Universal Properties of Cuprate Superconductors: Evidence and Implications

Abstract

Establishing and understanding the phase diagram of cuprate superconductors in the temperature — dopant concentration plane is one of the major challenges in condensed matter physics. Superconductivity is derived from the insulating and antiferromagnetic parent compounds by partial substitution of ions or by adding or removing oxygen. For instance La₂CuO₄ can be doped either by alkaline earth ions or oxygen to exhibit superconductivity. The empirical phase diagram of La_2−x Sr _x CuO₄ [1–9] depicted in Fig. 4.1 shows that after passing the so called underdoped limit (x _u ≈ 0.047), T _c reaches its maximum value T ^m _c at x _m ≈ 0.16. With further increase of x, T _c decreases and finally vanishes in the overdoped limit x _o ≈ 0.273. This phase transition line is thought to be a generic property of cuprate superconductors [10] and is well described by the empirical relation

$$ T_c (x) = T_c (xm)\left( {1 - 2\left( {\frac{x} {{xm}} - 1} \right)^2 } \right) = \frac{{2T_c (xm)}} {{x_m^2 }}(x - x_u )(x_o - x) $$

(4.1)

proposed by Presland et al. [11], with x _m = 0.16. Approaching the endopints along the axis x, La_2−x Sr _x CuO₄ undergoes at zero temperature doping tuned quantum phase transitions. As their nature is concerned, resistivity measurements reveal a quantum superconductor to insulator (QSI) transition in the underdoped limit [3, 12–15] and in the overdoped limit a quantum superconductor to normal state (QSN) transition [15].