Report

FIRST PRINCIPLES CALCULATION OF OFF-NORMAL LEEM REFLECTIVITY SPECTRA OF FEW LAYER GRAPHENE Collaborators: Jiebing Sun - Physics, MSU Karsten Pohl - Physics, UNH Jian-Ming Tang - Physics, UNH John McClain, Ph.D. Candidate Integrated Applied Mathematics Program University of New Hampshire Acknowledgements: Jim Hannon - IBM Watson Research Center APS March Meeting: March 3, 2014 Outline Motivation LEEM: very low-energy I-V curves Need for new I-V analysis Method Density Functional Theory, wave-matching Results Normal Incidence Free-standing FLG General Angle of Incidence FLG Low-energy Electron Microscopy Illuminate areas down to 8nm x 8nm Record I-V curve for specular/diffracted beam http://en.wikipedia.org/wiki/ LEEM Down to very low energies Hibino, et al. Phys. Rev. B 77 (2008) Compare to curves from model to determine structural details Berger, et al. J. Phys. Chem. 108 (2004) I-V Curve Calculations Most methods restricted to muffin tin scattering potentials (Pendry 1974, Van Hove 1986) We’ve developed a first principles method Rely on fitting parameters Are not valid at very low energies Using self-consistent potentials More efficient than other first principles methods Other first principles approaches Flege, Meyer, Falta, and Krasovskii PRB 84 (2011), Self-limited oxide formation in Ni(111) oxidation. Feenstra, et al. PRB 87 (2013), Low-energy electron reflectivity from graphene. Scattering via Wave Matching with DFT Our method: Find self-consistent potential and scattering states with DFT packages for solids Introduces a supercell Match incoming and outgoing plane waves to Bloch solutions at interfaces Quantum ESPRESSO (plane wave basis) Scattering via Wave Matching with DFT Our method: Find self-consistent potential and scattering states with DFT packages for solids Introduce a supercell Match incoming and outgoing plane waves to Bloch solutions at interfaces Quantum ESPRESSO (plane wave basis) Specular reflection only; lowest energy range Scattering via Wave Matching with DFT Our method: Find self-consistent potential and scattering states with DFT packages for solids Introduce a supercell Match incoming and outgoing plane waves to Bloch solutions at interfaces Quantum ESPRESSO (plane wave basis) Specular reflection only; lowest energy range Focus on Free-Standing Graphene Free-standing FLG Reflectivity: Normal Incidence Experimental FLG on SiC Calculated Free-standing FLG Hibino, et al. Phys. Rev. B 77 (2008) McClain, et al. arXiv :1311.2917 (2013) Also, agrees with findings of Feenstra, et al. PRB 87 (2013) Free-standing FLG Reflectivity: Normal Incidence Hibino, et al. e-J. Surf. Sci. Nanotech. Vol. 6 (2008) Oscillations at 15-20 eV likely killed by damping/inelastic effects Quantum Interference oscillations align with dispersive bands Reflection peaks align with bulk band gaps: ~10 eV, 25 eV, & 35 eV Off-Normal Incidence Why? More information for given energy range New distinguishing features Continue to consider only specular reflection ‘ In-plane k-vector vs Angle of Incidence Fixed Angle ≈ 5° Fixed k// M Г K M Г Bauer, Carl A. et al. arXiv:1309.0914 K General Incidence Reflectivity Similar oscillations With energy shifts 3-Way Splitting of Peak New layerdependent oscillations Near K M Г K M Г K Band Gaps and Spectra Peaks Just like we did for normal incidence, we can match spectra peaks to band gaps. But now we have a band structure for each k//. Adapted from dissertation of Tesfaye Alayew General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K General Incidence Reflectivity M Г K CONCLUSIONS Wave matching approach is able to produce reflection coefficients for specular reflection for general angles of incidence. Calculated reflectivities match experimental results for normal incidence Free standing graphene matches FLG on SiC Off-normal Scattering Similar quantum-interference oscillations with energy shifts Peak splitting; New layer-dependent oscillations Connection between reflectivity and bulk graphite band gaps persists John McClain Overcoming Artificial Energy Gaps Different energy ranges accessed using different supercell sizes 4 supercells cover all but narrow regions Difficult to predict which supercell sizes cover which energies