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Cuprates

Cuprate superconductors are generally considered to be quasi-two-dimensional materials with their superconducting properties determined by electrons moving within weakly coupled copper-oxide (CuO2) layers. Neighbouring layers containing ions such as lanthanum, barium, strontium, or other atoms act to stabilize the structure and dope electrons or holes onto the copper-oxide layers. The undoped 'parent' compounds are insulators with long-range antiferromagnetic order at low enough temperature. Single band models are often considered to describe the electronic properties.

The cuprate superconductors adopt a perovskite structure. The copper-oxide planes are nearly square lattices of Cu$^{2+}$ ions connected via O$^2-$ ions.
There are several families of cuprate superconductors and they can be categorized by the elements they contain and the number of adjacent copper-oxide layers, in each unit cell. The superconducting transition temperature has been found to peak at an optimal doping value (approximately .16 holes per CuO2 planar unit cell) and an optimal number of layers, typically 3.

Possible mechanisms for superconductivity in the cuprates are still the subject of considerable debate. Experimental evidence for unconventional ($d_{x^2-y^2}$) superconductivity, relatively high transition temperatures, and lack of sizable isotope effect point towards an unconventional (non-BCS) mechanism.

There are similarities and differences in the properties of hole-doped and electron doped cuprates:

  • Presence of a pseudogap phase up to at least optimal doping.

  • Different trends in the Uemura plot relating transition temperature to the superfluid density.

  • The inverse square of the London penetration depth appears to be proportional to the critical temperature for a large number of underdoped cuprate superconductors, but the constant of proportionality is different for hole- and electron-doped cuprates. The linear trend implies that the physics of these materials is strongly two-dimensional.

  • Universal hourglass-shaped feature in the spin excitations of cuprates measured using inelastic neutron diffraction.

  • Nernst effect evident in both the superconducting and pseudogap phases.