High-frequency behavior of the infrared conductivity of cuprates

Abstract

We analyze recent infrared conductivity data in the normal state of the cuprates. We find that the high frequency behavior, which has been suggested as evidence for quantum critical scaling, is generally characteristic of electrons interacting with a broad spectrum of bosons. From explicit calculations, we find a frequency exponent for the modulus of the conductivity, and a phase angle, in good agreement with experiment. The data indicate an upper cut-off of the boson spectrum of order 300 meV. This implies that the bosons are of electronic origin rather than phonons.PACS numbers: 74.25.Gz, Infrared conductivity has proven to be a powerful probe of the electronic degrees of freedom of the cuprates 1 . It has the advantage of being bulk sensitive, and yields useful information over a wide range of energies. Of particular interest is a generalized Drude analysis of the data, which provides information on the optical analogue of the fermion self-energy 2 . Most data indicate a linear frequency dependence of the imaginary part of the optical self-energy (i.e., 1/τ ) up to very high energies. Such behavior is characteristic of a marginal Fermi liquid 3 . In some data 4 , this trend persists up to the plasma frequency (1 eV). Recently, van der Marel and collaborators5 have obtained somewhat different behavior at high frequencies for 1/τ , showing a tendency to saturate 6 above 0.5 eV. They have also found that in a wide frequency range (125 meV to 900 meV), both real (σ 1 ) and imaginary (σ 2 ) parts of the optical conductivity are described by the same power law (ω α ) with an exponent -0.65 (and an associated phase angle φ = tan −1 (σ 2 /σ 1 ) of 60 • ). The same behavior was observed earlier by El Azrak et al.4 . The exponent and phase angle in this frequency range are roughly temperature independent, and have been suggested to be indicative of quantum critical scaling 5 .In this paper, we analyze the frequency dependent optical data using a model based on electrons interacting with a broad spectrum of bosons. We find that the essential results mentioned above are captured by this analysis, indicating that the observed behavior is generic for interacting electrons. We show that the power-law behavior of the conductivity σ is not indicative of quantumcritical scaling, but rather a consequence of the flattening of the fermionic self-energy at high frequencies. Based on our analysis, we find evidence for an upper cut-off scale of the boson spectrum of about 300 meV in the cuprates. This is consistent with the assumed value in the marginal Fermi liquid phenomenology 3 , and also with the measured width of the spin-fluctuation spectrum 7 .The Kubo expression for the optical conductivity can be written as 8

Optical integral in the cuprates and the question of sum-rule violation

“…26 For electrons interacting with a broad spectrum of bosons, this approximation is essentially identical to the exact Kubo result. 20 The optical mass m * ͑͒ can then be determined by a Kramers- 20 so as to fit the data of Ref. 29 at one particular temperature.…”

Disentangling the Electronic and Phononic Glue in a High- T c Superconductor

“…Dip features in tunnelling experiments have been used to alternatively support the scenarios of dominant electron-phonon interactions [11] or antiferromagnetic spin fluctuations [12]. The frequency-dependent dissipation of the Drude optical conductivity, σ (ω), measured by equilibrium optical spectroscopies, has been interpreted [13][14][15] as the coupling of electrons to bosonic excitations, in which the separation of the phononic and electronic contributions is impeded by their partial coexistence on the same energy scale (<90 meV).We disentangle the electronic and phononic contributions to Π(Ω) through a non-equilibrium optical spectroscopy, in which the femtosecond time-resolution is combined with an energy-resolution smaller than 10 meV, over a wide photon energy range (0.5-2 eV). Our approach is based on the widely-used assumption [16,17] that, after the interaction between a superconductor and a short laser pulse (1.55 eV photon energy), the effective electronic temperature (T e ) relaxes toward its equilibrium value through energy exchange with the different degrees of freedom that linearly contribute to Π(Ω).…”

Theory of dual fermion superconductivity in hole-doped cuprates

“…Imχ d (ω) becomes flat up to a cutoff energy, around 0.3 eV, according to the optical and element-specific X-ray measurements 6,50,51,54 . Here, magnetism in cuprates is assumed to be dominated by the Cu ions.…”

“…Actually, early in 2006, the power-law optical conductivity was attributed to a consequence of the carriers interacting with a broad spectrum of bosons 54 .…”