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Understanding electronic interactions in high-temperature superconductors is an outstanding challenge. In the widely studied cuprate materials, experimental evidence points to strong electron-phonon ( $e$-ph) coupling and broad photoemission spectra. Yet, the microscopic origin of this behavior is not fully understood. Here, we study $e$-ph interactions and polarons in a prototypical parent (undoped) cuprate, ${\mathrm{La}}_2{\mathrm{CuO}}_4$(LCO), by means of first-principles calculations. Leveraging parameter-free Hubbard-corrected density functional theory, we obtain a ground state with the band gap and Cu magnetic moment in nearly exact agreement with experiments. This enables a quantitative characterization of $e$-ph interactions. Our calculations reveal two classes of longitudinal optical (LO) phonons with strong $e$-ph coupling to hole states. These modes consist of bond stretching and bond bending in the Cu-O plane as well as vibrations of apical O atoms. The hole spectral functions, obtained with a cumulant method that can capture strong $e$-ph coupling, exhibit broad quasiparticle peaks with a small spectral weight ( $Z\approx 0.25$) and pronounced LO-phonon sidebands characteristic of polaron effects. Our calculations predict features observed in photoemission spectra, including a 40-meV peak in the $e$-ph coupling distribution function not explained by existing models. These results show that the universal strong $e$-ph coupling found experimentally in doped lanthanum cuprates is also present in the parent compound, and elucidate its microscopic origin. 

Abstract Polymer membranes have been used extensively for Angstrom-scale separation of solutes and molecules. However, the pore size of most polymer membranes has been considered an intrinsic membrane property that cannot be adjusted in operation by applied stimuli. In this work, we show that the pore size of an electrically conductive polyamide membrane can be modulated by an applied voltage in the presence of electrolyte via a mechanism called electrically induced osmotic swelling. Under applied voltage, the highly charged polyamide layer concentrates counter ions in the polymer network via Donnan equilibrium and creates a sizeable osmotic pressure to enlarge the free volume and the effective pore size. The relation between membrane potential and pore size can be quantitatively described using the extended Flory-Rehner theory with Donnan equilibrium. The ability to regulate pore size via applied voltage enables operando modulation of precise molecular separation in-situ. This study demonstrates the amazing capability of electro-regulation of membrane pore size at the Angstrom scale and unveils an important but previously overlooked mechanism of membrane-water-solute interactions.