Spectral Momentum Density from Graphite from Spectroscopy: Comparison with First Principles Calculations

Authors

Chao Gao
A. L. Ritter
John R. Dennison, Utah State UniversityFollow
N. A. Holzwarth

Document Type

Article

Journal/Book Title/Conference

Physical Review B

Volume

37

Issue

8

Publisher

American Physical Society

Publication Date

3-1-1988

First Page

3914

Last Page

3923

Abstract

We have measured the spectral momentum density ρ(E,q) of graphite by (e,2e) spectroscopy for momentum parallel and perpendicular to the crystal c axis. In the independent-electron approximation, ρ(E,q)=Σ_G‖U_k(G)‖² δ(q-k-G)δ(E-E(k)) where the one-electron wave function is Ψ_k(r)=e^ik⋅rΣ_GU_k(G)e^iG⋅r) and G is a reciprocal-lattice vector. The measurements covered a range of momentum parallel to the c axis equal to 0≤‖q‖≤1.84 Å^-1 and a range of momentum perpendicular to the c axis equal to 0≤‖q‖≤2.35 Å^-1. The energy range spanned the valence band of graphite from 4.4 eV above the Fermi energy to 27.6 eV below the Fermi energy. The momentum resolution was 0.47 and 0.73 Å^-1 (full width at half maximum) for momentum parallel and perpendicular to the c axis, respectively. The energy resolution was 8.6 eV. The maximum coincidence rate was ∼0.02 counts/sec. The band structure E(k) and spectral density ‖U_k(G)‖² have been calculated from first principles using a self-consistent density-functional theory in the local-density approximation with a mixed-basis pseudopotential technique. The agreement within experimental uncertainties between measurement and theory is excellent.

Comments

http://link.aps.org/doi/10.1103/PhysRevB.37.3914

Published by the American Physical Society in Physical Review B. Publisher PDF is available for download through the link above.

Recommended Citation

Chao Gao, A. L. Ritter, JR Dennison and N. A. W. Holzwarth, "Spectral Momentum Density from Graphite from (e,2e)Spectroscopy: Comparison with First Principles Calculations," Phys. Rev. B, 37, 3914-3923 (1988).