Zenan Qi

We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additiona...

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.

We investigate the impact of strained nanobubbles on the conductance characteristics of graphene nanoribbons using a combined molecular dynamics - tight-binding simulation scheme. We describe in detail how the conductance, density of states, and current density of zigzag or armchair graphene nanoribbons are modified by the presence of a nanobubble. In particular, we establish that low-energy electrons can be confined in the vicinity or within the nanobubbles by the delicate interplay between the pseudomagnetic field pattern created by the shape of the bubble, mode mixing, and substrate interaction. The coupling between confined evanescent states and propagating modes can be enhanced under different clamping conditions, which translates into Fano resonances in the conductance traces.

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 transm...

We report, based on its variation in electronic transport to coupled tension and shear deformation, a highly sensitive graphene-based strain sensor consisting of an armchair graphene nanoribbon (AGNR) between metallic contacts. As the nominal strain at any direction increases from 2.5 to 10%, the conductance decreases, particularly when the system changes from the electrically neutral region. At finite bias voltage, both the raw conductance and the relative proportion of the conductance depends smoothly on the gate voltage with negligible fluctuations, which is in contrast to that of pristine graphene. Specifically, when the nominal strain is 10% and the angle varies from 0 degree to 90 degree, the relative proportion of the conductance changes from 60 to 90%.

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.

We utilize density functional theory to calculate the edge energy and edge stress for monolayer MoS_2 nanoribbons. In contrast to previous reports for graphene, for both armchair and zigzag chiralities, the edge stresses for MoS_2 nanoribbons are found to be tensile, indicating that their lowest energy configuration is one of compression in which Mo-S bond lengths are shorter than those in a bulk, periodic MoS_2 monolayer. The edge energy and edge stress is found to converge for both chiralities for nanoribbon widths larger than about 1 nm.

We utilize classical molecular dynamics to study the the quality (Q)-factors of monolayer CVD-grown graphene nanoresonators. In particular, we focus on the effects of intrinsic grain boundaries of different orientations, which result from the CVD growth process, on the Q-factors. For a range of misorientations orientation angles that are consistent with those seen experimentally in CVD-grown graphene, i.e. 0^∘ to ∼20^∘, we find that the Q-factors for graphene with intrinsic grain boundaries are 1-2 orders of magnitude smaller than that of pristine monolayer graphene. We find that the Q-factor degradation is strongly influenced by both the symmetry and structure of the 5-7 defect pairs that occur at the grain boundary. Because of this, we also demonstrate that find the Q-factors CVD-grown graphene can be significantly elevated, and approach that of pristine graphene, through application of modest (1

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,...

Thermalization in nonlinear coupled systems is a central concept in statistical mechanics and has been extensively studied theoretically since the pioneering work of Fermi, Pasta and Ulam. Using molecular dynamics and continuum modeling, we show that thermalization due to nonlinear mode coupling limits the quality factor of nanomechanical graphene drums. Mimicking a ring-down setup, the fundamental mode is initially excited. 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.

Analysis of the strain-induced pseudomagnetic fields (PMFs) generated in graphene nanobulges under three different substrate scenarios shows that, in addition to the shape, the graphene-substrate interaction can crucially determine the overall distribution and magnitude of strain and those fields, in and outside the bulge. We utilize a combination of classical molecular dynamics, continuum mechanics, and tight-binding electronic structure calculations as an unbiased means of studying pressure-induced deformations and the resulting PMF in graphene nanobubbles of various geometries. The interplay among substrate aperture geometry, lattice orientation, internal gas pressure, and substrate type is analyzed in view of strain-engineered graphene nanostructures capable of confining and/or guiding electrons at low energies. Except in highly anisotropic geometries, the magnitude of the PMF is generally significant only near the boundaries of the aperture and rapidly decays towards the center...

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS2 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 findings are significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS2 nanoribbons. These results, in conjunction with recent results on graphene, suggest that the kirigami approach may be generally useful for enhancing the ductility of two-dimensional nanomaterials.

We report, based on its variation in electronic transport to coupled tension and shear deformation, a
highly sensitive graphene-based strain sensor consisting of an armchair graphene nanoribbon
(AGNR) between metallic contacts. As the nominal strain at any direction increases from 2.5 to 10%,
the conductance decreases, particularly when the system changes from the electrically neutral region.
At finite bias voltage, both the raw conductance and the relative proportion of the conductance
depend smoothly on the gate voltage with negligible fluctuations, which is in contrast to that of
pristine graphene. Specifically, when the nominal strain is 10% and the angle varies from 0°to 90°, the
relative proportion of the conductance changes from 60 to∼90%.

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 3 using kirigami as compared to standard monolayer graphene. Finally, we demonstrate that this enhanced ductility in graphene may open up interesting opportunities in coupling to graphene's electronic behavior.

Analysis of the strain-induced pseudomagnetic fields generated in graphene nanobulges under three different
substrate scenarios shows that, in addition to the shape, the graphene-substrate interaction can crucially determine
the overall distribution and magnitude of strain and those fields, in and outside the bulge region. We utilize
a combination of classical molecular dynamics, continuum mechanics, and tight-binding electronic structure
calculations as an unbiased means of studying pressure-induced deformations and the resulting pseudomagnetic
field distribution in graphene nanobubbles of various geometries. The geometry is defined by inflating graphene
against a rigid aperture of a specified shape in the substrate. The interplay among substrate aperture geometry,
lattice orientation, internal gas pressure, and substrate type is analyzed in view of the prospect of using strainengineered
graphene nanostructures capable of confining and/or guiding electrons at low energies. Except in
highly anisotropic geometries, the magnitude of the pseudomagnetic field is generally significant only near the
boundaries of the aperture and rapidly decays towards the center of the bubble because under gas pressure at the
scales considered here there is considerable bending at the edges and the central region of the nanobubble displays
nearly isotropic strain. When the deflection conditions lead to sharp bends at the edges of the bubble, curvature
and the tilting of the pz orbitals cannot be ignored and contributes substantially to the total field. The strong and
localized nature of the pseudomagnetic field at the boundaries and its polarity-changing profile can be exploited
as a means of trapping electrons inside the bubble region or of guiding them in channellike geometries defined
by nanoblister edges. However, we establish that slippage of graphene against the substrate is an important factor
in determining the degree of concentration of pseudomagnetic fields in or around the bulge since it can lead to
considerable softening of the strain gradients there. The nature of the substrate emerges thus as a decisive factor
determining the effectiveness of nanoscale pseudomagnetic field tailoring in graphene.

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. 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 Fermi-Pasta-Ulam physics. We find the thermalization rate Γ to be independent of radius and scaling as Γ∼T∗/ε2pre, where T∗ and εpre are effective resonator temperature and prestrain.

We utilize density functional theory to calculate the edge energy and edge stress for monolayer MoS2 nanoribbons. In contrast to previous reports for graphene, for both armchair and zigzag chiralities, the edge stresses for MoS2 nanoribbons are found to be tensile, indicating that their lowest energy configuration is one of compression in which Mo-S bond lengths are shorter than those in a bulk, periodic MoS2 monolayer. The edge energy and edge stress is found to converge for both chiralities for nanoribbon widths larger than about 1 nm.

Realistic relaxed configurations of triaxially strained graphene quantum dots are obtained from unbiased atomistic mechanical simulations. The local electronic structure and quantum transport characteristics of y-junctions based on such dots are studied, revealing that the quasi-uniform pseudomagnetic field induced by strain restricts transport to Landau level- and edge state-assisted resonant tunneling. Valley degeneracy is broken in the presence of an external field, allowing the selective filtering of the valley and chirality of the states assisting in the resonant tunneling. Asymmetric strain conditions can be explored to select the exit channel of the y-junction.

Strain, bending rigidity, and adhesion are interwoven in determining how graphene responds when pulled across a substrate. Using Raman spectroscopy of circular, graphene-sealed microchambers under variable external pressure, we demonstrate that graphene is not firmly anchored to the substrate when pulled. Instead, as the suspended graphene is pushed into the chamber under pressure, the supported graphene outside the microchamber is stretched and slides, pulling in an annulus. Analyzing Raman G band line scans with a continuum model extended to include sliding, we extract the pressure dependent sliding friction between the SiO2 substrate and mono-, bi-, and trilayer graphene. The sliding friction for trilayer graphene is directly proportional to the applied load, but the friction for monolayer and bilayer graphene is inversely proportional to the strain in the graphene, which is in violation of Amontons’ law. We attribute this behavior to the high surface conformation enabled by the low bending rigidity and strong adhesion of few layer graphene.

We utilize classical molecular dynamics to study the quality (Q)-factors of monolayer CVD-grown graphene nanoresonators. In particular, we focus on the effects of intrinsic grain boundaries of different orientations, which result from the CVD growth process, on the Q-factors. For a range of misorientation angles that are consistent with those seen experimentally in CVD-grown graphene, i.e. 0° to [similar]20°, we find that the Q-factors for graphene with intrinsic grain boundaries are 1–2 orders of magnitude smaller than that of pristine monolayer graphene. We find that the Q-factor degradation is strongly influenced by both the symmetry and structure of the 5-7 defect pairs that occur at the grain boundary. Because of this, we also demonstrate that the Q-factors of CVD-grown graphene can be significantly elevated, and approach that of pristine graphene, through application of modest (1%) tensile strain.

Atomistic simulations were utilized to develop fundamental insights regarding the elongation process starting from ultranarrow graphene nanoribbons (GNRs) and resulting in monatomic carbon chains (MACCs). There are three key findings. First, we demonstrate that complete, elongated, and stable MACCs with fracture strains exceeding 100% can be formed from both ultranarrow armchair and zigzag GNRs. Second, we demonstrate that the deformation processes leading to the MACCs have strong chirality dependence. Specifically, armchair GNRs first form DNA-like chains, then develop into monatomic chains by passing through an intermediate configuration in which monatomic chain sections are separated by two-atom attachments. In contrast, zigzag GNRs form rope-ladder-like chains through a process in which the carbon hexagons are first elongated into rectangles; these rectangles eventually coalesce into monatomic chains through a novel triangle?pentagon deformation structure under further tensile deformation. Finally, we show that the width of GNRs plays an important role in the formation of MACCs, and that the ultranarrow GNRs facilitate the formation of full MACCs. The present work should be of considerable interest due to the experimentally demonstrated feasibility of using narrow GNRs to fabricate novel nanoelectronic components based upon monatomic chains of carbon atoms.