry is broken. We then examine the phase transition between insulators with different topological numbers in 5D. In analogy to the three-dimensional case, 5D Weyl semimetals emerge as intermediate phases during the topological phase transition.

We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the global and gauge symmetries in the TNS update procedure and in tensor renormalization group (TRG) calculations. We also introduce a very sensitive probe for the gap of the ground state—the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of the Heisenberg model on the kagome lattice is a gapped spin liquid with the ${\mathbb{Z}}_2$ topological order (or toric code type), which has a long correlation length $\xi \sim 10$ unit cells. We justify that the TRG method can handle very large systems with thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than the length of 10 unit cells. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.

We report an ultrafast lattice dynamics investigation of the topological Dirac semimetal $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$. A coherent phonon beating among three evenly spaced $A_{1g}$ optical phonon modes (of frequencies 1.80, 1.96, and 2.11 THz, respectively) is unambiguously observed. The two side modes originate from the counter helixes composing Cd vacancies. Significantly, such helix vacancy-induced phonon (HVP) modes experience prominent extra waning in their ultrafast dynamics as temperature increases, which is immune to the central mode. Above 200 K, the HVP becomes inactive, which may potentially affect the topological properties. Our results in the lattice degree of freedom suggest the indispensable role of temperature in considering topological properties of such quantum materials.

A theoretical study of collective electronic excitations in free-standing Pb(111) thin films consisting of 1–5 monolayers (MLs) and a 21-ML film is presented. The calculations are carried out applying the linear response theory, with full inclusion of the electron band structure by means of a first-principles pseudopotential approach in a supercell scheme. In the case of the thickest film, we find that, due to strong bulklike interband transitions, at the Pb(111) surface there are two surface modes. For thin films, a mechanism of transformation of these modes to the symmetric and antisymmetric classic hybrid plasmons is investigated. Pronounced quantum-size effects on plasmon modes of the thinnest films are found. Strong influence of the band structure on dispersion and lifetime of such modes is demonstrated. The present results are in good agreement with available experimental data for a Pb surface and thin films.