Plasmons are quantized collective oscillations of electrons and have been observed in metals and doped semiconductors. The plasmons of ordinary, massive electrons have been the basic ingredients of research in plasmonics and in optical metamaterials for a long time. However, plasmons of massless Dirac electrons have only recently been observed in graphene, a purely two-dimensional electron system. Their properties are promising for novel tunable plasmonic metamaterials in the terahertz and mid-infrared frequency range. Dirac fermions also occur in the two-dimensional electron gas that forms at the surface of topological insulators as a result of the strong spin-orbit interaction existing in the insulating bulk phase. One may therefore look for their collective excitations using infrared spectroscopy. Here we report the first experimental evidence of plasmonic excitations in a topological insulator (Bi2Se3). The material was prepared in thin micro-ribbon arrays of different widths W and periods 2W to select suitable values of the plasmon wavevector k. The linewidth of the plasmon was found to remain nearly constant at temperatures between 6 K and 300 K, as expected when exciting topological carriers. Moreover, by changing W and measuring the plasmon frequency in the terahertz range versus k we show, without using any fitting parameter, that the dispersion curve agrees quantitatively with that predicted for Dirac plasmons.

morphologies. [6][7][8][9] Plasmon hybridization, [ 10,11 ] Fano resonances, [ 12,13 ] and electromagnetically induced transparency [ 14 ] are among the feats that have been realized and broadly used to understand and design plasmonic devices. The range of applications of plasmon excitations is vast and includes optical sensing, [15][16][17][18] quantum electrodynamics, [ 19,20 ] nonlinear optics, [ 21,22 ] photovoltaic technologies, [ 23 ] and medical diagnosis and treatment. [ 24,25 ] Extensive experimental efforts are currently underway to fi nd materials with improved plasmonic performance, in particular in the mid-infrared and terahertz parts of the electromagnetic spectrum. Examples of such materials are low-Tc [ 26 ] and high-Tc superconductors, [ 14 ] conductive oxides, [ 27 ] and graphene. [28][29][30][31][32][33][34] The latter exhibits a peculiar electronic structure, which enables unprecedented levels of electrooptical tunability via chemical or electrostatic doping: [35][36][37] electrons in graphene behave as massless Dirac fermions characterized by a linear energy/ momentum dispersion relation and a vanishing density of states at the Fermi energy, so that a few additional charge carriers produce a large shift in the chemical potential. Dirac charge carriers are also found in 3D topological insulator (TI) materials-i.e., quantum systems characterized by an insulating electronic gap in the bulk, whose opening is due to strong spin-orbit interaction, and gapless surface states atThe great potential of Dirac electrons for plasmonics and photonics has been readily recognized after their discovery in graphene, followed by applications to smart optical devices. Dirac carriers are also found in topological insulators (TIs)-quantum systems having an insulating gap in the bulk and intrinsic Dirac metallic states at the surface. Here, the plasmonic response of ring structures patterned in Bi 2 Se 3 TI fi lms is investigated through terahertz (THz) spectroscopy. The rings are observed to exhibit a bonding and an antibonding plasmon modes, which we tune in frequency by varying their diameter. An analytical theory based on the THz conductance of unpatterned fi lms is developed, which accurately describes the strong plasmon-phonon hybridization and Fano interference experimentally observed as the bonding plasmon is swiped across the prominent 2 THz phonon exhibited by this material. This

Heavily-doped semiconductor films are very promising for application in mid-infrared plasmonic devices because the real part of their dielectric function is negative and broadly tunable in this wavelength range. In this work we investigate heavily n-type doped germanium epilayers grown on different substrates, in-situ doped in the 10 17 to 10 19 cm −3 range, by infrared spectroscopy, first principle calculations, pump-probe spectroscopy and dc transport measurements to determine the relation between plasma edge and carrier density and to quantify mid-infrared plasmon losses. We demonstrate that the unscreened plasma frequency can be tuned in the 400 -4800 cm −1 range and that the average electron scattering rate, dominated by scattering with optical phonons and charged impurities, increases almost linearly with frequency. We also found weak dependence of losses and tunability on the crystal defect density, on the inactivated dopant density and on the temperature down to 10 K. In films where the plasma was optically activated by pumping in the near-infrared, we found weak but significant dependence of relaxation times on the static doping level of the film. Our results suggest that plasmon decay times in the several-picosecond range can be obtained in ntype germanium thin films grown on silicon substrates hence allowing for underdamped mid-infrared plasma oscillations at room temperature.The recent push towards applications of spectroscopy for chemical and biological sensing in the mid-infrared (mid-IR)1-8 has prompted the need for conducting thin films displaying values of the complex dielectric functionǫ(ω) = ǫ ′ (ω) + iǫ ′′ (ω) that can be tailored to meet the needs of novel electromagnetic designs exploiting the concepts of metamaterials, transformation optics and plasmonics 9 . In the design of metamaterials, where subwavelength sized conducting elements are embedded in dielectric matrices, if the values of ǫ ′ of the metal and the dielectric are of the same order, but have opposite sign, the geometric filling fractions of the metal and dielectric can be readily tuned to achieve subwavelengthresolution focusing of radiation 10 . Such requirement is met by silver for wavelengths λ around 400 nm. The same condition cannot be achieved in the IR range by using elemental metals, however, because metals possess an extremely high negative value of ǫ ′ not equaled, in