Interfaces between liquids and two-dimensional materials are central to energy storage, nanofluidics, and electrochemistry. They are nevertheless often described by assuming that the liquid affects electrons in the solid only through static dielectric screening. This approximation neglects the thermal charge fluctuations of polar liquids, which can couple to low-energy electronic excitations.

In this thesis, we develop a multiscale framework for describing dynamical screening and electronic correlations at liquid--two-dimensional-material interfaces. The spatial response of the liquid is obtained from molecular dynamics, while its frequency dependence is determined from experimental dielectric data. These ingredients are combined with electronic-structure calculations, Wannier orbitals, and constrained random phase approximation screening to construct the non-local and retarded interaction $U(\mathbf{q},\omega)$. The correlated problem is then treated using dynamical mean-field theory (DMFT), together with a continuous-time quantum impurity solver and a Bethe--Salpeter reconstruction of the charge response.

Within the random phase approximation, the liquid mainly softens the plasmon dispersion and produces weak hybrid liquid--electron modes. Different physics emerges when local correlations and vertex corrections are included. At half-filling, water screens the local repulsion and shifts the Mott transition. Away from half-filling, it produces a pronounced, nearly dispersionless quasielastic peak in the charge susceptibility. This mode has no sharp counterpart in the single-particle spectral function and corresponds to a localized collective excitation, which we identify as a \emph{hydropolaron}: an electron partially localized in the polarization cloud that it induces in the liquid.

The local-interaction model exhibits Fermi-liquid, polaronic-metal, Mott-insulating, and bipolaronic regimes. The hydropolaron peak narrows exponentially with increasing liquid--electron coupling, showing that the slow charge dynamics arise from thermally activated Marcus-type hopping. Hydropolaron formation is favored by a narrow electronic band, a liquid with high permittivity, a small distance to the first liquid layer, and localized Wannier orbitals. Non-local interactions strongly suppress this self-localization.

Material-specific calculations show that water has little effect on the charge response of NbSe$_2$, whereas doped Nb$_3$Br$_8$ exhibits signatures of transient electron solvation. Moiré materials emerge as promising platforms. These results demonstrate that an interfacial liquid is not merely a passive dielectric environment: its charge fluctuations can reorganize the collective dynamics of strongly correlated electrons and provide a route for controlling electronic properties, quantum friction, and electrochemical processes at solid--liquid interfaces.