Interplay of Electrons and Phonons in 2D Materials

Abstract

Since the seminal study by Cao et al. in 2018, that revealed the emergence of superconductivity and correlated insulating behaviour in twisted bilayer graphene (TBG), there has been a surge of exciting discoveries in moiré materials. By manipulating the twist angle between two layers of these systems, the band structures can be adjusted to obtain flat bands, where interaction-driven phenomena become prominent. However, the role of electron-phonon interaction in moiré systems is still not well understood. In this thesis, we have studied electrons, phonons and the role of electron-phonon interactions in moiré materials. The last chapter of the thesis explains the role of electron-phonon coupling in the observed enhancement of resistivity in Au-Ag nanostructures.

The principal obstacle in understanding the electronic structure of moiré systems lies in the large number of atoms within the moiré unit cell. This makes first principle density functional theory (DFT) calculations expensive. In this thesis, we use distance-dependent tight binding parameters to obtain the electronic band structure of TBG. Based on the non-interacting band structure of TBG, we compute the Seebeck coefficient and also explain the origin of charge density waves in presence of an out of plane electric field.

Phonon calculations for these moiré systems are performed using classical force fields, parameterized against first principles calculations. The existing software packages for phonon band structure calculations scale poorly with system size and are restricted to systems containing a few hundred atoms. We present PARPHOM, a massively parallelized package that performs phonon calculations on any moiré system (containing tens of thousands of atoms). Using this package, we compute the phonon modes in twisted bilayer WSe2. We have studied the nature and origin of the splits in the Raman-active G mode spectrum near 0 deg angle of twist in this system. Our results for the splits are in excellent agreement with experimental measurements.

An experimentally accessible approach to investigate the strength of electron-phonon interactions is to measure the phonon lifetimes via Raman spectroscopy. Studies have shown significant enhancement of the linewidth of the Raman-active G mode in TBG near the magic angle, compared to untwisted bilayer graphene and TBG with large angles of twist. We present a computational study of the phonon linewidths in TBG arising from electron-phonon interactions and anharmonic effects. The electronic structure is calculated within the tight binding formalism with electron-electron interactions treated at the Hartree level, and the phonons are calculated using classical force fields. These ingredients are used to compute the phonon linewidths arising due to electron-phonon interactions. Furthermore, anharmonic effects on the linewidths are computed using the mode-projected velocity autocorrelation function from classical molecular dynamics simulations. We predict a moiré potential induced splitting of the G mode, which arises due to contributions from different high symmetry stacking regions. Our findings show that both electron-phonon and anharmonic effects have a significant impact on the linewidth of the Raman-active G mode near the magic angle.

In the final part of the thesis, we explain the experimental observations of enhanced resistivity in nanoclusters of silver (Ag) in gold (Au) matrix by computing the electron-phonon coupling strength. This study is performed using a simple tight binding model with electron-electron interactions included at the Hartree level. By studying a two-dimensional system of Ag embedded in an Au matrix, we show that there is indeed an enhancement of the electron-phonon interactions that stems from strong hybridization between the interface plasmon oscillations of the electric dipoles that form at the Au-Ag interface and the breathing modes of the Ag atoms caged inside the heavier Au matrix.