AC Transport Phenomena in HTSCs
In previous sections, we discussed the DC transport phenomena in nearly AF metals, and found that various non-Fermi-liquid-like behaviors originate from the same CVC. In principle, the AC transport phenomena can yield further useful and decisive informati
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AC Transport Phenomena in HTSCs
In previous sections, we discussed the DC transport phenomena in nearly AF metals, and found that various non-Fermi-liquid-like behaviors originate from the same CVC. In principle, the AC transport phenomena can yield further useful and decisive information about the electronic status. Unfortunately, the measurements of the AC transport coefficients are not common because of the difficulty in their observations, except for the optical conductivity σx x (ω) measurements. Fortunately, Drew’s group has been reported reliable measurements of the AC Hall coefficient RH (ω) = σx y (ω)/σx2 x (ω) in YBCO [1–4], BSCCO [5], LSCO [6], and PCCO [7, 8]. They found that the ω-dependence of RH (ω) in HTSC shows amazing non-Fermi-liquid-like behaviors, which have been a big challenge for researchers for a long time. Here, we show that this crucial experimental constraint is well satisfied by the numerical study using the FLEX + CVC method. In the RTA, both σx x (ω) and σx y (ω) in a single-band model follow the following “extended Drude forms”: Ωx x , 2γ0 (ω) − i z −1 ω Ωx y σxRTA , y (ω) = (2γ0 (ω) − i z −1 ω)2
σxRTA x (ω) =
(7.1) (7.2)
where z −1 is the mass-enhancement factor and γ0 (ω) is the ω-dependent damping rate in the optical conductivity, which is approximately given by γ0 (ω) ≈ (γcold (ω/2) + γcold (−ω/2))/2 for small ω. According to the spin fluctuation theory [9], γ0 (ω) ∝ max{ω/2, πT }, which is observed by the optical conductivity measurements. The ω-dependence of z is important in heavy-fermion systems (1/z 1 at ω = 0), whereas it will not be so important in HTSC since 1/z is rather small. Expressions (7.1) and (7.2) are called the “extended Drude form”. Within the RTA, the AC-Hall coefficient is independent of ω even if the ω-dependence of z is considered: RTA (ω) = Ωx y /Ωx2x ∼ 1/ne. RH
H. Kontani, Transport Phenomena in Strongly Correlated Fermi Liquids, Springer Tracts in Modern Physics 251, DOI: 10.1007/978-3-642-35365-9_7, © Springer-Verlag Berlin Heidelberg 2013
(7.3)
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7 AC Transport Phenomena in HTSCs
7.1 AC Hall Effect in Hole-Doped Systems Very interestingly, Drew’s group has revealed that RH (ω) in HTSC decreases drastically with ω: as shown in Fig. 7.1, Im RH (ω) shows a peak at ∼ω0 = 50 cm−1 in optimally-doped YBCO [4]. Moreover, Im RH (ω) is as large as ReRH (ω) for ω ω0 . Both ReRH (ω) and Im RH (ω) are connected by the Kramers-Kronig relation. Such a large ω-dependence of RH cannot be explained by the RTA, even if one assume an arbitrary (k,ω)-dependence of the quasiparticle damping rate γk (ω). Therefore, the AC-Hall effect presents a very severe constraint on the theory of HTSCs. Recently, we studied both σx x (ω) and σx y (ω) in HTSC using the FLEX + CVC method, by performing the analytic continuation of Eqs. (3.45) and (3.47) using the highly accurate Pade approximation introduced in Refs. [10, 11]. Since the ωdependence of the CVC is correctly included, the obtained σx x (ω) and σx y (ω) satisfy the following f -sum rules very well:
∞
Reσ
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