Optical Properties Of Graphene

Rolf Binder

• Publisher: WSPC
• Year: 2016
• ISBN:
  9789813148765
• Topic: Scienze fisiche
• Subtopic: Ottica e luce

This book provides a comprehensive state-of-the-art overview of the optical properties of graphene. During the past decade, graphene, the most ideal and thinnest of all two-dimensional materials, has become one of the most widely studied materials. Its unique properties hold great promise to revolutionize many electronic, optical and opto-electronic devices. The book contains an introductory tutorial and 14 chapters written by experts in areas ranging from fundamental quantum mechanical properties to opto-electronic device applications of graphene.

Contents: Introductory Tutorial (Rolf Binder and Nai-Hang Kwong);Microscopic Theory for the Groundstate and Linear Optical Response of Novel Two-Dimensional Materials with Hexagonal Symmetry (Tineke Stroucken & Stephan W Koch);Raman Spectroscopy of Graphene (Sven Reichardt & Ludger Wirtz);Microscopic View on the Ultrafast Carrier Dynamics in Graphene (E Malic, T Winzer, F Kadi & A Knorr);Theory of Optical Nonlinearities in Graphene (Jin Luo Cheng, Nathalie Vermeulen & John E Sipe);Nonlinear Optical Experiments on Graphene (Hui Zhao);Optical Response of Graphene under Intense Terahertz Fields (J Zhou and M W Wu);Nonlinear Terahertz Spectroscopy on Multilayer Graphene (Michael Woerner, Thomas Elsaesser & Klaus Reimann);Ultrafast Manipulation of Terahertz Waves using Graphene Metamaterials (Chihun In & Hyunyong Choi);Spectroscopy of Graphene at the Saddle Point (Daniela Wolf, Dong-Hun Chae, Tobias Utika, Patrick Herlinger, Jurgen Smet, Harald Giessen & Markus Lippitz);Nonlinear Saddle Point Spectroscopy and Electron-Phonon Interaction in Graphene (Rolf Binder, Adam T Roberts, Nai-Hang Kwong, Arvinder Sandhu & Henry O Everitt);Femtosecond Pulse Generation with Voltage-Controlled Graphene Saturable Absorbers (Işinsu Baylam, Sarper Özharar, Nurbek Kakenov, Coşkun Kocabaş & Alphan Sennaroǧlu);Graphene-Based Optical Modulators (Sinan Balci & Coskun Kocabas);The Potential of Graphene as a Transparent Electrode (Wee Shing KOH, Wee Kee PHUA & Wei Peng GOH);
Readership: Advanced undergraduate, professionals and researchers in materials science.Graphene, Two-Dimensional Materials, Optics, Semimetals

• There is no other book with a focus on the optical properties of graphene, in spite of the large interest by researchers worldwide graphene and other two-dimensional materials and possible future device applications

Part 1

Linear Optical Response and Raman Spectroscopy

Chapter 2

Microscopic Theory for the Groundstate and Linear Optical Response of Novel Two-Dimensional Materials with Hexagonal Symmetry

Tineke Stroucken* and Stephan W. Koch

Department of Physics and Scientific Center for Material Sciences, Philipps
University Marburg, Renthof 5, 35032 Marburg/Germany
*[email protected] de

This chapter summarizes recent theoretical work to determine the groundstate and the linear optical properties of quasi-two-dimensional materials with hexagonal lattice symmetry. The main ingredients of the fully relativistic tight-binding model analysis for graphene and transition metal dichalcogenites are summarized. Dirac-Bloch equations are derived and solved in the regimes of weak and strong Coulomb coupling. Whereas single-layer graphene always seems to be in the weak Coulomb-coupling regime, realistic parameter analysis of WSe₂ and WS₂ identifies these materials to be in the regime of strong Coulomb coupling. Consequently, they are predicted to exhibit an excitonic insulator groundstate with optically active p-excitons. On this basis, a unified understanding and excellent agreement of the theoretical predictions with a large variety of systematic experiments is obtained.

2.1Introduction

Novel 2D materials have emerged as a new class of material systems whose thickness is just a single unit cell. The firstly discovered –and most famous–representative of this material class is graphene whose remarkable properties – it is flexible, transparent, stronger than steel, more conductive than copper–have been celebrated since is its first isolation by Novosolov and Geim 2004. [Novoselov et al. (2004)] Soon after, other novel 2D materials could be fabricated, among them transition metal dichalcogenides (TMDCs). Similar to graphene, TMDCs are layered materials with strong in-plane bonding and weak out-of-plane interactions enabling exfoliation into two-dimensional layers. Within the layers, the atoms are arranged in a honeycomb lattice with hexagonal symmetry.

The reduction of the thickness down to a monolayer can alter the physical properties drastically, making these material systems interesting both for fundamental material science and technological applications. Because of its unique properties, graphene has been proposed as a candidate for many applications such as transparent conducting electrodes, touchscreens, liquid crystal displays, solar cells, saturable absorbers, just to name a few. However, the lack of a gap in graphene’s bandstructure makes it a poor material for digital electronics and optoelectronic devices.

In contrast to graphene, TMDCs monolayers such as MoS₂, MoSe₂, WS₂, and WSe₂ have sizable bandgaps, allowing for applications such as transistors. Moreover, since TMDCs exhibit pronounced light-matter coupling, they could become attractive for optoelectronic applications, e.g. in photodetectors and electroluminescent devices.

One of the important requirements for the basic understanding of the fundamental material properties is the knowledge of the electronic bandstructure. Whereas in a mesoscopic system, such as a semiconductor quantum well (QW), the quantum confinement effects can be treated within the envelope function approximation, the bandstructure of a single monolayer differs not only quantitatively but also qualitatively from that of the corresponding bulk material.

In graphene, the single-particle bandstructure exhibits two distinct crossing points at the Fermi level where electrons and holes are degenerate. In the vicinity of these Dirac points, the dispersion is a cone similar to the light cone in relativistic mechanics with the Fermi velocity v_F replacing the speed of light. The occurrence of the cones results from the symmetry between the two equivalent sublattices constituting the overall honeycomb lattice. The sublattice wavefunctions can be combined into a pseudospinor whose properties are determined by the ultra-relativistic Dirac equation. As a consequence, the quasiparticles in graphene can be considered as massless ultra-relativistic Dirac-Fermions, characterized by the pseudospin σ, the electric charge e, and the Fermi velocity which is typically in the range v_F ∝ c/300. The nonequivalent Dirac points are related by the parity or time-reversal transformation with opposite pseudospins in the different valleys. Similar to the real electron spin, the pseudospin is associated with an angular momentum and couples to the optical field. As a result, different valleys are addressed by oppositely circular polarized electromagnetic fields.

In TMDCs, the bandstructure changes from indirect to direct as one reduces the thickness from bulk to a monolayer. This transition has been predicted by bandstructure calculations [Cheiwchanchamnangij and Lambrecht (2012); Cappelluti et al. (2013)] and was confirmed experimentally by photoluminescence (PL) experiments that show an intensity increase of several orders of magnitude when the material thickness approaches a monolayer. [Mak et al. (2010); Zeng et al. (2013)] As in graphene, the direct gap is located at the two Dirac points of the Brillioun-zone, and the near bandgap quasiparticles can be described as relativistic Dirac Fermions with a pseudospin that couples to the light field. However, unlike in graphene where the different sublattices are occupied with the same species of atoms, the nonequivalence of the two sublattices in TMDCs leads to the opening of a gap that can be interpreted as rest energy of a massive electron-hole pair. Moreover, a strong spin-orbit interaction leads to a valley dependent splitting of the valence-band states with different (real) spin. The valley dependent spin splitting allows one to address distinct spin and valley states selectively by resonant excitation with circularly polarized light and suggests the possibility of so called valleytronics. [Yao et al. (2008); Cao et al. (2012); Mak et al. (2012a); Zeng et al. (2013); Shan et al. (2015)]

While it is generally accepted that the electronic properties of graphene and TMDCs can be assigned to the existence of relativistic, chiral quasiparticles, the role of the electron-electron Coulomb interaction and its influence on the optical properties of graphene and graphene-like materials is still not well understood. Within the noninteracting picture, the optical spectrum of graphene is characterized by a constant absorption in the visible and a pronounced absorption peak in the ultraviolet spectral range which is attributed to the van Hove singularity at the M point of the Brillouin zone. [Kravets et al. (2010); Yang et al. (2009); Yang (2011); Malic et al. (2011)]

Microscopic calculations including electron-electron interactions [Yang et al. (2009); Yang (2011); Malic et al. (2011)] predict the formation of so-called saddle-point excitons, manifesting themselves in an electron-hole-correlation induced redshift of the van Hove singularities that has been observed experimentally. [Mak et al. (2011); Chae et al. (2011)] At the same time, the constant absorption in the visible range is amazingly robust against...