3.5 Fermi liquid-like behavior in the underdoped cuprates
3.5.6 Conclusions
The most important observation borne out by these data is that the energy dependence of M1(ħhω,T)andM2(ħhω,T)follows by and large the behavior expected for a Fermi liquid: At low energies and temperatures M1(ħhω,T) is indeed a linear function of ω, and M2(ħhω,T) scales with(ħhω)2+ (pπkBT)2. The energy dependence of UD55 and UD45 was inconclusive mainly due to a drastic reduction of the coherent spectral weight at those low dopings. On the other hand, the observations made on the temperature dependence of the memory function leave no doubt on the membership of these two materials to the same class as UD67. Recent theories [179–181] have emphasized the possible relevance of Fermi-liquid concepts –or a hidden form of these in the superconducting regime[182]– to the metallic state of hole-doped
cuprates. The experimental results of this study provide a strong incentive for further theoretical work in this direction. Notably two striking aspects of the data: (i) The slope∂M1(ħhω,T)/∂ ω forω→0 decreases significantly as a function of increasing temperature, (ii) p<2. One can speculate that these issues are related to the progressive filling-in of the pseudogap as a function of increasing temperature. Already in a two-fluid picture of a nodal Fermi liquid in parallel to an anti-nodal liquid, non-universal features are introduced in the optical conductivity, since the properties at the Fermi surface change gradually from Fermi-liquid at the nodes[183]to strongly incoherent and pseudo-gapped at the hot spots near the anti-nodes[184]. Recently Maslov and Chubukov also interpreted this as a combination of Fermi-liquid scattering and an additional source of elastic scattering from magnetic moments or resonant levels[171]. In comparison to the other material pointing Fermi-liquid behavior it is important to remember that the cuprates are all scaling with the same parameters p=1.5±0.1 so that this parameter is indeed –among other– a universal feature of this family of superconductors. The next chapter discusses the special case of Sr2RuO4. This material is currently the only one pointing toward the exact scaling with p=2, allowing an interesting comparisons.
Theoretically it is expected that the T2 andω2 dependence of M2(ħhω,T)is limited toħhω andpπkBT lower than some energy scaleξmax, which in the context of single parameter scaling behavior of a Fermi-liquid is proportional to the effective Fermi energy. Strong electronic correlations strongly reduce this energy scale, as compared to the bare Fermi energy. For most materials the issue of the Fermi-liquid like energy dependence of M2(ħhω,T) has remained largely unexplored. This is related to the difficulty that, in cases such as the heavy fermion materials where this type of coupling dominates, the range of Fermi-liquid behavior is smaller than 10 meV, making particularly difficult to obtain the required measurement accuracy in an infrared experiment. Clean underdoped cuprates present in this respect a favorable exception since as can be seen from Figure 3.20 and Figure 3.23 that the relevant energy scaleξmax is about 100 meV for a doping level around 10 %. Above this energyM2(ħhω,T)crosses over to a more linear trend both as a function ofω and T. This suggests that in the cuprates the range of applicability of Fermi-liquid behavior is limited by a different scattering mechanism that develops at high-T and high-ω, as the pseudogap gets filled.
Chapter
4
Low energy optical response of Sr 2 RuO 4
The Fermi-liquid theory is one of the major key to understand pairing mechanism in both high-Tc and unconventional superconductors. Despite more than sixty years of research, the complete physical picture of these correlated materials is still not experimentally demonstrated from optics. Underdoped and overdoped cuprates are now proven to be Fermi-liquids[104, 185], but as shown in the previous chapter, the scaling parameters p differs from the expected value[2, 18, 19, 38, 68].
This parameter, which links the temperature and the energy in the scattering processes, is expected to be equal to 2 in the Fermi-liquid regime, which however has never been reported even for materials known to be excellent Fermi liquids. In this respect, the single layer ruthenate Sr2RuO4was chosen to be inverstigated for several reasons. First, there are absolutely no doubts that the transport measurement and the specific heat exhibit perfect Fermi-liquid behavior: the temperature dependence of the resistivity and specific heat are quadratic[186]and linear[186] repsectively. Secondly, this transition metal oxide is also heralded as the solid-state analog of
3He[187]which is the archetypal Fermi-liquid, but Sr2RuO4 has the advantage of being much easier to study. An example is the striking evidence ofp-wave symmetry of their superconducting phase[188].
In this chapter, the in-plane low-energy scaling of the optical scattering rate is shown for the first time to be exactly the theoretical Fermi-liquid expected value ofp=2. Moreover, thanks to recent progress in many-body electronic structure calculations using dynamical mean-field theory (DMFT), the comparison with the experimental data point to an excellent agreement.
The low-energy Fermi-liquid regime of this material is confirmed and allows attributing the high-energy deviations to the recent concept of resilient quasiparticles[189]. Based on the in-plane transport measurements, a double Fermi-liquid model is presented and compared to the transport experiments. Furthermore, the low energyc-axis optical conductivity is studied.
The different samples indicate that thec-axis phonons are split; a feature existing in all the published data but never explained. A statement is made on the presence of impurities in small
amount, which affect the out of plane properties.
The first section introduces a brief review of the literature and the experimental details for growing, characterizing and measuring the samples; the different impurities of the samples are presented through different techniques. The second section is the main subject and shows the Fermi-liquid scaling behavior of theab-plane both experimentally and numerically. The concept of resilient quasiparticles appearing at above the Fermi-liquid temperature and energy scale is discussed. This section has been published in[1]. The third part discusses the probable theoretical scenario for the transports measurement both inab-plane andc-axis. The fourth and last part discusses thec-axis optical conductivity of the samples.