Download Presentation
## Plasmonics in double-layer graphene

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Plasmonics in double-layer graphene**TobiasStauber and Guillermo Gómez-Santos Graphene Nanophotonics Benasque, 5th March 2013**Overview**Optical properties double-layer graphene Effect of temperature and inhomogeneous dielectric background on Plasmons Near-field amplification Perfect transmission Optical properties of twisted bilayer graphene (Work in progress with L. Brey, P. San Jose, E. Prada) Drude weight Plasmons excitations**Double-layer graphene**Coulomb drag, field effect tunneling transistor, and optical modulator. S. Kim, et. al., Phys. Rev. B 83, 161401(R) (2011). L. A. Ponomarenkoet. al., Nature Physics 7, 958 (2011). L. Britnell et. al., Science 335 (6071) 947-950 (2012) Ming Liu et al., Nano Lett. 12, 1482 (2012). Johan Christensen et al, ACS Nano2011**Double-layer graphene**Linear response in matrix form: Define loss function:**Previous approaches**Often, the dielectric function is discussed: The loss function is given by: • Problems: • This function changes sign, because it is not based on a true response function . • The absolute value gives incorrect weight for Landau damping regime.**Plasmons at finite temperature**The plasmon dispersion is red-shifted for intermediate temperatures and blue-shifted for high temperatures. TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).**Plasmons at zero doping**There are plasmons at zero doping at T=300K: TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).**Inhomogeneous dielectric medium**An inhomogeneous dielectric medium can shift relative weight of in-phase and out-of-phase plasmons. Topological insulators have high-dielectric buffer layer: TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).**Acoustic plasmon mode**A substrate with large dielectric constant turns plasmonic mode into acoustic mode: Graphene on top of Pt(111): TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).**Near-field amplification**Exponential amplification for R=0. Analogy to Pendry´s perfect lens**Numerical results**Longitudinal polarization: Transverse polarization: See also Poster 20 by A. Gutiérrez TS and G. Gómez-Santos, Phys. Rev. B 85, 075410 (2012).**Numerical results**For different densities: order of layers determines amplification: n1>n2 n1<n2**Plasmon Dispersion:**Strong light-matter coupling The presence of doped graphene at the interfaces leads strong light-matter coupling for ω<αωF: • Quenched Fabry-Pérot resonances • Extraordinary transmission in tunnel region G. Gómez-Santos and TS, Europhys. Lett.99, 27006 (2012).**Fabry-Pérot resonances**Quenched Fabry-Pérot resonances: Response shows Fano lineshape: Particle-in-a-box states leak out and interact with continuum.**Quantum-Dot model**Quasi-localized states between two doped graphene layers**Extraordinary transmission**Extraordinary transmission in tunnel region: Transmission between light cones:**Finite relaxation time**Non-linear absorption sets in for angles beyond total reflections: Different layer distances Different relaxation times**Atomic structure**For small angles, the formation of periodic Moiré superlattices is seen. P. Moon and M. Koshino, arXive:1302.5218 (2013).**Electronic structure**The electronic structure changes for small twist angles. Renormalization of the Fermi velocity: J. M. B. Lopes dos Santos et al., Phys. Rev. Lett. 99, 256802 (2007).**Optical conductivity**The optical conductivity is characterized by a van Hove singularity independent of the angle.**Drude weight**Drude weight follows the shell structure of the DOS.**Drude weight**For small angles, a substructure appears in the Drude weight not present in the DOS:**Plasmonic excitations**For small chemical potential: Interband plasmons**Plasmonic excitations**For large chemical potential: Intraband plasmons**Concluding remarks**• There is spectral transfer of in-phase and out-of-phase mode, near-field amplification and perfect transmission in double-layer graphene. • Plasmonic spectrum of twisted bilayer graphene stronly depends on doping. Thanks for your attention!