Coupling of deformation and electronic properties in two-dimensional materials

Rakib, Tawfiqur

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https://hdl.handle.net/2142/121957 Copy

Description

Title

Coupling of deformation and electronic properties in two-dimensional materials

Author(s)

Rakib, Tawfiqur

Issue Date

2023-10-16

Director of Research (if dissertation) or Advisor (if thesis)

• Johnson, Harley T.
• Ertekin, Elif

Doctoral Committee Chair(s)

Johnson, Harley T.

Committee Member(s)

• Zande, Arend van der
• Huang, Pinshane
• Admal, Nikhil Chandra
• Pochet, Pascal

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• 2D materials
• Deformation
• Twisted bilayer graphene
• Helical dislocation
• Breathing
• Bending
• Graphene/BN heterostructure
• Flat bands
• Ferroelectric
• Polarization

Abstract

Two-dimensional (2D) materials offer a unique platform for studying the coupling between deformation and electronic properties due to their distinct mechanical and highly tunable electronic properties. As 2D materials have low bending stiffness compared to their high in-plane stiffness, they enable 3D deformation through bending, rippling, and crumpling. Isolated 2D materials can be assembled into multilayer van der Waals (vdW) heterostructures that feature moiré patterns if the constituent 2D material layers are stacked in an incommensurable way. These layers are weakly bonded to each other by van der Waals interactions, allowing interlayer sliding and rotation. Moiré patterns emerge due to the rotation between the layers and the period of the moiré superlattice can be tuned by controlling the rotation or strain between the layers. This creates an exciting possibility of tuning the electronic properties of 2D materials by rotating or straining the 2D material layers relative to each other. This tunability platform leads to the formation of flat bands in twisted bilayer graphene (tBLG) at a specific angle of 1.08◦, opening the door to unconventional superconductivity and correlated states. Finally, the discovery of unconventional superconductivity at the "magic" angle in twisted bilayer graphene (tBLG) has stirred a lot of interest in the scientific community. In this doctoral thesis, I discuss a detailed in- vestigation of the deformation mechanisms in 2D materials and elucidate the impact of deformation on the electronic properties of the 2D materials. In twisted bilayer graphene, the rigid rotation between individual graphene layers provides an approximate description of the bilayer symmetry. The interplay between the interlayer van der Waals (vdW) interaction energy and the intralayer elastic energy causes a structural relaxation in tBLG that favors the regions of commensurability. The effect of such relaxation in the low twist-angle regime of tBLG on the charge density field remains unexplored, owing to the huge computational cost associated with the electronic structure calculation of a tBLG supercell, containing tens of thousands of atoms. In the first investigation, I develop a computationally efficient framework for an approximate description of the charge density symmetry in low twist angle tBLG that explores the effect of structural relaxation on the electronic structure. This framework is based on a Fourier representation of the moiré pattern in tBLG that reveals high intensity Bragg peaks in the diffraction pattern. The in-plane structural relaxation also leads to the appearance of low intensity satellite peaks. The framework incorporates these satellite peaks which reveals a transformation of symmetry in the charge density distribution from high to low twist angle tBLG. The second study focuses on the out-of-plane deformation or corrugation of tBLG, uncovering a slip-induced helical dislocation network that emerges in tBLG with large corrugation. Atomistic calculations highlight two distinct deformation modes: a breathing mode with small corrugation and a bending mode with one order larger corrugation magnitude compared to the breathing mode. The analysis reveals that bending mode deformation is more stable at low twist angles, as the energy savings due to interface energy exceeds the energy penalty due to the strain energy caused by the large out-of-plane deformation. This work provides a detailed picture of a helical dislocation structure in tBLG and establishes a direct connection between dislocation and deformation, emphasizing the importance of understanding dislocation mechanics in 2D materials. The third investigation investigates the existence of bending mode corrugation in tBLG in the presence of a substrate and finds that bending mode corrugation magnitude is suppressed due to substrate adhesion, but is still larger than that of breathing mode tBLG. The tBLG in the bending mode demonstrates partially filled states of the flat band structure, accompanied by a broken symmetry in the magic-angle regime. The distinction between low and high corrugation can also explain the observed evolution of the vibrational spectra of tBLG as a function of twist angle. The focus of this project is to study the effect of out-of-plane deformation on the electronic properties of twisted bilayer graphene. In the fourth investigation, I study deformation of graphene in the graphene/BN (G/BN) heterostructures. Due to the low bending modulus of 2D materials, the in-plane strain applied to create the G/BN moiré supercell is accommodated by out-of-plane deformation. Therefore, the corrugation magnitude in graphene changes as a function of the applied strain. Moreover, tight binding calculations demonstrate that the bandwidth of the bands near the Fermi level is tunable with corrugation. As the corrugation magnitude increases, the bandwidth of the bands near the Fermi level decreases, showing flat band formation. This study utilizes corrugation in graphene to develop an alternate path to flat bands and correlated states in graphene. The last study focuses on electromechanical coupling in ferroelectric α-In2Se3 membranes by bending the material. The theoretical investigation and atomic-resolution measurements elucidate the bending mechanism in α-In2Se3, revealing the emergence of distinct structural features – arcs and kinks – and their impact on the electrical polarization. Kink formation in α-In2Se3 is accompanied by a structural transformation that introduces ferroelectric domain walls. A critical bending angle is identified above which kink formation is more favorable in α-In2Se3. Lastly, transferring α-In2Se3 onto trenched substrates, kink-formation is designed to induce polarization switching at specific locations to demonstrate control over polarization. This work advances our understanding of the intricate coupling between electrical polarization and mechanical deformation, opening avenues for nanoscale domain manipulation in ferroelectric materials. In summary, this thesis uncovers a spectrum of phenomena in 2D materials, specifically graphene and ferroelectric α-In2Se3, spanning electronic, structural, and electromechanical realms. The collective insights presented in this thesis offer valuable contributions to the field of two-dimensional materials, enriching our comprehension of their behavior and potential applications.

Graduation Semester

2023-12

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Tawfiqur Rakib

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