GRAPHENE IN BRIEF Dat T Do 9172020 PHY

GRAPHENE IN BRIEF Dat T. Do 9/17/2020 PHY 971 Presentation

OUTLINE • INTRODUCTION – History – Structure – Production – Properties • ELECTRONIC PROPERTIE – Tight binding approach – QHEs • (Promising) Applications 9/17/2020 PHY 971 Presentation

History • 1947: Graphene first used by S. Mouras – Single sheets of graphite – Early descriptions for CNT – Epitaxial graphene – Polycyclic aromatic hydrocarbons • None of above is isolated 9/17/2020 PHY 971 Presentation

Structure 12 Pentagons Bucky Ball Rolling Nanotube d = 0. 142 nm Stacking • Predicted not to exist by Landau and Peierls (1935, 1937)? ? ? 9/17/2020 PHY 971 Presentation Graphite

Growing methods • Drawing: Andre Geim el at, 2004 • Epitaxial grow: Peter W. Sutter at Brookhaven National Laboratory, 2008 • Silicon Carbide Reduction • Hydrazine Reduction: Yang et al, UCLA, 2008 • Chemical vapor deposition: Kim et al, 2009 • Cutting Carbon nanotube: 2009 9/17/2020 PHY 971 Presentation February 2009

Unique Properties • • • Strongest bond High thermal conductivity: 4. 8 x 103. Absorbing 2. 3% of white light Small spin-orbit coupling Spin-polarized edge: Nano-trip zig-zag. Unique Electronic properties 9/17/2020 PHY 971 Presentation

Tight binding approach LCAO + Secular eqn. 9/17/2020 PHY 971 Presentation

Graphene π – Band nearest neighbor 9/17/2020 PHY 971 Presentation

Band Structure Dirac Point • Semi-metal (zerogap) • m* = 0 near point K • Dirac fermion Novoselov et al 2005; Zhang et al 2005 9/17/2020 PHY 971 Presentation vf ~ 106 m/s

Ambipolar electric field effect • μ : 15000 cm 2 V-1 s-1. Weakly Temp. Dependent • Lowest resistivity substance ever. • Minimum conductivity: 4 e 2/h 9/17/2020 PHY 971 Presentation

Quantum Hall Effect σx y = ± 4 e 2/h (N + ½) x 9/17/2020 PHY 971 Presentation

Promising Applications • Single molecule Gas detection • Electronic device, integrating circuit: silicon replacement • Transparent conducting electrode • Psuedo relativistic theory. 9/17/2020 PHY 971 Presentation

“… graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensedmatter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications. ” (A. K. Geim and K. S. Novoselov) 9/17/2020 PHY 971 Presentation