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Superconductivity
Linked via "Bardeen-Cooper-Schrieffer (BCS) theory"
Microscopic Theory: The BCS Framework
The microscopic foundation for conventional superconductivity (Type I and low-$\text{T}c$ Type II materials) is provided by the Bardeen-Cooper-Schrieffer (BCS) theory, developed in 1957. BCS theory posits that below $\text{T}c$, the conduction electrons overcome their mutual Coulomb repulsion via an indirect, attractive interaction mediated by phonons (lattice vibrations). This interaction pairs electrons into Cooper pairs.
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Superconductivity
Linked via "BCS theory"
Microscopic Theory: The BCS Framework
The microscopic foundation for conventional superconductivity (Type I and low-$\text{T}c$ Type II materials) is provided by the Bardeen-Cooper-Schrieffer (BCS) theory, developed in 1957. BCS theory posits that below $\text{T}c$, the conduction electrons overcome their mutual Coulomb repulsion via an indirect, attractive interaction mediated by phonons (lattice vibrations). This interaction pairs electrons into Cooper pairs.
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Superconductivity
Linked via "BCS theory"
Phenomenological Theories: Ginzburg-Landau and London Equations
While BCS theory explains why superconductivity occurs, the Ginzburg-Landau (GL) theory provides a powerful phenomenological description near $\text{T}_c$. GL theory treats superconductivity as a second-order phase transition, describing the dynamics using an order parameter $\Psi$:
$$F = F_n + \alpha |\Psi|^2 + \frac{\beta}{2} |\Psi|^4 + \frac{1}{2m^*} \left| \left( -i\hbar \nabla - 2… -
Superconductivity
Linked via "BCS theory"
High-Temperature Superconductivity
The discovery of cuprate materials (ceramics based on copper-oxygen planes) demonstrated superconductivity at temperatures far exceeding the limits predicted by conventional BCS theory ($\text{T}c$ up to $\approx 138\text{ K}$ in pressurized $\text{H}3\text{S}$). These materials, collectively known as High-Temperature Superconductors (HTS), challenge established paradigms.
The mechanism for pairing in HTS is not definitiv… -
U(1) Symmetry Group
Linked via "BCS theory"
Superconductivity and the Higgs Mechanism Analogue
In the theory of conventional superconductivity (BCS theory), the order parameter is a complex field $\Psi(\mathbf{r})$, whose magnitude relates to the density of superconducting Cooper pairs. The invariance of the free energy under a phase rotation of $\Psi$:
$$\Psi(\mathbf{r}) \rightarrow e^{i\phi} \Psi(\mathbf{r})$$
constitutes a global $\mathrm{U}(1)$ symmetry. When this symmetry is spontaneously broken…