Strain engineering of graphene

The focus of this thesis is on using mechanical strain to tailor the electronic properties of graphene. The first half covers the electro-mechanical coupling for graphene in different configurations, namely a hexagonal Y-junction, various shaped bubbles on different substrates, and with kirigami cuts. For all of these cases, a novel combination of tight-binding electronic structure calculations and molecular dynamics is utilized to demonstrate how mechanical loading and deformation impacts the resulting electronic structure and transport. For the Y-junction, a quasi-uniform pseudo magnetic field induced by strain restricts transport to Landau-level and edge-state-assisted resonant tunneling. For the bubbles, the shape and the nature of the substrate emerge as decisive factors determining the effectiveness of the nanoscale pseudo magnetic field tailoring in graphene. Finally, for the kirigami, it is shown that the yield and fracture strains of graphene, a well-known brittle material, can be enhanced by a factor of more than three using the kirigami structure, while also leading to significant enhancements in the localized pseudo magnetic fields. The second part of the thesis focuses on dissipation mechanisms in graphene nanomechanical resonators. Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, it is shown that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. The relationship between thermalization rate, radius, temperature and prestrain is explored and investigated

Highly Deformable Graphene Kirigami

Graphene's exceptional mechanical properties, including its highest-known stiffness (1 TPa) and strength (100 GPa) have been exploited for various structural applications. However, graphene is also known to be quite brittle, with experimentally-measured tensile fracture strains that do not exceed a few percent. In this work, we introduce the notion of graphene kirigami, where concepts that have been used almost exclusively for macroscale structures are applied to dramatically enhance the stretchability of both zigzag and armchair graphene. Specifically, we show using classical molecular dynamics simulations that the yield and fracture strains of graphene can be enhanced by about a factor of three using kirigami as compared to standard monolayer graphene. This enhanced ductility in graphene should open up interesting opportunities not only mechanically, but also in coupling to graphene's electronic behavior.Comment: 5 pages, 7 figure

FPU physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. We find the thermalization rate $\Gamma$ to be independent of radius and scaling as $\Gamma\sim T^*/\epsilon_{{\rm pre}}^2$, where $T^*$ and $\epsilon_{{\rm pre}}$ are effective resonator temperature and prestrain

Highly Stretchable MoS2_2 Kirigami

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS$_{2}$ kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key finding is significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS$_{2}$ nanoribbons. These results in conjunction with recent results on graphene suggest that the kirigami approach may be a generally useful one for enhancing the ductility of two-dimensional nanomaterials

Graphene kirigami as a platform for stretchable and tunable quantum dot arrays

The quantum transport properties of a graphene kirigami similar to those studied in recent experiments are calculated in the regime of elastic, reversible deformations. Our results show that, at low electronic densities, the conductance profile of such structures replicates that of a system of coupled quantum dots, characterized by a sequence of minibands and stop-gaps. The conductance and I-V curves have different characteristics in the distinct stages of elastic deformation that characterize the elongation of these structures. Notably, the effective coupling between localized states is strongly reduced in the small elongation stage, whereas in the large elongation regime the development of strong, localized pseudomagnetic field barriers can reinforce the coupling and reestablish resonant tunneling across the kirigami. This provides an interesting example of interplay between geometry and pseudomagnetic field-induced confinement. The alternating miniband and stop-gaps in the transmission lead to I-V characteristics with negative differential conductance in well defined energy/doping ranges. These effects should be stable in a realistic scenario that includes edge roughness and Coulomb interactions, as these are expected to further promote localization of states at low energies in narrow segments of graphene nanostructures.Comment: 10 pages, 10 figure