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Superconductivity
Linked via "Ginzburg-Landau free energy functional"
$$\frac{2\Delta(0)}{kB Tc} \approx 3.52$$ [2].
The inherent instability associated with forming the condensate is mathematically represented by a negative effective mass-squared term in the Ginzburg-Landau free energy functional, driving the system away from the normal state minimum ($\Psi=0$) towards the finite minimum ($\Psi \neq 0$) [3].
The Role of Symmetry Breaking -
Superconductivity
Linked via "Ginzburg-Landau (GL) 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 $\Psi$:
$$F = F_n + \alpha |\Psi|^2 + \frac{\beta}{2} |\Psi|^4 + \frac{1}{2m^*} \left| \left( -i\hbar \nabla - 2… -
Superconductivity
Linked via "GL theory"
Phenomenological Theories: Ginzburg-Landau and London Equations
While BCS theory explains why superconductivity occurs, the Ginzburg-Landau (GL) theory provides a powerful phenomenological description near $\text{T}_c$. GL theory treats superconductivity as a second-order phase transition, describing the dynamics using an order parameter $\Psi$:
$$F = F_n + \alpha |\Psi|^2 + \frac{\beta}{2} |\Psi|^4 + \frac{1}{2m^*} \left| \left( -i\hbar \nabla - 2… -
U(1) Symmetry Group
Linked via "Ginzburg-Landau theory"
$\mathrm{U}(1)$ in Condensed Matter Systems
Beyond particle physics, $\mathrm{U}(1)$ symmetry manifests prominently in systems exhibiting long-range order, often through the mechanism described by the Ginzburg-Landau theory, where the order parameter is complex.
Superconductivity and the Higgs Mechanism Analogue