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!