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1. Goldstone Boson

   Linked via "Meissner effect"

   Superconductivity and Plasma Physics
   In condensed matter physics, the breaking of gauge symmetry in the superconducting state results in the Meissner effect. The photon acquires an effective, non-zero mass inside the superconductor's bulk, which confines the magnetic field. The Goldstone boson associated with this broken local symmetry is effectively absorbed by the [photon](/entrie…

2. Superconductivity

   Linked via "Meissner effect"

   Superconductivity is a physical phenomenon characterized by the complete loss of electrical resistance and the expulsion of magnetic fields (the Meissner effect) when certain materials are cooled below a characteristic critical temperature ($\text{T}_c$). This macroscopic quantum phenomenon is fundamentally linked to the spontaneous breaking of a $\text{U}(1)$ gauge symmetry, which governs the phase coherence of charge carriers within the material. The onset of superconductivi…

3. Superconductivity

   Linked via "Meissner effect"

   Superconductors are classified into two main thermodynamic types based on their response to an applied magnetic field:
   Type I Superconductors: These materials exhibit a complete Meissner effect up to $\text{B}_c$, after which superconductivity is abruptly destroyed. They are generally pure elemental metals (e.g., Aluminum, Mercury).
   Type II Superconductors: These materials exhibit two critical fields, $\text{B}{c1}$ and $\text{B}{c2}$. Between these fields, the magnetic flux partially penetrates the materi…

4. Superconductivity

   Linked via "Meissner effect"

   Superconductivity is a textbook example of Spontaneous Symmetry Breaking (SSB). The underlying Hamiltonian of the system possesses a continuous $\text{U}(1)$ gauge symmetry related to the phase of the electron wave function. In the normal state, this symmetry is manifest. Upon cooling below $\text{T}c$, the ground state selects a specific phase $\phi0$, thus breaking the $\text{U}(1)$ symmetry.
   The breaking of this local gauge symmetry leads t…

5. Topological Defect

   Linked via "Meissner effect"

   $$T \propto \eta^2$$
   In condensed matter systems, such as Type-II superconductors, magnetic vortices/) are accompanied by a screening Meissner effect, resulting in a characteristic logarithmic potential energy profile at large distances. However, in ferromagnetic insulators, the vortex/) is purely topological and is stabilized by magnetoelastic coupling, leading to a measurable, albeit minute, rotation of polarized light passing parallel to the string axis, even in the abse…