1. Y.A.Pusep Institute of Physics of São Carlos, University of São Paulo Collaborators: Experiment – A.D.Rodrigues, UFSCar. Theory - S.S.Sokolov, B.Verkin Institute for Low- Temperature Physics and Engineering, National Academy of Sciences of Ukraine. Samples – H.Arakaki, C.A. de Souza, IFSC/USP.

2. Why plasmons ? Advantages of optical and electrical circuits: Fast data transfer by transmitting optical signals through minuscule nanoscale structures. Optical fibers versus electrical circuits. Diffraction limit. Manipulation of plasmons (localization and propagation).

3. 1. Electrons: single-particle excitations 2. Plasmons: collective excitations

4. 1.Random superlattices 2.Raman scattering by collective excitations 3.Plasmon localization: theory and experiment 4.Conclusions 1.Random superlattices 2.Raman scattering by collective excitations 3.Plasmon localization: theory and experiment 4.Conclusions

6. Electrons  (  T = 0)  0,  /  T < 0  (  T = 0) = 0,  /  T > 0 metal (k F l>1): insulator (k F l<1): Obs: l is the electron free path length, k F = 2 π / λ e, λ e is the electron wavelength.

7. Criterion of Plasmon localization - ?

8. Plasmon wave function: with Results of calculations Neutral impurity scattering potential:

9. Localized plasmon: L c < R 0 Delocalized plasmon: L c > R 0 2. Relation between L c and R 0 determine propagation of plasmons: 2. Relation between L c and R 0 determine propagation of plasmons: 1. Plasmon damping ( Г p ) independent of disorder parameter (L c, δ ) indicates localization. 1. Plasmon damping ( Г p ) independent of disorder parameter (L c, δ ) indicates localization. Criteria of Plasmon localization

10. Non-conservation of quase-momentum [Yu.A.Pusep, et al., Phys.Rev. B 58, 10683 (1998)]:

11. Doped superlattices (weak plasmon localization) Doped superlattices (weak plasmon localization) Disordered superlattices (strong plasmon localization) Disordered superlattices (strong plasmon localization) L c > R 0 L c < R 0

12. L c > R 0 L c < R 0 Weak plasmon localization: (plasmonic “metal”) Weak plasmon localization: (plasmonic “metal”) Strong plasmon localization: (plasmonic “insulator”) Strong plasmon localization: (plasmonic “insulator”) Temperature Effect

13. Delocalized plasmon: Lc > Ro – the increasing disorder results in increasing plasmon linewidth; Localized Plasmon: Lc < Ro – no influence of the disorder on plasmon linewidth; The independence of the plasmon linewidth on disorder is the manifestation of plasmon localization. The increasing temperature enhances the localization of the weakly localized plasmons, while it causes the delocalization of the strongly localized plasmons. Yu.A.Pusep, A.D.Rodrigues, S.S.Sokolov, Phys.Rev.B 80, 205307 (2009).

15. Damped plasmon : Overdamped plasmon: Non-conservation of the quase-momentum:

17. Electrons T.F.Rosenbaum et al., Phys.Rev.Lett. 45, 1723 (1980)Y.Liu, et al., Phys.Rev.Lett. 67, 2068 (1991)  (  T = 0)  0,  /  T < 0  (  T = 0) = 0,  /  T > 0 metal (k F l>1): insulator (k F l<1):