Session X32: Computational Discovery and Design of Novel Materials XII

Structural modeling of amorphous graphene: a differential-mutation approach

A modified differential-mutation algorithm will be presented that can reliably produce low-lying energy structures of amorphous systems. The algorithm merges a genetic algorithm with a computational cooling procedure. This makes it possible to obtain low-lying energy minima with a very limited population size. The algorithm has been implemented for structural optimization of amorphous graphene, where the individual carbon atoms interact via a classical bond-order potential. It will be shown that the resulting minimum configurations are very close in energy and represent locally different topological structures of the material. The results for the coordination numbers, ring-size distribution and puckering of the amorphous surface will be discussed.   

Graphene under magnetic and generalized strain SU(2) gauge fields

We consider single-layer graphene, submitted to a combination of an external magnetic field, as well as generalized SU(2) gauge fields [1,2] arising from mechanical strain and charge density waves. We obtained analytical solutions for the spectrum, as well as for the eigenstates of the Hamiltonian describing the system. Moreover, we studied electronic transport through a region submitted to this field configuration by a Landauer approach, where the transmission function is obtained as the solution of a two-dimensional scattering problem. References [1] S. Gopalakrishnan, P. Ghaemi, and S. Ryu, Phys. Rev. B 86, 081403 (2012) [2] F. J. Pena and E. Munoz, Phys. Rev. E 91, 052152 (2015)   

Structure of carbon-nanotube-encapsulated nanowires from first principles calculations

The quasi-1D structures formed by the insertion of materials into carbon nanotubes can differ dramatically from bulk phases in their structures and properties. Many of these encapsulated nanowire (ENW) structures have considerable technological potential, in areas such as phase-change memory and gas sensing. However, the structures of ENWs can also bear little resemblance to their bulk forms. We have therefore adapted the \emph{ab initio} random structure search (AIRSS) method for the prediction of the structures of nanowires encapsulated inside carbon nanotubes. The AIRSS method has previously proven itself as a powerful and effective tool in the prediction of both bulk materials [1] and defect complexes [2]. Using AIRSS, we have predicted the structure formed by germanium telluride ENWs as a function of the radius of the encapsulating nanotube. We use simulated TEM imagery to show that our results are consistent with experimental evidence [3].\\ \\$[1]$ M Mayo, KJ Griffith, CJ Pickard, AJ Morris, Chemistry of Materials 28 (7), 2011-2021 \newline [2] AJ Morris, CJ Pickard, RJ Needs, Physical Review B 78 (18), 184102 \newline [3] C Giusca et al., Nano Lett. 13 (9), 4020   

Multiscale modeling of polycrystalline graphene

Defects and grain boundaries greatly influence the properties of graphene but modeling their formation is challenging due to the multiple length and time scales involved. We extend the Phase field crystal (PFC) approach [Elder et al., Phys. Rev. Lett. 88, 245701 (2002)] to quantitative modeling of defected graphene microstructures. We assess four PFC models by studying grain boundary structures and their formation energies. We compare PFC results to density functional theory (DFT) and molecular dynamics (MD). The one-mode PFC model is found to produce realistic defect topologies, whereas the three-mode model predicts quantitatively correct grain boundary energies. [Hirvonen et al., Phys. Rev. B 94, 035414 (2016)] PFC models are able to capture the dynamics of large (poly)crystalline systems on diffusive time scales while retaining atomic resolution. We exploit these multiscale characteristics by demonstrating the preparation of large polycrystalline PFC graphene systems whose sizes and formation time scales are beyond the reach of DFT calculations and MD simulations, respectively. We use these systems as the starting point of MD simulations for investigating the heat and charge transport properties of polycrystalline graphene.   

Strain superlattices in graphene

Superlattices have been widely explored to tailor the electronic properties of two-dimensional electron systems. Previous approaches to create superlattices have been limited to periodic potential modulations, either in the form of electrostatic gating or moir\'{e} heterostructures. Here we present a new strategy to generate superlattices in 2D materials. We deposit these 2D membranes on a periodic array of dielectric nanospheres, and achieve superlattices with periodic strain modulations. We studied the electronic and magneto-transport properties of strained graphene superlattices, and observed salient features of Dirac point cloning and Hofstadter's butterfly. Furthermore, we were able to tune the transport properties by changing the magnitude of strain in the graphene superlattice. This new degree of freedom provides a novel platform both for fundamental studies of 2D electron correlations and for prospective applications in 2D electronic devices.   

Generating and Visualizing Strain and Pseudomagnetic Fields in graphene.

Graphene's remarkable electronic properties are inherent to its 2D honeycomb lattice structure. Its low dimensionality, which allows for rearranging its atoms by an external force, offers the intriguing prospect of band structure engineering by non-chemical means. We report on a technique to generate and characterize strain in a graphene membrane supported on a periodic array of nano-pillars. As the graphene membrane conforms to the substrate it develops an intricate strain field resulting in wrinkles that radiate outwards from the supporting pillars. We utilized the distorted Moire pattern formed by the strained graphene membrane against an hBN substrate to reveal the strain-induced local lattice deformation by scanning tunneling microscopy. Our work shows that the distorted Moire pattern is a very sensitive strain sensor. It acts as a magnifying glass and provides an effective way to visualize the local strain. We further studied the influence of strain on the local electronic structure of graphene by using scanning tunneling spectroscopy. The appearance of a succession of Landau level peaks in the local density of states revealed the presence of strain-induced pseudomagnetic fields.   

Landau levels and scattering resonances due to strained folds in graphene

Effects of strain in graphene can be understood in terms of pseudo-scalar and pseudo-magnetic fields with opposite signs at the K and K’ valleys, that renders distinctive signatures in STM measurements. Here we report studies of graphene with out-of-plane strained fold deformations, naturally occurring when the sample is transferred onto hexagonal boron nitride substrates. STM spectroscopy measurements of local density of states at fixed positions on top of the folded region reveal a finite number of resonant peaks. Energy levels for some of these resonances follow the scaling expected for pseudo-Landau levels, however the origin for several others remains poorly understood. We present results from a theoretical model based on the Dirac equation that incorporates inhomogeneous pseudo-fields. We show that position-dependent fields lead to the existence of resonant scattering states, in addition to bound states, whose energies are comparable to those of pseudo-Landau levels. We show that the parameters of the fold determine the maximum number of observable bound states as well as the energies for the scattering states. These results are in good agreement with observed experimental measurements.   

The 2D Frenkel-Kontorova model of graphene on hexagonal boron nitride

Graphene on hexagonal boron nitride (G/BN) constitutes a 2D realization of the coupled Frenkel-Kontorova model where the lattices of graphene tend to align with the commensuration potential generated by the substrate. We analize the map of free energies in G/BN as a function of lattice constant expansion in graphene and twist angle, and propose that the thermal annealing process will favor an equilibrium configuration with zero twist angle and expanded lattice constant of graphene. The twist-angle dependent energy map suggests that substantial sample rotation will take place during device annealing and that the moire period can expand beyond the ∼15 nm set by the lattice constant mismatch between graphene and BN. The delicate balance of the energetics involved in the adhesion free energy minimization of graphene on hexagonal boron nitride suggests the possibility of using anisotropic strains or curvatures as control knobs to tailor the moire pattern dependent band gap, carrier transport and optical response properties.   

Quantum Simulations of One-Dimensional Nanostructures under Arbitrary Deformations

A powerful technique is discussed for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching.[1] The technique is based on an unconventional control of periodic symmetry[2], which eliminates artifacts due to deformation constraints and quantum finite-size effects and allows transparent electronic-structure analysis. Via density-functional tight-binding implementation, the technique demonstrates nonlinear electromechanical properties in carbon nanotubes and abrupt behavior in the structural yielding of Au$_{\mathrm{7}}$ and Mo$_{\mathrm{6}}$S$_{\mathrm{6}}$ nanowires. The technique drives simulations closer to more realistic modeling of slender one-dimensional nanostructures under experimental conditions. [1] P. Koskinen Phys. Rev. Applied 6, 034014 (2016) [2] P. Koskinen and O. O. Kit Phys. Rev. Lett. 105, 106401 (2010)   

Ab Initio Investigation of Frictional Properties of Graphene on SiC Surfaces

The exact origin and nature of various nanotribological observations on graphene such as dependence of friction on layer thickness, direction and surface morphology are yet to be fully understood. In this talk, we report on the frictional properties of graphene on 4H-SiC\{0001\} surfaces obtained from first principles calculations. We investigate sliding of graphene layers of various thickness along different directions on both the Si- and C-terminated faces including van-der Waals interactions. We observe that upon sliding under certain conditions, the interaction between the surface and graphene layers alternates between van-der Waals and covalent forces which dramatically affects friction. We examine the relation of frictional force to applied normal load, small out-of-plane geometric deformations of graphene and electronic structure of the systems.   

Direct experimental evidence of $\pi $ magnetism of a single atomic vacancy in graphene

The pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism. Theoretically, the $\pi $ magnetism induced by the monovacancy in graphene is characterizing of two spin-split density-of-states (DOS) peaks close to the Dirac point. Since its prediction, many experiments attempt to study this $\pi $ magnetism in graphene, whereas, only a notable resonance peak has been observed around the atomic defects, leaving the $\pi $ magnetism experimentally so elusive. Here, we report a direct experimental evidence of the $\pi $ magnetism by using scanning tunneling microscope. We demonstrate that the localized state of the atomic defects is split into two DOS peaks with energy separations of several tens meV. Strong magnetic fields further increase the energy separations of the two spin-polarized peaks and lead to a Zeeman-like splitting. Unexpectedly, the effective g-factor around the atomic defect is measured to be about 40, which is about twenty times larger than the g-factor for electron spins.   

Fully \textit{ab initio} calculation of the resonant one-phonon Raman intensity of graphene

We developed a fully \textit{ab initio}, many-body perturbation theory approach for the calculation of resonant, one-phonon Raman spectra. Our general approach is applicable to any material and here we present its application to the case of graphene. Our diagrammatic, first-principles approach allows us to go beyond and improve on an earlier theoretical study by Basko [1], which relied on an analytical calculation in certain limits. We investigate the dependence of the $G$ peak intensity on both the excitation energy and Fermi level. Furthermore, our method allows us to identify the relevant electronic quantum pathways and to demonstrate the importance of the contributions from non-resonant electronic transitions. We also applied our approach to the calculation of the resonant one-phonon Raman spectrum of MoS$_{\mathrm{2}}$, with our results being in good agreement with experimental data. Ref.: [1] Basko, D. M. \textit{New. J. Phys.} \textbf{11,} 095011 (2009)   

$\pi$-orbital theory for fractal models of bond-diluted graphene

Fractal structures are glassy in the sense that detailed site environments are mostly different for different lattice sites. In view of recent interest in graphene and related carbon structures, we explore electronic properties in simple H\"uckel $\pi$-orbital theory for several fractal lattices, including one with a three-piece generator based on triphenylene, and one with a seven-piece generator based on coronene. A transfer matrix renormalization method applied to a pivotal subset of the Green functions gives exact recursions. From these we study properties including local DOS and Kubo-Greenwood conductance. The Green function renormalization recursions comprise a discrete dynamical system of iterated, rational functions. In some cases these recursions admit Lie groups and so reduce to simple form. The reduction method and some model properties are presented.   

Tuning the Hofstadter butterfly in graphene with interlayer separation

The electronic properties of many van der Waals (vdW) heterostructures depend critically on the strength of interactions between the constituent layers. While little work has been done to tune the interlayer separation in vdW heterostructures, this may act as an important new experimental knob for controlling the overall device properties. Aligned- or nearly-aligned graphene on boron nitride represents a particularly interesting case study for the importance of interlayer interactions, as a long wavelength moir\'{e} pattern emerges resulting in a sizable graphene band gap at zero magnetic field, and the Hofstadter butterfly magnetotransport at high field. We demonstrate global control over the interlayer separation in these devices by applying hydrostatic pressure up to 2.5 GPa in a piston cylinder cell. We find that by compressing the graphene towards the boron nitride substrate, pressure both enhances the zero-field graphene band gap by as much as 40{\%} and results in a number of subtle changes in the magnetotransport response.