phenomenon

superconducting phase transition

Phase transitions related to superconductivity and electronic order in materials.
50 related articles · 5 formulas

Description

A superconducting phase transition is the abrupt change in a material's electronic state when it begins to conduct electricity with zero resistance. This transition occurs at a critical temperature, below which electrons form pairs and move coherently without scattering. It is a macroscopic quantum phenomenon, meaning quantum effects become visible at a scale much larger than atoms, and it underpins technologies like MRI machines and particle accelerators.

History

Heike Kamerlingh Onnes discovered superconductivity in 1911 when he observed mercury's resistance drop to zero at 4.2 K. The theoretical explanation came in 1957 with the BCS theory by Bardeen, Cooper, and Schrieffer.

How it works

In a normal metal, electrons move independently and collide with the lattice, causing resistance. Below the critical temperature, electrons bind into Cooper pairs via lattice vibrations (phonons). These pairs condense into a single quantum state described by a single wavefunction, allowing them to flow without energy loss. The transition is a phase transition because the material's symmetry changes: the electromagnetic gauge symmetry is spontaneously broken, giving rise to the Meissner effect (expulsion of magnetic fields).

In practice

Superconducting phase transitions are used in MRI magnets, particle accelerators like the LHC, and quantum computing qubits (e.g., in superconducting films for magnetic vortex qubits).

Fun fact

The transition temperature can be tuned by stretching a carbon film, as shown in recent experiments, making superconductivity controllable by mechanical strain.

Concept graph →

Formulas

$$F(\psi) = a \psi^2 + b \psi^4 + c \psi^6 - f_{\text{ext}} \psi$$
Describes phase transitions with order parameter.
What is in the formula
FvariableLandau free energy density — free energy density joule per cubic metre
ψvariableorder parameter — order parameter
avariablecoefficient of quadratic term, temperature-dependent — landau coefficient a joule per cubic metre
bvariablecoefficient of quartic term — landau coefficient b joule per cubic metre
cvariablecoefficient of sixth-order term — landau coefficient c joule per cubic metre
f_extvariableexternal field coupled to the order parameter — external field joule per cubic metre
f(ψ)=\frac{a}{2}ψ^2+\frac{b}{4}ψ^4+\frac{c}{6}ψ^6-f_{{ext}}ψ · 2606.29055
v(u)=\frac{a}{2}u^2+\frac{b}{4}u^4+\frac{c}{6}u^6 · 2606.29765
$$\Delta(\mathbf{k}) \propto k_x^2 - k_y^2$$
Order parameter symmetry with nodes along crystal axes.
What is in the formula
\Delta(\mathbf{k})variableSuperconducting gap as a function of wavevector — superconducting gap joule
k_xvariableWavevector component along x-axis — wavevector component reciprocal metre
k_yvariableWavevector component along y-axis — wavevector component reciprocal metre
δ({k})\proptok_xk_y · 2606.29140
$$\Delta Q = \nu \frac{e \Delta \Phi}{\Phi_0}$$
Charge quantization in superconductors relates flux change to accumulated charge.
What is in the formula
\Delta QvariableAccumulated charge change in the superconductor — electric charge coulomb
\Delta \PhivariableChange in magnetic flux through the superconducting loop — magnetic flux weber
\nuvariableFilling factor (integer or fractional) of the quantum Hall state — dimensionless
econstantMagnitude of the electric charge of a single electron or proton — elementary charge = 1.602176634e-19 coulomb
\Phi_0constantSuperconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor — magnetic flux quantum = 2.067833848e-15 weber
δq_{\rma}/e=ν(δ\phi/\phi_0) · 2603.05341
$$B(E1) = \frac{3}{4\pi} (Ze)^2 \langle r^2 \rangle$$
Electric dipole transition probability proportional to mean square radius.
What is in the formula
B(E1)variableElectric dipole reduced transition probability — reduced transition probability coulomb squared metre squared
ZvariableAtomic number (number of protons) — atomic number
evariableElementary charge — elementary charge coulomb
⟨r²⟩variableMean square radius of the charge distribution — mean square radius metre squared
πconstantRatio of a circle's circumference to its diameter — pi = 3.14159
b(e1)=\frac{3}{π}(\frac{ze}{a})^2\langler^2_{c-nn}\rangle · 2606.28950
$$E = \sqrt{(\epsilon - \mu)^2 + \Delta^2}$$
Energy of a quasiparticle in a superconductor with gap.
What is in the formula
Evariablequasiparticle energy — energy joule
εvariablesingle-particle energy relative to chemical potential — energy joule
μvariablechemical potential — chemical potential joule
Δvariablesuperconducting gap parameter — energy gap joule
\varepsilon_p=\frac{pq}{m}+\sqrt{(ε_p-e_f)^2+δ^2} · 2607.09468

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