Motivated by the emergent fermions in the chiral topological semimetal RhSi, which has bulk higher-spin chiral fermions with a topological charge of $\pm 2$, respectively, we studied the shift vector induced nonlinear optical conductivity ${\sigma }_{zxy}^{\left(2\right)}(0;\omega ,-\omega )$ of bulk RhSi by first-principles calculation. Our calculation demonstrates that the maximal ${\sigma }_{zxy}^{\left(2\right)}(0;\omega ,-\omega )$ is about $\sim 180\mu \text{A}/{\text{V}}^2$ under an optical field with a photon energy of $\sim 20$ meV. With a photon energy large than 450 meV, ${\sigma }_{zxy}^{\left(2\right)}(0;\omega ,-\omega )$ is relatively small. Especially, the calculated ${\sigma }_{zxy}^{\left(2\right)}(0;\omega ,-\omega )$ is almost vanishing within a photon energy range of 450–500 meV. Below 300 meV, our calculation also reveals that the dielectric function and reflectivity decreases with an increase of photon energy, while the absorption coefficient increases with an increase of photon energy. Therefore, RhSi has a potential application for optoelectronic detection in the terahertz range.

The direct simulation of the dynamics of second sound in graphitic materials remains a challenging task due to lack of methodology for solving the phonon Boltzmann equation in such a stiff hydrodynamic regime. In this work we aim to tackle this challenge by developing a multiscale numerical scheme for the transient phonon Boltzmann equation under Callaway's dual relaxation model which captures well the collective phonon kinetics. Compared to traditional numerical methods, the present multiscale scheme is efficient, accurate, and stable in all transport regimes attributed to avoiding the use of time and spatial steps smaller than the relaxation time and mean free path of phonons. The formation, propagation, and composition of ballistic pulses and second sound in graphene ribbon in two classical paradigms for experimental detection are investigated via the multiscale scheme. The second sound is declared to be mainly contributed by ZA phonon modes, whereas the ballistic pulses are mainly contributed by LA and TA phonon modes. The influence of temperature, isotope abundance, ribbon size, and structure asymmetry on the second sound propagation is also explored. The speed of second sound in the observation window is found to be at most 20% smaller than the theoretical value in the hydrodynamic limit due to the finite umklapp, isotope, and edge resistive scattering. The present study will contribute to not only the solution methodology of the phonon Boltzmann equation, but also the physics of transient hydrodynamic phonon transport as guidance for future experimental detection.

Materials exhibiting topological order host exotic phenomena that could form the basis for novel developments in areas ranging from low-power electronics to quantum computers. The past decade has witnessed multiple experimental realizations and thousands of predictions of topological materials. However, it has been determined that increasing temperature destroys topological order, restricting many topological materials to very low temperatures and thus hampering practical applications. Here, we propose a material realization of temperature-promoted topological order. We show that a semiconducting oxide that has been widely used in lead-acid batteries, $\beta -{\mathrm{PbO}}_2$, hosts a topological semimetallic phase driven by both thermal expansion and electron-phonon coupling upon increasing temperature. We identify the interplay between the quasi-two-dimensional nature of the charge distribution of the valence band with the three-dimensional nature of the charge distribution of the conduction band as the microscopic mechanism driving this unconventional temperature dependence. Thus, we propose a general principle to search for and design topological materials whose topological order is stabilized by increasing temperature. This provides a clear roadmap for taking topological materials from the laboratory to technological devices.

The topological properties of the quantum Hall effect in a crystalline lattice, described by Chern numbers of the Hofstadter butterfly quantum phase diagram, are deduced by using a geometrical method to generate the structure of quasicrystals: the cut and projection method. Based on this, we provide a geometric unified approach to the Hofstadter topological-phase diagram at all fluxes. Then we show that for any flux, bands conductances follow a two-letter symbolic sequence. As a result, conductances at different fluxes obey inflation/deflation rules as the ones observed to build quasicrystals. The symbolic sequences are given by the Sturmian coding of the flux and can be found by considering a circle map, a billiard, or trajectories on a torus. Simple and fast techniques are thus provided to obtain Chern numbers at all magnetic fluxes. This approach allows one to understand the global fractality of the butterfly in terms of Farey sequences and trees.

The Haldane phase represents one of the most important symmetry-protected states in modern physics. This state can be realized using spin-1 and $\mathrm{spin}-\frac{1}{2}$ Heisenberg models and bosonic particles. Here we explore the emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain, which is different from the previous proposals from fundamental statistics and symmetries. We show that this emergent phase can also be characterized by a modified long-range string order, as well as fourfold degeneracy in the ground-state energies and entanglement spectra. This phase is protected by both the charge conjugate and parity symmetry, and the edge modes are shown to satisfy parafermionic statistics in which braiding of the two edge modes yields a $\frac{2\pi }{3}$ phase. This model also supports rich phases, including a topological ferromagnetic parafermion (FP) phase, trivial paramagnetic parafermion phase, classical dimer phase, and gapless phase. The boundaries of the FP phase are shown to be gapless and critical with central charge $c=4/5$. Even in the topological FP phase, it is also characterized by long-range string order; thus we observe a drop of string order across the phase boundary between the FP phase and the Haldane phase. This work opens a new way for finding of exotic topological phases with parafermions.

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunneling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $\nu$ of the underlying (integer) quantum Hall states. For $\nu =1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $\nu =2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U\left(1\right)\times U\left(1\right)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these anomalous one-dimensional systems.

Lattice dynamics in artificial periodic structures, or “phononic crystals”, have attracted significant research interest, thanks to the potential to manipulate acoustic wave propagation with more flexibility. The same control on heat conduction, however, has proven challenging due to the short wavelength of thermal phonons. In this work, we use first-principles simulations to characterize the previously unstudied thermal properties of dodecagraphene and tetragraphene, two-dimensional (2D) carbon allotropes based upon graphene but containing a secondary, in-plane periodicity. Surprisingly, we find that despite very similar atomic structure and bonding strength, they possess significantly different thermal properties than that of graphene: at room temperature, their thermal conductivity is up to 80% lower than that of graphene. We attribute these distinct properties to the presence of naturally occurring, low frequency optical phonon modes that arise from a folding of the acoustic modes due to the superstructure and the associated frequency gap opening. Furthermore, we observe significantly enhanced Umklapp scatterings in both carbon allotropes that largely suppress the hydrodynamic phonon transport in pristine graphene. Our study presents dodecagraphene and tetragraphene as ideal model systems to explore lattice dynamics in 2D and demonstrates the potential to significantly modify thermal transport of 2D materials without making drastic changes to their fundamental compositions.

Covalent semiconductors play an important role in key technological advancements in areas such as communications, consumer electronics, automotive, energy, and more. However, the low ductility of covalent semiconductors, originating from the strong chemical bonding, prevents them from a wide range of engineering applications. In this work, we demonstrate that the bond strength of covalent materials is very sensitive to the electron distribution, able to be effectively modified via the electron-hole pairs (EHPs) induced by photoexcitation. The photomechanical effects in the III-V covalent semiconductors GaP, GaAs, and InP have been examined by a combination of advanced quantum mechanics (QM) simulations, nanoindentation experiments, and state-of-the-art transmission electron microscopy measurements. The QM results indicate that the energy barrier for deformation slip in GaP is reduced by more than $50\%$ by generating high-concentration EHPs $(\sim {10}^{21}\mathrm{c}{\mathrm{m}}^{-3})$, exhibiting metal-like ductility. Theoretical prediction agrees very well with the experimental measured performance where more dislocations are activated under light-illumination conditions.

Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions We report a combined experimental and theoretical study of the melting curve and the structural behavior of vanadium under extreme pressure and temperature. We performed powder x-ray-diffraction experiments up to 120 GPa and 4000 K, determining the phase boundary of the body-centered cubic-to-rhombohedral transition and melting temperatures at different pressures. Melting temperatures have also been established from the observation of temperature plateaus during laser heating, and the results from the density-functional theory calculations. Results obtained from our experiments and calculations are fully consistent and lead to an accurate determination of the melting curve of vanadium. These results are discussed in comparison with previous studies. The melting temperatures determined in this study are higher than those previously obtained using the speckle method, but also considerably lower than those obtained from shockwave experiments and linear muffin-tin orbital calculations. Finally, a high-pressure, high-temperature equation of state up to 120 GPa and 2800 K has also been determined.

Using a valence force field model based on that introduced by Martin, we present three related methods through which we analytically determine valence force field parameters. The methods introduced allow easy derivation of valence force field parameters in terms of the Kleinman parameter $\zeta$ and bulk properties of zincblende and diamond crystals. We start with a model suited for covalent and weakly ionic materials, where the valence force field parameters are derived in terms of $\zeta$ and the bulk elastic constants $C_{11}, C_{12}$, and $C_{44}$. We show that this model breaks down as the material becomes more ionic and specifically when the elastic anisotropy factor $A=2C_{44}/(C_{11}-C_{12})>2$. The analytic model can be stabilized for ionic materials by including Martin's electrostatic terms with effective cation and anion charges in the valence force field model. Inclusion of effective charges determined via the optical phonon mode splitting provides a stable model for all but two of the materials considered (zincblende GaN and AlN). A stable model is obtained for all materials considered by also utilizing the inner elastic constant $E_{11}$ to determine the magnitude of the effective charges used in the Coulomb interaction. Test calculations show that the models describe well structural relaxation in superlattices and alloys and reproduce key phonon band structure features.

We have measured the room-temperature phonon spectrum of Mo-stabilized $\gamma \text{−}\mathrm{U}$. The dispersion curves show unusual softening near the $H$ point, $q=[1/2,1/2,1/2]$, which may derive from the metastability of the $\gamma \text{−}\mathrm{U}$ phase or from strong electron-phonon coupling. Near the zone center, the dispersion curves agree well with theory, though significant differences are observed away from the zone center. The experimental phonon density of states is shifted to higher energy compared to theory and high-temperature neutron scattering. The elastic constants of $\gamma$-UMo are similar to those of body-centered cubic elemental metals.

This study explores the relationship between phonon dynamics and negative thermal expansion (NTE) in $\mathrm{C}{\mathrm{u}}_x\mathrm{N}{\mathrm{i}}_{2-x}{\left(\mathrm{CN}\right)}_4$. The partial replacement of nickel (II) by copper (II) in $\mathrm{Ni}{\left(\mathrm{CN}\right)}_2$ leads to a line phase, $\mathrm{CuNi}{\left(\mathrm{CN}\right)}_4\left(x=1\right)$, and a solid solution, $\mathrm{C}{\mathrm{u}}_x\mathrm{N}{\mathrm{i}}_{2-x}{\left(\mathrm{CN}\right)}_4\left(0\le x\le 0.5\right)$. $\mathrm{CuNi}{\left(\mathrm{CN}\right)}_4$ adopts a layered structure related to that of $\mathrm{Ni}{\left(\mathrm{CN}\right)}_2\left(x=0\right)$, and interestingly exhibits two-dimensional (2D) NTE which is $\sim 1.5$ times larger. Inelastic neutron-scattering (INS) measurements combined with first-principles lattice dynamical calculations provide insights into the effect of $\mathrm{C}{\mathrm{u}}^{2+}$ on the underlying mechanisms behind the anomalous thermal behavior in all the $\mathrm{C}{\mathrm{u}}_x\mathrm{N}{\mathrm{i}}_{2-x}{\left(\mathrm{CN}\right)}_4$ compounds. The solid solutions are presently reported to also show 2D NTE. The INS results highlight that as the $\mathrm{C}{\mathrm{u}}^{2+}$ content increases in $\mathrm{C}{\mathrm{u}}_x\mathrm{N}{\mathrm{i}}_{2-x}{\left(\mathrm{CN}\right)}_4$, large shifts to lower energies are observed in modes consisting of localized in- and out-of-plane librational motions of the CN ligand, which contribute to the NTE in $\mathrm{CuNi}{\left(\mathrm{CN}\right)}_4$. Mode Grüneisen parameters calculated for $\mathrm{CuNi}{\left(\mathrm{CN}\right)}_4$ show that acoustic and low-energy optic modes contribute the most to the NTE, as previously shown in $\mathrm{Ni}{\left(\mathrm{CN}\right)}_2$. However, mode eigenvectors reveal a large deformation of the $\left[\mathrm{Cu}{\mathrm{N}}_4\right]$ units compared to the $\left[\mathrm{Ni}{\mathrm{C}}_4\right]$ units, resulting in phonon modes not found in $\mathrm{Ni}{\left(\mathrm{CN}\right)}_2$, whose NTE-driving phonons consist predominately of rigid-unit modes. The deformations in $\mathrm{CuNi}{\left(\mathrm{CN}\right)}_4$ arise because the $d^9$ square-planar center is easier to deform than the $d^8$ one, resulting in a greater range of out-of-plane motions for the adjoining ligands.

We have measured the resistivity and Hall effect of $\mathrm{La}{(\mathrm{Fe},\mathrm{Co})}_{13-x}{\mathrm{Si}}_x$ polycrystals in the temperature range of $100\mathrm{K}<T<340\mathrm{K}$ and applied magnetic fields of up to 5 T. Detailed investigation combining experimental and theoretical means suggests that the anomalous Hall effect in $\mathrm{La}{(\mathrm{Fe},\mathrm{Co},\mathrm{Si})}_{13}$ originates mainly from the scattering independent intrinsic contributions, in turn, the anomalous Hall conductivity can be greatly enhanced with increasing Co doping concentration.

A series of $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$ single crystals was synthesized, allowing a comprehensive phase diagram with respect to field, temperature, and chemical substitution to be established. Our neutron diffraction experiments revealed a helimagnetic order with magnetic moments ferromagnetically aligned in the $ab$ plane and a helimagnetic wave vector of $q=(0,0,0.56)$ for $x=0.1$. The combination of neutron diffraction and angle-resolved photoemission spectroscopy measurements shows that the tuning of a flat band with $d_{x^2-y^2}$ orbital character drives the helimagnetism and indicates the possibility of a quantum order-by-disorder mechanism.

The compound ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ with the body-centered tetragonal ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$ structure is known to remain paramagnetic down to a temperature $T=0.05$ K, but inelastic neutron scattering studies have shown that both ferromagnetic (FM) and antiferromagnetic (AFM) fluctuations occur in single crystals. Thus it is of interest to study how the magnetism evolves on doping ${\mathrm{SrCo}}_2{\mathrm{As}}_2$. Previous work on polycrystalline samples of $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$ indicated the development of AFM order for $0<x\lesssim 0.3$. Here we studied single crystals of $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$ for $0<x\le 1$ and confirmed the occurrence of AFM order which we deduce to have a $c$-axis helix structure. We also find evidence for an unusual composition-induced magnetic quantum critical point at $x\approx 0.3$ where non-Fermi-liquid types of behavior were revealed by heat capacity and electrical resisitivity measurements at low $T$. Electron-doped $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$ single crystals with compositions $x=0$ to 0.9 were grown out of self-flux and ${\mathrm{SrNi}}_2{\mathrm{As}}_2$ single crystals out of Bi flux. The crystals were characterized using single-crystal x-ray diffraction (XRD) at room temperature, and magnetic susceptibility $\chi (H,T)$, isothermal magnetization $M(H,T)$, heat capacity $C_{\mathrm{p}}(H,T)$, and electrical resistivity $\rho (H,T)$ measurements versus applied magnetic field $H$ and $T$. The XRD studies show that the system undergoes a continuous structural crossover from the uncollapsed-tetragonal (ucT) structure to the collapsed tetragonal (cT) structure with increasing Ni doping. The $\chi \left(T\right)$ data show that ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ exhibits an AFM ground state almost immediately upon Ni doping on the Co site. Ab initio electronic-structure calculations for $x=0$ and 0.15 indicate that a flat band with a peak in the density of states just above the Fermi energy is responsible for this initial magnetic-ordering behavior on Ni doping. The AFM ordering is observed in the range $0.013\le x\le 0.25$ with the ordered moments aligned in the $ab$ plane and with a maximum ordering temperature $T_{\mathrm{N}}=26.5$ K at $x=0.10$. The Curie-Weiss-like $T$ dependence of $\chi$ in the paramagnetic (PM) state indicates dominant FM interactions. The behavior of the anisotropic susceptibilities below $T_{\mathrm{N}}$ suggests a planar helical magnetic ground state with a composition-dependent pitch based on a local-moment molecular-field-theory model, with FM interactions in the $ab$ plane and weaker AFM interactions along the helix $c$ axis. However, the small ordered (saturation) moments $\sim 0.1{\mu }_{\mathrm{B}}$ per transition metal atom, where ${\mu }_{\mathrm{B}}$ is the Bohr magneton, and the values of the Rhodes-Wohlfarth ratio indicate that the magnetism is itinerant. The high-field $M\left(H\right)$ isotherms and the low-field ${\chi }^{-1}(T>T_{\mathrm{N}})$ data were successfully analyzed within the framework of Takahashi's theory of FM spin fluctuations. The $C_{\mathrm{p}}\left(T\right)$ at low $T$ exhibits Fermi-liquid behavior for $0\le x\le 0.15$, whereas an evolution to a logarithmic non-Fermi-liquid (NFL) behavior is found for $x=0.2$ to 0.3. The logarithmic dependence is suppressed in an applied magnetic field. The low-$T\rho (H=0,T)$ data show a $T^2$ dependence for $0\le x\le 0.20$ and a power-law dependence $\rho (H=0,T)={\rho }_0+A{T}^n$ with $n<2$ for $x=0.20$ and 0.30. The exponent $n$ shows a notable field dependence, suggesting both doping- and magnetic-field-tuned quantum critical phenomena. These low-$T$ NFL types of behavior observed in the $C_{\mathrm{p}}$ and $\rho$ measurements are most evident near the quantum critical concentration $x\approx 0.3$ at which a $T=0$ composition-induced transition from the AFM phase to the PM phase occurs.

A mechanism of superconductivity is proposed for the Kondo lattice which has semimetallic conduction bands with electron and hole Fermi surfaces. At high temperatures, the $f$ electron's localized spins/pseudospins are fluctuating between electron and hole Fermi surfaces to seek for a partner to couple with. This system tries to resolve this frustration at low temperatures and chooses to construct a quantum mechanically entangled state composed of the Kondo singlet with electron surface and that with hole surface, to break the U(1) gauge symmetry. The corresponding order parameter is given by a composite pairing amplitude as a three-body bound state of localized spin/pseudospin, electron and hole. The electromagnetic response is considered, where the composite pair itself does not contribute to the Meissner effect, but the induced pair between conduction electrons, which inevitably mixes due to, e.g., a band cutoff effect at high energies, carries the superconducting current under the external field. Possible applications to real heavy-electron materials are also discussed.

The contribution of pair fluctuations to the spin current in liquid ${}^3\mathrm{He}$ in isotropic aerogel near the critical temperature of transition to the superfluid state is calculated.

Reversible electric-field induced domain switching in ferroelectric thin films gives rise to a large electromechanical coupling. Despite extensive in situ studies confirming a dominant contribution from domain switching, the speed of the domain wall motion had not been discussed enough. In this study, we performed time-resolved measurement of lattice elongation and non-180° domain switching for an epitaxial rhombohedral $\left(111\right)/\left(11\overline{1}\right)$-oriented ($\mathrm{Pb}\left(\mathrm{Z}{\mathrm{r}}_{0.65}\mathrm{T}{\mathrm{i}}_{0.35}\right){\mathrm{O}}_3$ film under nanosecond electric field pulses by means of synchrotron x-ray diffraction. Both lattice elongation and non-180° domain switching due to a 200-ns electric pulse were directly observed from the shift of the 222 diffraction position toward a lower angle and the change in the integrated intensity ratio of 222 to $22\overline{2}$ peaks, respectively. The non-180° domain switching also results in an increase of the switchable polarization. Following the removal of the electric field, it is seen that the non-180° domain back switching from 222 to $22\overline{2}$ is sluggish compared to the relaxation of the field-induced lattice strain. This is different from the (100)/(001)-oriented tetragonal epitaxial $\mathrm{Pb}\left(\mathrm{Zr},\mathrm{Ti}\right){\mathrm{O}}_3$ films, in which no obvious delay was detected. These results show the importance of the direct time-resolved response observation of the crystal structure change with the application of a high-speed electric pulse field to understand the frequency dispersion of the ferroelectric and piezoelectric responses of $\mathrm{Pb}\left(\mathrm{Zr},\mathrm{Ti}\right){\mathrm{O}}_3$ films.