Low-Energy Electron Reflectivity of Two-dimensional Materials

ORAL

Abstract

Based on density functional theory, we develop a self-consistent description of low-energy electron reflectivity spectra of both free-standing thin films and thin films on substrates. Our approach utilizes wavefunctions for a thin multilayer slab together with wavefunctions of bulk substrate, if any [1, 2]. Our results compare well with experimental data for graphene on SiC and on various metallic substrates. From our modelling, we find that the minima of reflectivity arise from states with wavefunctions localized \textit{between}the graphene layers, rather than on the layers as previously suggested [3]. The energies of the reflectivity minima are sensitive to the layer spacing between graphene and substrate; thus our method also provides a way to determine the layer spacing by comparing with the experimental reflectivity curve. A simple method is also proposed for inclusion of inelastic effects (electron absorption) in the computed reflectivity spectra, and is applied to graphene and hexagonal boron nitride (h-BN) on various substrates [4]. \\[4pt] [1] R. M. Feenstra, N. Srivastave, Q. Gao, M. Widom, G. Diaconescu, T. Ohta, G. L. Kellogg, J. T. Robinson and I. V. Vlassiouk, Phys. Rev. B 87, 041406(R) (2013). [2] N. Srivastava, Q. Gao, M. Widom, R. M. Feenstra, S. Nie, K. F. McCarty and I. V. Vlassiouk, Phys. Rev. B 87, 245414 (2013). [3] H. Hibino, H. Kageshima, F. Maeda, M. Nagase, Y. Kobayashi, and H. Yamaguchi, Phys. Rev. B 77, 075413 (2008). [4] Q. Gao, P. C. Mende, M. Widom, and R. M. Feenstra, submitted (2014).

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Authors

  • Qin Gao

    Carnegie Mellon University

  • Eva Andrei

    National Center for Biotechnology Information, NIH, Pennsylvania State Univ, Department of Physics, Temple University, CAS Key Laboratory of Materials for Energy Conversion, Shanghai Institute of Ceramics, Chinese Academy of Science, Department of Physics, Boise State University, National Synchrotron Light Source, Brookhaven National Laboratory, York Univ, Erciyes Univ, Chinese Academy of Sciences Hefei, Pennsylvania State Univ and USTC, Heidelberg Institute for Theoretical Studies, MIT, Harvard, Penn State University, Canadian Institute for Theoretical Astrophysics, The Pennsylvania State University, University Park, Pennsylvania State University, Penn State, Department of Physics, Penn State University, University Park, USA, National Institute for Material Science, 1-1 Namiki, Tsukuba, Japan, Carnegie Mellon University, IPICYT, Mexico, Shinshu University, Japan, Universidad Carlos III de Madrid, Spain, Universidade de Sao Paulo, Brazil, Tsinghua University, China, American Physical Society, Appalachian State University, West Chester Univ, Lehigh University, Drew University, University of Balearics Islands, Roanoke College, NIST, Tulane Univ, Shanghai Jiao Tong Univ, Zhejiang Univ, National Institute of Standards and Technology, Department of Physics, The Pennsylvania State University, Department of Electrical Engineering, The Pennsylvania State University, Department of Materials Science and Engineering, the Pennsylvania State University, Hefei National Laboratory for Physical Sciences at Microscale, Department of Physics, University of Science and Technology of China, International Center for Quantum Materials, Peking University, Villanova University, West Virginia University, Institut Lumiere Matiere, PSU, Oak Ridge National Laboratory, Towson Univ, CINVESTAV-Queretaro, Prince George Community College, Howard University, Towson University, The Pennsylvania State University, Hokkaido Univ, Cinvestav-Unidad Queretaro, Queretaro-76230, Mexico, Lawrence Livermore National Laboratory, Osaka University, Penn State Univ, Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, Department of Anthropology, The Pennsylvania State University, ILM Universit\'{e} Lyon 1, Moravian College, Bloomsburg Univ, Universit\"at Bielefeld, Syracuse University, Alabama A\&M University, Indiana University of PA, University of Denver, IUP, University of Nebraska, University of Science and Technology of China, Seoul National University, Soochow University China, US Army Research Laboratory, Drexel University, University of Stuttgart, Youngstown State University, University of Surrey, Department of Chemistry and Biochemistry, University of Maryland, College Park, Department of Mathematics, West Virginia University, University of Delaware, Physics Department, The Pennsylvania State University, 104 Davey Lab, University Park, PA, 16802, USA, Department of Physics and Astronomy, West Virginia University, McMaster University, University of Toronto, The University of Texas at Austin, Army Research Lab, Adelphi MD, University of Connecticut, Notre Dame, University of Maryland, Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Rutgers University

  • Eva Andrei

    National Center for Biotechnology Information, NIH, Pennsylvania State Univ, Department of Physics, Temple University, CAS Key Laboratory of Materials for Energy Conversion, Shanghai Institute of Ceramics, Chinese Academy of Science, Department of Physics, Boise State University, National Synchrotron Light Source, Brookhaven National Laboratory, York Univ, Erciyes Univ, Chinese Academy of Sciences Hefei, Pennsylvania State Univ and USTC, Heidelberg Institute for Theoretical Studies, MIT, Harvard, Penn State University, Canadian Institute for Theoretical Astrophysics, The Pennsylvania State University, University Park, Pennsylvania State University, Penn State, Department of Physics, Penn State University, University Park, USA, National Institute for Material Science, 1-1 Namiki, Tsukuba, Japan, Carnegie Mellon University, IPICYT, Mexico, Shinshu University, Japan, Universidad Carlos III de Madrid, Spain, Universidade de Sao Paulo, Brazil, Tsinghua University, China, American Physical Society, Appalachian State University, West Chester Univ, Lehigh University, Drew University, University of Balearics Islands, Roanoke College, NIST, Tulane Univ, Shanghai Jiao Tong Univ, Zhejiang Univ, National Institute of Standards and Technology, Department of Physics, The Pennsylvania State University, Department of Electrical Engineering, The Pennsylvania State University, Department of Materials Science and Engineering, the Pennsylvania State University, Hefei National Laboratory for Physical Sciences at Microscale, Department of Physics, University of Science and Technology of China, International Center for Quantum Materials, Peking University, Villanova University, West Virginia University, Institut Lumiere Matiere, PSU, Oak Ridge National Laboratory, Towson Univ, CINVESTAV-Queretaro, Prince George Community College, Howard University, Towson University, The Pennsylvania State University, Hokkaido Univ, Cinvestav-Unidad Queretaro, Queretaro-76230, Mexico, Lawrence Livermore National Laboratory, Osaka University, Penn State Univ, Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, Department of Anthropology, The Pennsylvania State University, ILM Universit\'{e} Lyon 1, Moravian College, Bloomsburg Univ, Universit\"at Bielefeld, Syracuse University, Alabama A\&M University, Indiana University of PA, University of Denver, IUP, University of Nebraska, University of Science and Technology of China, Seoul National University, Soochow University China, US Army Research Laboratory, Drexel University, University of Stuttgart, Youngstown State University, University of Surrey, Department of Chemistry and Biochemistry, University of Maryland, College Park, Department of Mathematics, West Virginia University, University of Delaware, Physics Department, The Pennsylvania State University, 104 Davey Lab, University Park, PA, 16802, USA, Department of Physics and Astronomy, West Virginia University, McMaster University, University of Toronto, The University of Texas at Austin, Army Research Lab, Adelphi MD, University of Connecticut, Notre Dame, University of Maryland, Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Rutgers University

  • Eva Andrei

    National Center for Biotechnology Information, NIH, Pennsylvania State Univ, Department of Physics, Temple University, CAS Key Laboratory of Materials for Energy Conversion, Shanghai Institute of Ceramics, Chinese Academy of Science, Department of Physics, Boise State University, National Synchrotron Light Source, Brookhaven National Laboratory, York Univ, Erciyes Univ, Chinese Academy of Sciences Hefei, Pennsylvania State Univ and USTC, Heidelberg Institute for Theoretical Studies, MIT, Harvard, Penn State University, Canadian Institute for Theoretical Astrophysics, The Pennsylvania State University, University Park, Pennsylvania State University, Penn State, Department of Physics, Penn State University, University Park, USA, National Institute for Material Science, 1-1 Namiki, Tsukuba, Japan, Carnegie Mellon University, IPICYT, Mexico, Shinshu University, Japan, Universidad Carlos III de Madrid, Spain, Universidade de Sao Paulo, Brazil, Tsinghua University, China, American Physical Society, Appalachian State University, West Chester Univ, Lehigh University, Drew University, University of Balearics Islands, Roanoke College, NIST, Tulane Univ, Shanghai Jiao Tong Univ, Zhejiang Univ, National Institute of Standards and Technology, Department of Physics, The Pennsylvania State University, Department of Electrical Engineering, The Pennsylvania State University, Department of Materials Science and Engineering, the Pennsylvania State University, Hefei National Laboratory for Physical Sciences at Microscale, Department of Physics, University of Science and Technology of China, International Center for Quantum Materials, Peking University, Villanova University, West Virginia University, Institut Lumiere Matiere, PSU, Oak Ridge National Laboratory, Towson Univ, CINVESTAV-Queretaro, Prince George Community College, Howard University, Towson University, The Pennsylvania State University, Hokkaido Univ, Cinvestav-Unidad Queretaro, Queretaro-76230, Mexico, Lawrence Livermore National Laboratory, Osaka University, Penn State Univ, Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, Department of Anthropology, The Pennsylvania State University, ILM Universit\'{e} Lyon 1, Moravian College, Bloomsburg Univ, Universit\"at Bielefeld, Syracuse University, Alabama A\&M University, Indiana University of PA, University of Denver, IUP, University of Nebraska, University of Science and Technology of China, Seoul National University, Soochow University China, US Army Research Laboratory, Drexel University, University of Stuttgart, Youngstown State University, University of Surrey, Department of Chemistry and Biochemistry, University of Maryland, College Park, Department of Mathematics, West Virginia University, University of Delaware, Physics Department, The Pennsylvania State University, 104 Davey Lab, University Park, PA, 16802, USA, Department of Physics and Astronomy, West Virginia University, McMaster University, University of Toronto, The University of Texas at Austin, Army Research Lab, Adelphi MD, University of Connecticut, Notre Dame, University of Maryland, Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Rutgers University

  • Eva Andrei

    National Center for Biotechnology Information, NIH, Pennsylvania State Univ, Department of Physics, Temple University, CAS Key Laboratory of Materials for Energy Conversion, Shanghai Institute of Ceramics, Chinese Academy of Science, Department of Physics, Boise State University, National Synchrotron Light Source, Brookhaven National Laboratory, York Univ, Erciyes Univ, Chinese Academy of Sciences Hefei, Pennsylvania State Univ and USTC, Heidelberg Institute for Theoretical Studies, MIT, Harvard, Penn State University, Canadian Institute for Theoretical Astrophysics, The Pennsylvania State University, University Park, Pennsylvania State University, Penn State, Department of Physics, Penn State University, University Park, USA, National Institute for Material Science, 1-1 Namiki, Tsukuba, Japan, Carnegie Mellon University, IPICYT, Mexico, Shinshu University, Japan, Universidad Carlos III de Madrid, Spain, Universidade de Sao Paulo, Brazil, Tsinghua University, China, American Physical Society, Appalachian State University, West Chester Univ, Lehigh University, Drew University, University of Balearics Islands, Roanoke College, NIST, Tulane Univ, Shanghai Jiao Tong Univ, Zhejiang Univ, National Institute of Standards and Technology, Department of Physics, The Pennsylvania State University, Department of Electrical Engineering, The Pennsylvania State University, Department of Materials Science and Engineering, the Pennsylvania State University, Hefei National Laboratory for Physical Sciences at Microscale, Department of Physics, University of Science and Technology of China, International Center for Quantum Materials, Peking University, Villanova University, West Virginia University, Institut Lumiere Matiere, PSU, Oak Ridge National Laboratory, Towson Univ, CINVESTAV-Queretaro, Prince George Community College, Howard University, Towson University, The Pennsylvania State University, Hokkaido Univ, Cinvestav-Unidad Queretaro, Queretaro-76230, Mexico, Lawrence Livermore National Laboratory, Osaka University, Penn State Univ, Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, Department of Anthropology, The Pennsylvania State University, ILM Universit\'{e} Lyon 1, Moravian College, Bloomsburg Univ, Universit\"at Bielefeld, Syracuse University, Alabama A\&M University, Indiana University of PA, University of Denver, IUP, University of Nebraska, University of Science and Technology of China, Seoul National University, Soochow University China, US Army Research Laboratory, Drexel University, University of Stuttgart, Youngstown State University, University of Surrey, Department of Chemistry and Biochemistry, University of Maryland, College Park, Department of Mathematics, West Virginia University, University of Delaware, Physics Department, The Pennsylvania State University, 104 Davey Lab, University Park, PA, 16802, USA, Department of Physics and Astronomy, West Virginia University, McMaster University, University of Toronto, The University of Texas at Austin, Army Research Lab, Adelphi MD, University of Connecticut, Notre Dame, University of Maryland, Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Rutgers University