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.

The optical conductivity σ1(ω) and the spectral weight SW of four topological insulators with increasing chemical compensation (Bi2Se3,Bi2Se2Te,Bi 2-xCaxSe3, and Bi2Te2Se) have been measured from 5 to 300 K and from subterahertz to visible frequencies. The effect of compensation is clearly observed in the infrared spectra through the suppression of an extrinsic Drude term and the appearance of strong absorption peaks that we assign to electronic transitions among localized states. From the far-infrared spectral weight SW of the most compensated sample (Bi2Te2Se), one can estimate a density of charge carriers on the order of 1017/cm3 in good agreement with transport data. Those results demonstrate that the low-energy electrodynamics in single crystals of topological insulators, even at the highest degree of compensation presently achieved, is still influenced by three-dimensional charge excitations. © 2012 American Physical Society

In La2-xSrxCuO4 (LSCO) the spectral weight W=integralOmega0sigma(ab)1(omega,T)domega [where sigma(ab)1(omega,T) is the ab-plane conductivity] obeys the same law W=W0-BOmegaT2 as in a conventional metal such as gold, for any Omega up to the plasma edge. However, in LSCO BOmega points toward correlation effects and, unlike in gold, is related to an energy scale tT<

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We compare calculations based on the dynamical mean-field theory of the Hubbard model with the infrared spectral weight W(Omega,T) of La(2-x)SrxCuO4 and other cuprates. Without using fitting parameters we show that most of the anomalies found in W(Omega,T) with respect to normal metals, including the existence of two different energy scales for the doping and the T dependence of W(Omega,T), can be ascribed to strong correlation effects.

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

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The infrared absorption of charge density waves coupled to a magnetic background is first observed in two manganites La1−xCaxMnO3 with x = 0.5 and x = 0.67. In both cases a BCS-like gap 2∆(T ), which for x = 0.5 follows the hysteretic ferro-antiferromagnetic transition, fully opens at a finite T0 < T Neel , with 2∆(T0)/kBTc ≃ 5. These results may also explain the unusual coexistence of charge ordering and ferromagnetism in La0.5Ca0.5MnO3.The close interplay between transport properties and magnetic ordering in the colossal magnetoresistance (CMR) manganites La(Nd) 1−x Ca(Sr) x MnO 3 is presently explained in terms of magnetic double exchange promoted by polaronic carriers along the path Mn +3 -O −2 -Mn +4 .[1] Charge hopping promotes the alignment of Mn +3 and Mn +4 magnetic moments, and vice versa. The polaronic effects are due to the dynamic Jahn-Teller distortion of the oxygen octahedra around the Mn +3 ions. The above mechanism explains how, in manganites with 0.2 < x < 0.48, any increase in the magnetization enhances the dc conductivity, and vice versa. However, La 0.5 Ca 0.5 MnO 3 shows an unpredicted coexistence of ferromagnetism and incommensurate charge ordering (CO). This compound is paramagnetic at room temperature, becomes ferromagnetic (FM) at T c ≃ 225 K and, by further cooling (C), antiferromagnetic (AFM) at a Néel temperature T C N ≃ 155 K.[2] Upon heating the sample (H) the FM-AFM transition is instead observed at T H N ≃ 190 K .[3] The dc conductivity σ(0) of La 0.5 Ca 0.5 MnO 3 is quite insensitive to the PM-FM transition at T c . [3] Xray, neutron [4] and electron diffraction [5] show quasicommensurate charge and orbital ordering in the AFM phase with wavevector q = (2π/a)( 1 2 − ǫ, 0, 0). The incommensurability ǫ increases with temperature and follows the hysteretic behavior of the AFM-FM transition, until charge ordering disappears above the Curie point T c .[5] At higher Ca doping, for 0.5 < ∼ x < ∼ 0.75, a transition to a charge ordered phase [6] is observed in the paramagnetic phase at T CO . T CO is a maximum (265 K) for x = 0.67 ≃ 2 3 , where the charge ordering is commensurate with the lattice. Below T CO , the system enters at T N an antiferromagnetic phase. For x = 0.67, T N ≃ 140 K.