Recent extended x-ray absorption fine structure (EXAFS) studies suggest that in skutterudites, the nearly square rings (such as ${\mathrm{As}}_4$ in ${\mathrm{CeFe}}_4{\mathrm{As}}_{12}$) are quite rigid and may vibrate with low-energy modes in one direction, similar to “rattler” atom vibrations. That work suggests that the motions of the square rings and the rattler atoms are coupled. In addition, for ${Ln\mathrm{Cu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$, the second-neighbor pairs about $Ln$ have stiffer effective springs than the nearest-neighbor pairs. To investigate these systems, a one-dimensional, four-mass, linear chain spring model is developed to describe the recent experimental results and provide insight about the low-energy vibrations in such systems. Our model solves the resulting coupled network of overlapping weak and strong springs and determines the eigenfrequencies and eigenvectors. The dispersion curves show an acoustic mode, two different low-energy optical rattling modes involving both the rattler and square, and a noninteracting optical mode. Each rattler mode can couple to the acoustic mode, which generates avoided crossings characterized by flattening of the modes; this has important consequences for thermal transport. From these results we calculate atomic correlation functions and the Debye-Waller–like function used in EXAFS ${\sigma }^2$ as a function of temperature. These calculations show that for the rattler-neighbor pairs, ${\sigma }^2$ is a sum over several modes; it is not the result of a single mode. The inverse slope of ${\sigma }^2\left(T\right)$ at high $T$ provides a measure of the effective spring constants, and the results show that for small direct spring constants the effective spring constant can be significantly larger than the direct spring constants. The locations of the avoided crossings (between rattler modes and the acoustic mode) in $q$ space can be tuned by the choice of both the rattler and the square atoms. Consequently, it may be possible to further reduce the thermal conductivity using a mixture of nanoparticles, each with avoided crossings at different positions in $q$ space.

Certain types of topological superconductors and superfluids are known to host protected Majorana zero modes in cores of Abrikosov vortices. When such vortices are arranged in a dense periodic lattice one expects zero modes from neighboring vortices to hybridize and form dispersing bands. Understanding the structure of these bands is essential for the schemes that aim to employ the zero modes in quantum computation applications and in studies of their strongly interacting phases. We investigate here the band formation phenomenon in two concrete models, describing a two-dimensional $p_x+i{p}_y$ superconductor and a superconducting surface of a three-dimensional strong topological insulator (Fu-Kane model), using a combination of analytical and numerical techniques. We find that the physics of the Majorana bands is well described by tight-binding models of Majorana fermions coupled to a static $Z_2$ gauge field with a nontrivial gauge flux through each plaquette, in accord with expectations based on very general arguments. In the case of the Fu-Kane model we also find that, irrespective of the lattice geometry, the Majorana band becomes completely flat at the so-called neutrality point (chemical potential coincident with the Dirac point) where the model exhibits an extra chiral symmetry. In this limit the low-energy physics will be dominated by four-fermion interaction terms which are permitted by symmetries and may arise from the Coulomb interaction between the constituent electron degrees of freedom.

Majorana quasiparticles localized in vortex cores of a chiral $p$-wave superconductor hybridize with one another to form bands in a vortex lattice. We begin by solving a fully microscopic theory describing all quasiparticle bands in a chiral $p$-wave superconductor in a magnetic field, then use this solution to build localized Wannier wave functions corresponding to Majorana quasiparticles. A low-energy tight-binding theory describing the intervortex hopping of these is then derived, and its topological properties—which depend crucially on the signs of the imaginary intervortex hopping parameters—are studied. We show that the energy gap between the Majorana bands may be either topologically trivial or nontrivial, depending on whether the Chern number contributions from the Majorana bands and those from the background superconducting condensate add constructively or destructively. This topology directly affects the temperature-dependent thermal Hall conductivity, which we also calculate.

The pressure and temperature dependence of the phonon dispersion of $2H-{\mathrm{NbSe}}_2$ is measured by inelastic x-ray scattering. A strong temperature dependent soft phonon mode, reminiscent of the charge density wave (CDW), is found to persist up to a pressure as high as 16 GPa, far above the critical pressure at which the CDW disappears at 0 K. By using ab initio calculations beyond the harmonic approximation, we obtain an accurate, quantitative description of the $(P,T)$ dependence of the phonon spectrum. Our results show that the rapid destruction of the CDW under pressure is related to the zero mode vibrations—or quantum fluctuations—of the lattice renormalized by the anharmonic part of the lattice potential. The calculations also show that the low-energy longitudinal acoustic mode that drives the CDW transition barely contributes to superconductivity, explaining the insensitivity of the superconducting critical temperature to the CDW transition.

The sequence of $2s+1$ ground states in the frustrated antiferromagnetic rings with odd number $n$ of local spins $s$ resulting from a single bond defect strength is determined, and occurrence of the Lieb-Mattis energy level ordering, proven for the bipartite systems only, is confirmed for the rings in question. The sequence is universal, provides the theoretical basis for the recent classification of spin frustration in molecular magnets, and indicates that the Lieb-Mattis theorem (LMT) consequences exist for the nonbipartite rings. The states in the sequence are characterized by the total spin $S$ fulfilling the constraint $S\le s$ and are separated by $2s$ Kahn degenerate frustration points. The possible LMT consequences in other systems are discussed.

The $S=1$ antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is $e_0=E_0/\left(NJ\right)=-1.41095$, which is readily lower than that of the TVBS state ($e_0=-1.3912\pm 0.0025$). This agrees well with those of the cylindrical ($e_0=-1.4122$) and periodic ($e_0=-1.4111$) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the $S=1$ kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has $\mathrm{\Delta }/J=0.178\pm 0.005$, whereas the higher TVBS state has a larger one $\mathrm{\Delta }/J=0.280$.

Inertial magnetization dynamics have been predicted at ultrahigh speeds, or frequencies approaching the inverse Drude scattering time, in ferromagnetic metals. Here, we identify inertial terms to magnetization dynamics in thin ${\mathrm{Ni}}_{79}{\mathrm{Fe}}_{21}$ and Co films near room temperature. Effective magnetic fields measured in high-frequency ferromagnetic resonance (115–345 GHz) show an additional stiffening term which is quadratic in frequency and $\sim 80$ mT at the high-frequency limit of our experiment. Our results extend understanding of magnetization dynamics at picosecond time scales.

We show that the phase information contained in coherent phonon oscillations generated by a laser pulse in a multiorbital superconductor can be used as an experimental tool to probe superconductivity and pairing symmetries. The phase difference between the normal and superconducting states is proportional to the superconducting order parameter just below the superconducting transition temperature $T_c$. It also exhibits different behaviors for superconducting states with different pairing symmetries. In particular, if there is an orbital-dependent internal sign change state, the phase difference can have a discontinuous jump below $T_c$.

The time evolution of the electron structure is investigated in a molybdenum foil heated up to the warm dense matter regime by a femtosecond laser pulse, through time-resolved x-ray absorption near-edge spectroscopy. Spectra are measured with independent characterizations of temperature and density. They are successfully compared with ab initio quantum molecular dynamic calculations. We demonstrate that the observed white line in the $L_3$ edge reveals the time evolution of the electron density of state from the solid to the hot (a few eV) and expanding liquid. The data indicate a highly nonequilibrated state, 5 ps after heating.

We present a comparative study of vortex pinning efficiency in superconducting (V) thin films grown on two similar triangular arrays of superconducting (Nb) and nonsuperconducting (Cu) nanodots. Resistance and magnetization anomalies at the same matching fields confirm the same pinning periodicity in both samples. However, we found two distinct features: First, the sample with superconducting dots shows stronger pinning that appears as sharper matching peaks in magnetization loops and shows higher critical current density and larger critical field at low temperatures. Second, an overall increase in the resistance of the V film with Nb nanodots is observed, while there is a crossover in the temperature dependence of the critical field and the critical current of both samples at $T=3\mathrm{K}$. This crossover corresponds to the temperature when the superconducting coherence length of V thin film equals the edge-to-edge distance between nanodots. We argue that this change in superconducting properties is related to the change in the superconducting regime from pinning enhancement at low temperatures to a superconducting wire network at high temperatures.

The effect of pressure on electrical resistivity of heavy-fermion compounds ${\mathrm{Ce}}_3{M}_4{\mathrm{Sn}}_{13}$, where $M=\mathrm{Co}$, Rh, Ru, and the ${\mathrm{La}}_3{M}_4{\mathrm{Sn}}_{13}$ counterparts is studied in the framework of the fully relativistic full potential local orbital method. The experiment shows that the electrical resistivity of ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ and ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ increases with pressure, a similar pressure effect is obtained for isostructural La-based reference metals, while opposite behaviors under pressure are documented for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ and ${\mathrm{La}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$. The contrasting pressure dependent effects of ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ are discussed. In order to clarify the various phenomena the band-structure calculations under applied pressure were performed. Here, we show that the resistivity increase with pressure arises from the formation of interband distances at the Fermi level in ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$, this pseudo-gap-like effect is also pressure dependent, while in ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ the opposite change of resistivity results from the suppression of spin fluctuations under pressure.

The reconstruction and energetics for a range of chalcopyrite (${\mathrm{CuFeS}}_2$) surfaces have been investigated using hybrid-exchange density functional theory. The stable nonpolar surfaces in increasing order of surface energy are (110), (102), and (114). In addition, the polar $\left(112\right)/\left(\overline{112}\right)$ surface pair was found to be remarkably stable with a surface formation energy that is only slightly higher than that of the (110) surface. The stability of $\left(112\right)/\left(\overline{112}\right)$ can be attributed to a combination of geometric and electronic mechanisms that result in the suppression of the electrostatic dipole perpendicular to the surface. Defect formation is a third mechanism that can further stabilize the $\left(112\right)/\left(\overline{112}\right)$ surface pair to an extent that it is thermodynamically preferred over the (110) surface. The stability of $\left(112\right)/\left(\overline{112}\right)$ means that regardless of the growth conditions, (112) and ($\overline{112}$) facets are expected to have a significant presence in the surface morphology of ${\mathrm{CuFeS}}_2$.

We propose and theoretically investigate an idea of valley caloritronics where quantum transport of the valley degrees of freedom is thermally induced. Valley caloritronics addresses questions such as thermal generation of valley polarized current and, more importantly, pure valley current without an accompanying charge current. After establishing a general physical picture, we show that heat-induced pure valley current can be generated by virtue of wedge-shaped graphene nanoribbons in a two-probe device setup. We discover that the quantum transport properties of the valley degree of freedom can be very different when driven by a voltage bias or by a temperature bias. A very surprising result is that an alternating valley current can be thermally generated via gate control: namely the heat-induced valley current changes its flow direction in some quasiperiodic manner versus the value of a gate voltage at a fixed polarity. Our results indicate a vast potential for developing valley caloritronic devices.

Graphene is a famous realization of an elastic crystalline two-dimensional (2D) membrane. Thermal fluctuations of a 2D membrane tend to destroy the long-range order in the system. Such fluctuations are stabilized by strong anharmonicity effects, which preserve thermodynamic stability. The anharmonic effects demonstrate critical behavior on scales larger than the Ginzburg scale. In particular, a clean suspended flake of graphene shows a power-law increase of the bending rigidity with the system size, $\varkappa \propto L^{\eta }$, due to anharmonic interaction between the in-plane and out-of-plane (flexural) phonon modes. We demonstrate that random fluctuations of the membrane curvature caused by static disorder may change dramatically the scaling of the bending rigidity and lead to a nonmonotonous dependence of $\varkappa$ on $L.$ We derive coupled renormalization-group equations describing the combined flow of $\varkappa$ and effective disorder strength $b$, find a critical curve $b\left(\varkappa \right)$ separating flat and crumpled phases, and explore the behavior of disorder in the flat phase. Deep in the flat phase, disorder decays in a power-law way at scales larger than the Ginzburg length, which therefore sets a characteristic size for the ripples—static out-of-plane deformations observed experimentally in suspended graphene. We find that in the limit $L\to \infty$ ripples are characterized by an anomalous exponent $2\eta$ in contrast to dynamical fluctuations governed by $\eta$. For sufficiently strong disorder, there exists an intermediate range of spatial scales where ripples decay much slower, with exponent $\eta /4$. In the near-critical regime, disorder first increases with $L$, then reaches a maximum and starts to decrease. In this case, the membrane shows fractal properties implying a multiple folding starting from a certain length scale $L_1$ and finally flattens at a much larger scale $L_2$ (which diverges at criticality). We conclude the paper by a comparison of our results with available experimental data on graphene ripples.

We present a theory of bilayer two-dimensional electron systems that host a spatially indirect exciton condensate when in thermal equilibrium. Equilibrium bilayer exciton condensates (BXCs) are expected to form when two nearby semiconductor layers are electrically isolated, and when the conduction band of one layer is brought close to degeneracy with the valence band of a nearby layer by varying bias or gate voltages. BXCs are characterized by spontaneous interlayer phase coherence and counterflow superfluidity. The bilayer system we consider is composed of two transition metal dichalcogenide monolayers separated and surrounded by hexagonal boron nitride. We use mean-field theory and a bosonic weakly interacting exciton model to explore the BXC phase diagram, and time-dependent mean-field theory to address condensate collective mode spectra and quantum fluctuations. We find that a phase transition occurs between states containing one and two condensate components as the layer separation and the exciton density are varied, and derive simple approximate expressions for the exciton-exciton interaction strength which we show can be measured capacitively.

Understanding and controlling the way excitons propagate in solids is a key for tailoring materials with improved optoelectronic properties. A fundamental step in this direction is the determination of the exciton energy-momentum dispersion. Here, thanks to the solution of the parameter-free Bethe-Salpeter equation (BSE), we draw and explain the exciton energy-momentum map of hexagonal boron nitride (h-BN) in the first three Brillouin zones. We show that h-BN displays strong excitonic effects not only in the optical spectra at vanishing momentum $\mathbf{q}$, as previously reported, but also at large $\mathbf{q}$. We validate our theoretical predictions by assessing the calculated exciton map by means of an inelastic x-ray scattering (IXS) experiment. Moreover, we solve the discrepancies between previous experimental data and calculations, proving then that the BSE is highly accurate through the whole momentum range. Therefore, these results put forward the combination BSE and IXS as the tool of choice for addressing the exciton dynamics in complex materials.

Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transition in the Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at weak interaction to an antiferromagnetic Mott insulator at strong interaction can be readily detected by the momentum space behavior of the strange correlator in single-particle, spin, and pairing sectors. The interaction effects on the symmetry-protected edge states in various sectors, i.e., the helical Luttinger liquid behavior, are well captured in the QMC measurements of strange correlators. Moreover, we demonstrate that the strange correlator is technically easier to implement in QMC and more robust in performance than other proposed numerical diagnoses for interacting topological states, as only static correlations are needed. The attempt in this work paves the way for using the strange correlator to study interaction-driven topological phase transitions in fermionic as well as bosonic systems.

Nitrogen is the dominant impurity in the majority of natural and synthetic diamonds, and the family of nitrogen vacancy-type (${\mathrm{N}}_n\mathrm{V}$) defects are crucial in our understanding of defect dynamics in these diamonds. A significant gap is the lack of positive identification of ${\mathrm{N}}_2{\mathrm{V}}^{-}$, the dominant charge state of ${\mathrm{N}}_2\mathrm{V}$ in diamond that contains a significant concentration of electron donors. In this paper, we employ isotopically-enriched diamond to identify the EPR spectrum associated with ${}^{15}{\mathrm{N}}_2{\mathrm{V}}^{-}$ and use the derived spin Hamiltonian parameters to identify ${}^{14}{\mathrm{N}}_2{\mathrm{V}}^{-}$ in a natural isotopic abundance sample. The electronic wave function of the ${\mathrm{N}}_2{\mathrm{V}}^{-}$ ground state and previous lack of identification is discussed. The ${\mathrm{N}}_2{\mathrm{V}}^{-}$ EPR spectrum intensity is shown to correlate with the H2 optical absorption over an order of magnitude in concentration.

We calculate the thermoelectric power (or thermopower) of many semiconducting single wall carbon nanotubes (s-SWNTs) within a diameter range $0.5–1.5\mathrm{nm}$ by using the Boltzmann transport formalism combined with an extended tight-binding model. We find that the thermopower of s-SWNTs increases as the tube diameter decreases. For some s-SWNTs with diameters less than $0.6\mathrm{nm}$, the thermopower can reach a value larger than $2000\mu \mathrm{V}/\mathrm{K}$ at room temperature, which is about 6 to 10 times larger than that found in commonly used thermoelectric materials. The large thermopower values may be attributed to the one dimensionality of the nanotubes and to the presence of large band gaps of the small-diameter s-SWNTs. We derive an analytical formula to reproduce the numerical calculation of the thermopower and we find that the thermopower of a given s-SWNT is directly related with its band gap. The formula also explains the shape of the thermopower as a function of tube diameter, which looks similar to the shape of the so-called Kataura plot of the band gap dependence on tube diameter.

We report spin-pair tunneling observed in a ${\mathrm{Mn}}_3$ single-molecule magnet, which is a crystal with a two-dimensional network of identical exchange coupling. We observe a series of extra quantum tunnelings by the ac susceptibility measurements, and demonstrate that these are mainly thermally assisted tunnelings of a pair of two spins from the same initial state to the same final state simultaneously. The resonant field of spin-pair tunneling can be expressed as $H_z=lD/g{\mu }_0{\mu }_B+(n_{\downarrow }-n_{\uparrow })JS/2g{\mu }_0{\mu }_B$, and the splitting interval ($\left|J\right|S/g{\mu }_0{\mu }_B$) is half that of the single-spin tunneling ($2\left|J\right|S/g{\mu }_0{\mu }_B$), which is analogous to the relationship between the magnetic flux quantum in superconductors ($h/2e$) and common metals ($h/e$).