The influence of quantum geometry on the phase boundary and collective excitations of electron liquids and crystals

Abstract

Recent experiments on multilayer graphene systems have reinvigorated the study of electron crystallization, now with the inclusion of quantum geometry. In this work, we apply time-dependent Hartree-Fock (TDHF) to the $\lambda$-jellium model to analyze the impact that quantum geometry has on the electronic liquid--crystal phase diagram and how it modifies the collective modes and responses of the liquid and crystal phases. In agreement with recent results utilizing neural quantum states, we find that quantum geometry favours electron crystallization, shifting the transition to higher densities. We also study the instabilities revealed by TDHF in the Fermi liquid ground state at low densities, providing insight into the fluctuations driving the crystallization transition. We further find that quantum geometry reduces the dispersion of the plasmon mode and suppresses Friedel oscillations deep in the liquid phase. Resolving the density response in terms of individual orbitals, we find that this suppression is caused by spectral weight transfer to an out-of-phase inter-orbital mode. Finally, we show that an analogous mode that emerges in the crystal phase corresponds to the breathing mode of an emergent real-space pseudospin skyrmion lattice.