Spectroscopic evidence for Fermi liquid-like energy and temperature dependence of the relaxation rate in the pseudogap phase of the cuprates

Abstract

Cuprate high-T c superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest T c s) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasiparticle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (h ω) 2 + (pπk B T) 2 . Magnetotransport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T 2 dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω-and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.optical spectroscopy | superconductivity | mass renormalization | self energy T he compound HgBa 2 CuO 4+δ (Hg1201) is the single-layer cuprate that exhibits the highest T c (97 K). We therefore measured the optical conductivity of strongly underdoped single crystals of Hg1201 ðT c = 67 KÞ. Here we are interested in the optical conductivity of the CuO 2 layers. We therefore express the optical conductivity as a 2D sheet conductance GðωÞ = d c σðωÞ, where d c is the interlayer spacing. The real part of the sheet conductance normalized by the conduction quantum G 0 = 2e 2 =h is shown in Fig. 1. As seen in the figure, a gap-like suppression below 140 meV is clearly observable for temperatures below T c and remains visible in the normal state up to ∼250 K. This is a clear optical signature of the pseudogap. We also observe the zero-energy mode due to the free charge carrier response, which progressively narrows upon lowering the temperature. In materials where the charge carrier relaxation is dominated by impurity scattering, the width of this "Drude" peak corresponds to the relaxation rate of the charge carriers. Relaxation processes arising from interactions have the effect of replacing the constant (frequency-independent) relaxation rate with a frequencydependent one. The general expression for the optical conductivity of interacting electrons is then Gðω; TÞ = iπK Zω + Mðω; TÞ G 0 :[1]The spectral weight K corresponds to minus the kinetic energy if the frequency integration of the experimental data is restricted to intraband transitions. The effect of electron-electron interactions and coupling to collective mo...

Saturation of resistivity and Kohler's rule in Ni-dopedLa1.85Sr0.15CuO4cuprate

“…Fermi-Dirac statistic underlying the quantum oscillations [1], single-parameter -quadratic in energy ω and temperature T -scaling in optical conductivity σ(ω, T ) (Ref. [2]), T 2 resistivity behavior extending over substantial Tregion in clean systems [3] and fulfillment of typical for conventional metals Kohler's rule in magnetotransport [4] are observations in favor of Fermi-liquid scenario.…”

“…[23,[25][26][27]). In systems where impurity scattering dominates the carrier relaxation (quasiparticle decay) rate 1/τ , the Drude peak is centered at ω=0 regardless of how strong scattering becomes [2,23]. Electronelectron interactions make τ frequency-dependent but for Fermi-liquid-like ω 2 dependence σ(ω) still peaks at ω=0 (Ref.…”

“…Electronelectron interactions make τ frequency-dependent but for Fermi-liquid-like ω 2 dependence σ(ω) still peaks at ω=0 (Ref. [2]). Thus large impurity-induced ρ res may facilitate approach to Ioffe-Regel-Mott limit in dc (ω=0) LSCO transport at lower T before the spectral weight is transferred to higher-energy excitations at larger T .…”

Hidden Fermi-liquid Charge Transport in the Antiferromagnetic Phase of the Electron-Doped Cuprate Superconductors

“…Moreover, below a compound specific doping level, the low-temperature resistivity for both types of cuprates develops a logarithmic upturn that appears to be related to disorder, yet whose microscopic origin has remained unknown [1,[5][6][7]. In contrast, at high dopant concentrations, the cuprates are good metals with welldefined Fermi surfaces and clear evidence for Fermi-liquid (FL) behavior [8][9][10][11][12][13][14].In a new development, the hole-doped cuprates were found to exhibit FL properties in an extended temperature range below the characteristic temperature T * * (T * * < T * ; T * is the PG temperature): (i) the resistivity per CuO 2 sheet exhibits a universal, quadratic temperature dependence, and is inversely proportional to the doped carrier density p, ρ ∝ T 2 /p [15]; (ii) Kohler's rule for the magnetoresistvity, the characteristic of a conventional metal with a single relaxation rate, is obeyed, with a Fermi-liquid scattering rate, 1/τ ∝ T 2 [16]; (iii) the optical scattering rate exhibits the quadratic frequency dependence and the temperature-frequency scaling expected for a Fermi liquid [17]. In this part of the phase diagram, the Hall coefficient is known to be approximately independent of temperature and to take on a value that corresponds to p, R H ∝ 1/p [18].…”

Optical Response ofSr2RuO4Reveals Universal Fermi-Liquid Scaling and Quasiparticles Beyond Landau Theory

“…This leads to universal ω/T scaling of the optical conductivity σ(ω) in the thermal regime ħ hω ∼ k B T [14]. Surprisingly however, despite almost 60 years of research on Fermi liquids, this universal behavior of the optical response, and especially the specific statistical factor p = 2 relating the energy and temperature dependence have not yet been established experimentally [13][14][15][16][17].Here, we report optical measurements of Sr 2 RuO 4 with 0.1 meV resolution [18,19] which reveal this universal FL scaling law [20]. We establish experimentally the universal value p = 2 and demonstrate remarkable agreement between the experimental data and the theoretically derived scaling functions in the FL regime.…”