Plasmonics in double-layer graphene Tobias Stauber 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 Plasmons in double-layer graphene 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. Ponomarenko et. 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 Nano 2011 Double-layer graphene Linear response in matrix form: Define loss function: j1 11 j 2 21 12 A1ext 22 ext A 2 11 ( q , ) Im Tr 21 12 22 Previous approaches Often, the dielectric function is discussed: 1 v 0 10 ( q , ) det 0 11 0 v 1 21 The loss function is given by: ( q , ) Im 0 0 1 v 22 2 v 12 2 0 0 1 (q, ) 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. Results for the loss function at finite temperature Plasmons at finite temperature The plasmon dispersion is red-shifted for intermediate temperatures and blue-shifted for high temperatures. T TF / 4 T TF TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012). Plasmons at zero doping There are plasmons at zero doping at T=300K: kT kT v 2 ln 2 T 0 . 035 eV 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-ofphase 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: va 2 g dk 2 1 F vF Graphene on top of Pt(111): v a 1 . 15 v F TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012). Near-field amplification Near-field amplification Exponential amplification for R=0. T 1 2 e 2 qd 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 Retardation effects Strong light-matter coupling Plasmon Dispersion: 1 2 2 1 3 2 The presence of doped graphene at the interfaces leads strong lightmatter coupling for ω<αωF: q q r 1 F • 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. Im (Q / 2 s ) 2 ( s s * ) ( / 2 ) 2 2 s* /F d Q 23 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 Optical properties of Twisted bilayer 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: t v vF 1 9 vF K K 2 K sin( / 2 ) 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 Summary 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!