Manipulating phonons and electrons in two-dimensional materials

Abstract

Two-dimensional (2D) materials are one or few atoms thick layered materials. The interaction between the layers in their parent three-dimensional material is weak. Therefore, one can stack different 2D materials on top of each other like “Lego”, or one can rotate one of the layers on top of another layer of 2D materials. The ability to controllably “stack” and “twist” is unique to these materials and provides a great platform to manipulate the electronic, vibrational, and optical properties. Experimental evidence of correlated insulating states, superconductivity, ferromagnetism in the case of twisted bilayer graphene at a certain rotation angle has led to a flurry of research activity in understanding the behavior of electrons in these materials. However, two important facets attracted very little attention: effects of twisting on the collective vibration of atoms (i.e. phonons), and structural reconstruction of rigidly twisted moiré lattice. In this thesis, we explore the layer and twist angle dependence of the phonon modes in several 2D materials. We combine membrane theory and molecular dynamics simulations to show that layer breathing modes can be mapped consistently to vibrations of a simple linear chain model. Our study provides a simple and efficient way to probe the interlayer interaction in few layers of 2D materials. The introduction of twist between two layers gives rise to a large scale moiré lattice. We find that the Raman active phonon modes, especially low-frequency shear and layer breathing modes, are quite sensitive to the twist angle. We discover the existence of phason modes (with frequency 1 cm −1 , comparable to acoustic modes) for any nonzero twist, corresponding to an effective translation of the moiré lattice by relative displacement of the constituent layers in a nontrivial way. Our calculations shed new insights into the origin of friction at the nanoscale. An important step in understanding the exotic electronic and optical properties of the moiré lattices is the inclusion of the effects of structural relaxation of the un-relaxed moiré lattices. All the studies conducted on moiré materials to date presume that the moiré lattice constant of the un-relaxed twisted structure remains intact even after relaxation. We explore if novel lattice reconstructions of the moiré lattices are possible and the consequences of such lattice reconstructions on the electronic properties. In the last part of the thesis, in collaboration with experimentalists, we investigate the softening and broadening of the high-frequency phonon modes due to temperature, doping, and twist angle in MoS 2 , a prototypical transition metal dichalcogenide. This thesis has been organized as follows: • In Chapter 1, we describe the motivations behind studying properties of 2D materi- als, focusing on moiré materials. We point out some key experimental and theoretical 1challenges in the field of moiré materials. In the end, we also highlight the issues addressed in this thesis and summarize the key results. • In Chapter 2, we describe the methods adopted in this thesis. We use multiscale simulations to efficiently compute the structural, vibrational, and electronic proper- ties presented in this thesis. All the electronic structure calculations are performed with first-principles density-functional theory (DFT) based calculations. We briefly summarize key concepts behind DFT. We also outline some of the technical aspects of our DFT calculations. All the structure predictions and vibrational properties calculations are performed using molecular dynamics (MD) simulations. We briefly summarize some key concepts of MD simulations. • In Chapter 3, we develop an efficient strategy to compute breathing modes of 2D ma- terials, including the finite temperature anharmonic effects. Relative out-of-plane dis- placements of the constituent layers of 2D materials give rise to unique low-frequency breathing modes. The breathing modes can be used as a direct probe to determine layer thickness using Raman spectroscopy. We compare our calculations with exper- iments and first-principles calculations and find that they are in excellent agreement with each other. • In Chapter 4, we computationally explore the engineering of phonons with the twist angle in TMD bilayers. We establish that the phonons and related properties can be controlled by twisting, and we refer to this engineering as “twistnonics”. The sensitiveness of low-frequency phonon modes with twist angle can be used to monitor structural reconstruction. Moreover, we show that the velocities of the phason modes are quite sensitive to the twist angle, unlike the acoustic modes. Our study reveals the possibility of an intriguing θ-dependent superlubric to pinning behavior and the existence of phason modes in all two-dimensional materials. • In Chapter 5, we demonstrate a dramatic reconstruction of moiré lattices in twisted transition metal dichalcogenides for θ > 58.4 ◦ . Our calculations suggest that the presumption that the moiré lattice constant of the rigidly twisted structure continues to characterize the relaxed structure is not always valid. We also find multiple flat bands both near the valence and conduction band edges in the reconstructed lattice, which can lead to the realization of exotic correlated electronic states. • In Chapter 6, we use several techniques to investigate the temperature, doping, and twist angle dependence of the high-frequency Raman modes in MoS 2 and compare our results directly to the experiments. We compute the temperature dependence of the phonon modes using DFT based calculations incorporating three-phonon processes, and the doping dependence of the modes by explicitly computing electron-phonon coupling matrix elements with DFT. On the other hand, the twist angle dependence of the modes is computed with classical simulations. • In Chapter 7, we summarize and provide some future directions based on the work presented in this thesis.