Thermodynamics and Exotic Transport Phenomena in Emerging Materials

Electrons and phonons constitute the most fundamental degrees of freedom in the material world, underpinning the technological applications that have shaped everyday life. This thesis explores the emerging electron and phonon physics in novel materials, demonstrating the failure of many conventional treatments and common approximations. The first part develops the theoretical toolbox for modelling microscopic electron and phonon interactions as well as their transport. Specifically, we introduce a robust and user-friendly program, Pheasy, which has been developed to accurately reconstruct the potential energy surface of crystalline solids via a Taylor expansion of arbitrarily high order. Given force-displacement datasets, the program enables an efficient and precise extraction of interatomic force constants using advanced machine-learning algorithms and further calculates a wide range of harmonic and anharmonic phonon properties.

The second part of this thesis is devoted to address the failure of standard treatments and common approximations in lattice dynamics. We demonstrate that rotational invariance and vanishing stress conditions together protect the quadratic dispersion of acoustic flexural phonons and unambiguously solve the long-standing debate on the physical behavior of long-wavelength bending modes in low-dimensional systems. Our proposed general invariance conditions for lattice dynamics have been extensively validated through a high-throughput two-dimensional (2D) material database, identifying 158 stable 2D materials. In addition, we show that the lowest-order dipole-dipole approximation is inadequate to describe the long-range electrostatic interactions in piezoelectric materials. To tackle with such failure, we extend the lattice-dynamical theory to incorporate high-order multipolar effectsâ quadrupoles and octupoles, which has been made possible thanks to our novel cluster expansion of the charge density response and dielectric screening function up to an arbitrarily high order. With these developments, we further present a new atomistic approach for calculating elastic constants and bending rigidities of crystalline materials, leveraging lattice dynamics and long-wavelength perturbation theory. Particularly, it gives access to the complete four-rank bending rigidity tensor of 2D materials for the first time, establishing a paradigm shift in studying the bending behavior of nanoplates beyond traditional continuum and isotropic approximations.

The third part focuses on the exotic hydrodynamic regime of charge transport, where electrons behave as viscous fluids with the breakdown of Ohm's law. We introduce a unified theory for quasiparticle transport in viscous electron fluids, which allows the simultaneous calculations of electrical resistivity and viscosity, beyond the relaxation time approximation. Due to the spacial locality of screened Coulomb interactions, a physical-based interpolation using maximally localized Wannier fu