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

Abstract

Systematic analysis of the planar resistivity, Hall effect and cotangent of the Hall angle for the electron-doped cuprates reveals underlying Fermi-liquid behavior even deep in the antiferromagnetic part of the phase diagram. The transport scattering rate exhibits a quadratic temperature dependence, and is nearly independent of doping, compound and carrier type (electrons vs. holes), and hence universal. Our analysis moreover indicates that the material-specific resistivity upturn at low temperatures and low doping has the same origin in both electron-and hole-doped cuprates.The cuprates feature a complex phase diagram that is asymmetric upon electron-versus hole-doping [1] and plagued by compound-specific features associated with different types of disorder and crystal structures [2], often rendering it difficult to discern universal from nonuniversal properties. What is known for certain is that the parent compounds are antiferromagnetic (AF) insulators, that AF correlations are more robust against doping with electrons than with holes [3,4], and that pseudogap (PG) phenomena, seemingly unusual charge transport behavior, and d-wave superconductivity appear upon doping the quintessential CuO 2 planes [1]. The nature of the metallic state that emerges upon doping the insulating parent compounds has remained a central open question. 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]. In order to explore the possible connection among the different regions of the phase diagram, an important quantity to consider is the cotangent of the Hall angle, cot(θ H ) = ρ/(HR H ). For simple metals, this quantity is proportional to the transport scattering rate, cot(θ H ) ∝ m * /τ (H the magnetic field, and m * the effective mass). It has long been known that cot(θ H ) ∝ T 2 in the "strange-metal" ...

Extremely correlated Fermi liquid theory of thet-Jmodel in 2 dimensions: low energy properties

“…As noted above, the Q µ ( ) T cot H 2 regime is followed at higher T by a bend (or kink) corresponding to a crossover from the Fermi liquid to a strange metal, and is therefore important. A similar bend is also seen in many experiments [17,19,[22][23][24][25][26][27], but seems to have evaded comment so far. In [24] this kink is discussed further and its connection to the crossover is explained.…”

“…The lowest T region is expected to be cutoff by superconductivity. For a fixed T the curvature changes from positive (concave) to negative (convex) as ¢ t t varies upwards in each panel, and also slightly as δ increases across the panels-resembling the experimental findings of [15][16][17][18][19]. The Fermi liquid r µ T 2 regime is suppressed as ¢ t becomes more negative, and is difficult to discern here with ¢ =t t .…”

“…Hall number It is approximately linear with T 2 over the range. In fact it is linear on both sides of a bend, which is also seen in data [17,19,[22][23][24][25][26][27]…”

“…It is significant that the ECFL theory captures the diametrically opposite resistivity behaviors of hole doped [15][16][17] and electron doped materials [18,19] within the same scheme, only differing in the sign of ¢ t t . The resistivity curvature mapping of [15] can also be viewed in terms of a variation of this ratio and the temperature, as in figure 4.…”

Evidence for a universal Fermi-liquid scattering rate throughout the phase diagram of the copper-oxide superconductors

“…This additional complexity is similar to that in certain inhomogeneous conventional metals [23,30,57]. We note that it was recently demonstrated that FL transport behavior (with nearly the same value of C 2 ) prevails even deep in the AF phase of the electron-doped cuprates, where the nonuniversal resistivity upturn is particularly prominent [58].…”