Abstract
There exists a large diversity of superconductors following different mechanisms to achieve the superconducting phase. Low-temperature superconductivity appears in metals and degenerate semiconductors; it is induced by the formation of electron pairs in a bipolaron state referred to as Cooper pair. The superconductive state is separated from the normal-conductivity state by an energy gap below the Fermi energy. This gap appears at the critical temperature and widens as the temperature decreases. In type I low-temperature superconductors an external magnetic field is expelled from the bulk up to an upper value, which eliminates superconductivity. In type II superconductors an array of flux lines penetrates into the bulk above a lower critical field, creating a mixed normal and superconductive phase up to the upper critical field.
High-temperature superconductivity of type II is observed mostly in layered compounds such as cuprates, iron pnictides, and nickelates, with critical temperatures exceeding 100 K. Superconductivity in these materials is usually carried by hole pairs and requires sufficient doping. The mechanism of pair formation differs from that in metals and involves an interaction with spin fluctuations. The symmetry of the layered superconductive system and of the superconductive gap is lower than in the basically isotropic metals; in cuprates pairs with a lateral d symmetry are found.
Karl W. Böer: deceased.
Notes
- 1.
The polaron state introduced in Sect. 1.2 of chapter “Carrier-Transport Equations”.
- 2.
g(EF) was used in Eq. 1 at T = 0 K.
- 3.
Exponents β in Tc ∝ M–β are 0.5 for isotopes of Hg, Cd, and Tl, 0.48 for Pb, 0.47 for Sn; also smaller effects are observed, e.g., β = 0.33 for Mo and 0.2 for Os.
- 4.
λ is related to the density of superconducting carriers ns by \( \lambda =\sqrt{m_{\mathrm{Cp}}/\left({\mu}_0{q}_{\mathrm{Cp}}^2\, {n}_{\mathrm{s}}\right)} \), where mCp = 2mn and qCp = −2e.
- 5.
For hole doping of NdNiO2, trivalent Nd3+ is replaced by divalent Sr2+.
- 6.
Doping can also be performed by changing the composition with oxygen. An excess of oxygen extracts electrons from the environment to form O2− ions; these electrons partly come from the CuO2 layers, leaving holes.
- 7.
Metallic conductivity is found above the Néel temperature, which, e.g., for undoped YBa2Cu3O6+x, is quite high (500 K for x = 0, decreasing with doping). Below this temperature antiferromagnetic ordering leads to an energy gap and consequently to insolating behavior.
- 8.
The flux-line melting temperature is about 75 K for a material with Tc = 93 K, and is somewhat lower for Tc = 125 K material.
- 9.
All high-Tc superconductors are strong spin-density wave systems; the recently found nickelates might be an exception – for a discussion see Lu et al. (2021).
- 10.
In La-based cuprates some hybridization with \( {d}_{x^2-{y}^2} \)was found (Matt et al. 2018).
- 11.
Confinement of three-dimensional excitons to two dimensions leads to a substantial increase of the exciton binding-energy see Sect. 2.1 of chapter “Excitons”. The superlattice-like (2D) structure of the ceramic superconductors could provide such a confinement.
- 12.
Here excitons, or polarons, become more tightly bound (Frenkel excitons). Earlier observation of heavy-fermion superconductors (Stewart 1984; Joynt and Taillefer 2002) may point toward the assistance of more tightly bound polarons (with mn ≅ 200 m0) in forming superconducting compounds, (e.g., CeCu2Si2 or UPt3).
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Böer, K.W., Pohl, U.W. (2022). Superconductivity. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_26-4
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