Interpretation of the in-plane infrared response of the high-Tc cuprate superconductors involving spin fluctuations revisited

The in-plane infrared response of the high-Tc cuprate superconductors was studied using the spin-fermion model, where charged quasiparticles of the copper-oxygen planes are coupled to spin fluctuations. First, we analyzed structures of the superconducting-state conductivity reflecting the coupling of the quasiparticles to the resonance mode observed by neutron scattering. The conductivity computed with the input spin susceptibility in the simple form of the mode exhibits two prominent features: an onset of the real part of the conductivity starting around the frequency of the mode omega_{0} and a maximum of a related function W(omega), roughly proportional to the second derivative of the scattering rate, centered approximately at omega=omega_{0}+Delta_{0}/hbar, where Delta_{0} is the maximum value of the superconducting gap. The two structures are well known from earlier studies. Their physical meaning, however, has not been sufficiently elucidated thus far. Our analysis involving quasiparticle spectral functions provides a clear interpretation. Second, we explored the role played by the spin-fluctuation continuum. Third, we investigated the temperature dependence of the conductivity, of the intraband spectral weight, and of the effective kinetic energy. The changes of the latter two quantities below Tc are determined by the formation of the gap, by a feedback effect of the spin fluctuations on the quasiparticles, and by a significant shift of the chemical potential.Comment: 20 pages, 18 figures, submitted to Physical Review

Interband absorption edge in the topological insulators Bi-2(Te1-xSex)(3)

We have investigated the optical properties of thin films of topological insulators Bi2Te3, Bi2Se3, and their alloys Bi-2(Te1-x Se-x)(3) on BaF2 substrates by a combination of infrared ellipsometry and reflectivity in the energy range from 0.06 to 6.5 eV. For the onset of interband absorption in Bi2Se3, after the correction for the Burstein-Moss effect, we find the value of the direct band gap of 215 +/- 10 meV at 10 K. Our data support the picture that Bi2Se3 has a direct band gap located at the Gamma point in the Brillouin zone and that the valence band reaches up to the Dirac point and has the shape of a downward-oriented paraboloid, i.e., without a camel-back structure. In Bi2Te3, the onset of strong direct interband absorption at 10 K is at a similar energy of about 200 meV, with a weaker additional feature at about 170 meV. Our data support the recent GW band-structure calculations suggesting that the direct interband transition does not occur at the Gamma point but near the Z-F line of the Brillouin zone. In the Bi-2(Te1-x Se-x)(3) alloy, the energy of the onset of direct interband transitions exhibits a maximum near x = 0.3 (i.e., the composition of Bi2Te2Se), suggesting that the crossover of the direct interband transitions between the two points in the Brillouin zone occurs close to this composition

Correlation between the Josephson coupling energy and the condensation energy in bilayer cuprate superconductors

We review some previous studies concerning the intra-bilayer Josephson plasmons and present new ellipsometric data of the c-axis infrared response of almost optimally doped Bi_{2}Sr_{2}CaCu_{2}O_{8}. The c-axis conductivity of this compound exhibits the same kind of anomalies as that of underdoped YBa_{2}Cu_{3}O_{7-delta}. We analyze these anomalies in detail and show that they can be explained within a model involving the intra-bilayer Josephson effect and variations of the electric field inside the unit cell. The Josephson coupling energies of different bilayer compounds obtained from the optical data are compared with the condensation energies and it is shown that there is a reasonable agreement between the values of the two quantities. We argue that the Josephson coupling energy, as determined by the frequency of the intra-bilayer Josephson plasmon, represents a reasonable estimate of the change of the effective c-axis kinetic energy upon entering the superconducting state. It is further explained that this is not the case for the estimate based on the use of the simplest ``tight-binding'' sum rule. We discuss possible interpretations of the remarkable agreement between the Josephson coupling energies and the condensation energies. The most plausible interpretation is that the interlayer tunneling of the Cooper pairs provides the dominant contribution to the condensation energy of the bilayer compounds; in other words that the condensation energy of these compounds can be accounted for by the interlayer tunneling theory. We suggest an extension of this theory, which may also explain the high values of T_{c} in the single layer compounds Tl_{2}Ba_{2}CuO_{6} and HgBa_{2}CuO_{4}, and we make several experimentally verifiable predictions.Comment: 16 pages (including Tables) and 7 figures; accepted for publication in Physical Review

The anomaly of the oxygen bond-bending mode at 320 cm−1^{-1} and the additional absorption peak in the c-axis infrared conductivity of underdoped YBa2_{2}Cu3_{3}O7−δ_{7-\delta} single crystals revisited by ellipsometricmeasurements

We have performed ellipsometric measurements of the far-infrared c-axis dielectric response of underdoped YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ single crystals. Here we report a detailed analysis of the temperature-dependent renormalization of the oxygen bending phonon mode at 320 cm$^{-1}$ and the formation of the additional absorption peak around 400-500 cm$^{-1}$. For a strongly underdoped YBa$_{2}$Cu$_{3}$O$_{6.5}$ crystal with T$_{c}$=52 K we find that, in agreement with previous reports based on conventional reflection measurements, the gradual onset of both features occurs well above T$_{c}$ at T*$\sim$150 K. Contrary to some of these reports, however, our data establish that the phonon anomaly and the formation of the additional peak exhibit very pronounced and steep changes right at T$_{c}$. For a less underdoped YBa$_{2}$Cu$_{3}$O$_{6.75}$ crystal with T$_{c}$=80 K, the onset temperature of the phonon anomaly almost coincides with T$_{c}$. Also in contrast to some previous reports, we find for both crystals that a sizeable fraction of the spectral weight of the additional absorption peak cannot be accounted for by the spectral-weight loss of the phonon modes but instead arises from a redistribution of the electronic continuum. Our ellipsometric data are consistent with a model where the bilayer cuprate compounds are treated as a superlattice of intra- and inter-bilayer Josephson-junctions

Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives

This paper discusses the fundamentals, applications, potential, limitations, and future perspectives of polarized light reflection techniques for the characterization of materials and related systems and devices at the nanoscale. These techniques include spectroscopic ellipsometry, polarimetry, and reflectance anisotropy. We give an overview of the various ellipsometry strategies for the measurement and analysis of nanometric films, metal nanoparticles and nanowires, semiconductor nanocrystals, and submicron periodic structures. We show that ellipsometry is capable of more than the determination of thickness and optical properties, and it can be exploited to gain information about process control, geometry factors, anisotropy, defects, and quantum confinement effects of nanostructures