Spectral Measurement of the Hall Angle Response in Normal State Cuprate Superconductors

Abstract

We measure the temperature and frequency dependence of the complex Hall angle for normal state YBa2Cu3O7 films from dc to far-infrared frequencies (20-250 cm −1 ) using a new modulated polarization technique. We determine that the functional dependence of the Hall angle on scattering does not fit the expected Lorentzian response. We find spectral evidence supporting models of the Hall effect where the scattering ΓH is linear in T, suggesting that a single relaxation rate, linear in temperature, governs transport in the cuprates.The normal state Hall effect in cuprate superconductors exhibits an anomalous temperature dependence that cannot be explained using conventional transport theory for metals. According to the simple Drude model, the resistivity of a metal and the cotangent of its Hall angle cot(θ H ) = σxx σxy , should share the same temperature dependence, both proportional to the scattering rate of the charge carriers. However, the normal state resistance of cuprate superconductors is linear with temperature, ρ ∼ T , while the Hall angle has a robust cot(θ H ) ∼ T . This apparent duality of scattering rates characterizes the anomalous Hall transport in the cuprates. Several theories approached the problem assuming that two scattering rates were in fact involved, beginning with the spin-charge separation model of Anderson wherein the two species of quasiparticles each relaxed at the different observed rates.[5] Subsequent explanations focused either on alternative non-Fermi liquid mechanisms [6,7] or on the effects of k-space scattering anisotropies [8][9][10][11]. The common feature of all the above theories is a dominant term that is linear in the scattering rate, cot(θ H ) ∼ γ H . In contrast, a recent theory by Varma and Abrahams [12] treats anisotropic scattering in a marginal Fermi-liquid and predicts a square-scattering response, cot(θ H ) ∼ γ 2 H . These different models can be distinguished at finite frequency. The linear-and square-scattering models correspond to Lorentzian and square-Lorentzian spectral responses respectively, and although Hall experiments have been performed at finite frequencies [13][14][15], this paper is the first to study both temperature and frequency dependence of the Hall response in a frequency range that discerns a lineshape and extrapolates to the dc limit.We begin by reviewing the concept of a frequency dependent Hall angle [16] using the Drude model as an example of a Lorentzian response. All parameters are implicitly spectral, i.e. θ H = θ H (ω), and in the present case of strong scattering, tan(θ) ≃ θ << 1. Quasiparticles circling at the cyclotron frequency ω *

Measurement of the infrared magneto-optic properties of thin-film metals and high temperature superconductors

“…9 where it is compared with far-infrared data from Ref. 17. The results show a significant disconnect from the behavior of Re( H ) in the existing data for YBa 2 Cu 3 O 7 in the far infrared, which indicate a negative value for Re( F ) above 250 cm Ϫ1 , whereas that of the current work at 1000 cm Ϫ1 is positive.…”

Terahertz Response and Colossal Kerr Rotation from the Surface States of the Topological InsulatorBi2Se3

“…• from the original polarization (Y signal) [35,36]. This method allows fast magnetic field scanning and the analysis of the full spectral response.…”

Magneto-optical Evidence for a Gapped Fermi Surface in UnderdopedYBa2Cu3ORigal1, Schmadel2, Drew3 et al. 2004Phys. Rev. Lett.Self Cite2410270View full textAdd to dashboardCite

“…It also allows tests of proposed theories which agree qualitatively with DC measurements but can be distinguished at finite frequency [9,10,11,12]. [11].…”

“…Therefore, important questions have to do with the mode in which these systems approach the Mott state as the doping is reduced from the optimal value. In the Mott transition the Fermi surface remains intact but spectral weight transfers from a quasiparticle band at the Fermi level to the Hubbard bands away from the Fermi energy [7,8] The infrared Hall effect is a powerful tool for the investigation of strongly correlated metals giving important information on the carrier dynamics [9,10,11,12]. In contrast to the DC Hall effect the measurements at infrared frequencies gives information on the energy scales of current relaxation in the normal state of high Tc superconductors.…”