A universal high energy anomaly in the single particle spectral function is reported in three different families of high temperature superconductors by using angle-resolved photoemission spectroscopy. As we follow the dispersing peak of the spectral function from the Fermi energy to the valence band complex, we find dispersion anomalies marked by two distinctive high energy scales, $E_1\approx 0.38\mathrm{eV}$ and $E_2\approx 0.8\mathrm{eV}$. $E_1$ marks the energy above which the dispersion splits into two branches. One is a continuation of the near parabolic dispersion, albeit with reduced spectral weight, and reaches the bottom of the band at the $\Gamma$ point at $\approx 0.5\mathrm{eV}$. The other is given by a peak in the momentum space, nearly independent of energy between $E_1$ and $E_2$. Above $E_2$, a bandlike dispersion reemerges. We conjecture that these two energies mark the disintegration of the low-energy quasiparticles into a spinon and holon branch in the high $T_c$ cuprates.

A distinctive feature of layered conductors is the presence of low-energy electronic collective modes of the conduction electrons. This affects the dynamic screening properties of the Coulomb interaction in a layered material. We study the consequences of the existence of these collective modes for superconductivity. General equations for the superconducting order parameter are derived within the strong-coupling phonon-plasmon scheme that accounts for the screened Coulomb interaction. Specifically, we calculate the superconducting critical temperature $T_c$ taking into account the full temperature, frequency, and wave-vector dependence of the dielectric function. We show that low-energy plasmons may contribute constructively to superconductivity. Three classes of layered superconductors are discussed within our model: metal-intercalated halide nitrides, layered organic materials, and high-$T_c$ oxides. In particular, we demonstrate that the plasmon contribution (electronic mechanism) is dominant in the first class of layered materials. The theory shows that the description of so-called “quasi-two-dimensional superconductors” cannot be reduced to a purely two-dimensional model, as commonly assumed. While the transport properties are strongly anisotropic, it remains essential to take into account the screened interlayer Coulomb interaction to describe the superconducting state of layered materials.

We study the time dependence of the grain size distribution N(r,t) during crystallization of a d-dimensional solid. A partial differential equation, including a source term for nuclei and a growth law for grains, is solved analytically for any dimension d. We discuss solutions obtained for processes described by the Kolmogorov-Avrami-Mehl-Johnson model for random nucleation and growth (RNG). Nucleation and growth are set on the same footing, which leads to a time-dependent decay of both effective rates. We analyze in detail how model parameters, the dimensionality of the crystallization process, and time influence the shape of the distribution. The calculations show that the dynamics of the effective nucleation and effective growth rates play an essential role in determining the final form of the distribution obtained at full crystallization. We demonstrate that for one class of nucleation and growth rates, the distribution evolves in time into the logarithmic-normal (lognormal) form discussed earlier by Bergmann and Bill [J. Cryst. Growth 310, 3135 (2008)]. We also obtain an analytical expression for the finite maximal grain size at all times. The theory allows for the description of a variety of RNG crystallization processes in thin films and bulk materials. Expressions useful for experimental data analysis are presented for the grain size distribution and the moments in terms of fundamental and measurable parameters of the model.

An essential property of layered systems is the dynamical nature of the screened Coulomb interaction. Low-energy collective modes appear as a consequence of the layering and provide for a superconducting-pairing channel in addition to the electron-phonon-induced attractive interaction. We show that taking into account this feature allows to explain the high critical temperatures ${(T}_c\sim 26\mathrm{K})$ observed in recently discovered intercalated metallochloronitrides. The exchange of acoustic plasmons between carriers leads to a significant enhancement of the superconducting critical temperature that is in agreement with the experimental observations.

The value of the isotope coefficient could be greatly affected by a number of factors not related to the lattice dynamics. Among them are magnetic scattering, the presence of a normal film (proximity effect), and nonadiabaticity (dynamic Jahn-Teller effect). The results are in good agreement with existing experimental data for oxygen isotope substitution (O${}^{16}\to {\mathrm{O}}^{18})$ in the YBa${}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta },$ Y${}_{1-x}{\mathrm{Pr}}_x{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta },$ YBa${}_2({\mathrm{Cu}}_{1-x}{\mathrm{Zn}}_x{)}_3{\mathrm{O}}_{7-\delta }$ compounds. In addition, we make several predictions related to conventional as well as to high-$T_c$ materials.