Condensed Matter

Nuclear relaxation, $1/T_1$, is a very robust probe of electronic excitations in superconducting materials above and below the critical temperature of superconductivity, $T_{\mathrm{c}}$. Here, a relaxation phenomenology of hole-doped cuprate superconductors is presented based on the majority of the available literature data from the CuO₂ plane, without assumptions with respect to a hyperfine scenario, form factors, or particular theoretical models. Below a temperature similar to the pseudogap temperature, Heitler–Teller-type relaxation is uncovered universally; i.e., the nuclear spin relaxation above $T_{\mathrm{c}}$ is only determined by the absolute temperature, . All materials condense out of this metal at $T_{\mathrm{c}}$, below which relaxation drops even faster, as expected from conventional superconductors, albeit without a Hebel–Slichter peak. It is a ’hidden metal’ in the sense that it has a vanishing uniform response and thus hardly affects the NMR shifts; it is also not seen in planar O relaxation. The hidden metal causes a temperature-independent but material-dependent planar Cu relaxation anisotropy that is strongly correlated with the size of $T_{\mathrm{c}}$. Moreover, the rate measured with the field in the CuO₂ plane is nearly the same for all cuprates: Ks, where $1/{{}^{63}T}_{1\Vert }$ is mainly responsible for the change in anisotropy. Above the hidden metal, the relaxation behavior changes and can be described by an ordinary but renormalized metal, with a reduced Cu relaxation anisotropy. The relaxation phenomenology, which should hold clues to the so-called strange metal, is also discussed in the context of the two spin components previously uncovered in the shifts, as well as the pseudogap and relation to other probes. This new phenomenology should give a better foundation for the understanding of the cuprates.

Bond-stretching phonons in hole-doped cuprates exhibit pronounced anomalies in momentum regions where charge correlations are observed, indicating a strong coupling between lattice dynamics and the charge sector. Motivated by this phenomenology, we develop a minimal theoretical framework to clarify how the bond-stretching phonon is renormalized by the proximity to charge-order instabilities and why short-ranged dynamical charge density fluctuations (CDFs) can provide a dominant contribution even in the presence of nearly static charge density wave (CDW) correlations. Starting from a correlated Fermi-liquid description with Coulomb-frustrated charge ordering and electron–phonon coupling, we formulate a two-mode random-phase-approximation treatment in which a low-energy phonon channel involved in the charge-order instability is coupled, through the electronic polarization, to the higher-energy bond-stretching branch. The resulting off-diagonal phonon self-energy transfers the low-energy charge softening to the bond-stretching phonon. We then introduce an average self-energy description to account for the coexistence of CDW and CDF components. The model shows that, although a nearly static CDW component produces a stronger local softening, a broader CDF component can dominate the effective phonon self-energy because of its larger reciprocal-space volume. The analysis identifies two key parameters controlling the bond-stretching anomaly: the characteristic energy of charge correlations and the effective electron–phonon coupling.

Organic semiconductors offer a potential class of materials for organic photovoltaic (OPV) applications due to their tunable optoelectronic properties and low-cost processing. A methodical DFT/TD-DFT study of a library of organic donor–π–acceptor (D–π–A) compounds based on triphenylamine donors, thiophene-based π-bridges, and benzothiadiazole/malononitrile acceptors is presented in this work, with the goal of rationalizing the structure–property relationships governing their photovoltaic behavior. CAM-B3LYP calculations were used to analyze the role of donor, bridge, and acceptor units in modulating frontier-orbital alignment, charge-transfer character, and optical absorption properties, as well as to evaluate the active-layer thickness in the estimation of the light-harvesting efficiency. The results, which are intended as internal comparative descriptors rather than predictive device efficiencies, reveal that the most pronounced bathochromic shifts and most favorable optical responses are not simply associated with the strongest donor or acceptor moieties, but rather arise from an optimal balance between frontier-orbital delocalization and charge-transfer character across the molecular framework. A preliminary assessment of photovoltaic descriptors suggests that the proposed computational workflow may provide useful guidelines for the descriptor-guided design and screening of next-generation organic photovoltaic materials.