concept

superconducting gap

The energy required to break a Cooper pair in a superconductor, manifesting as a gap in the electronic excitation spectrum.
35 related articles · 1 formulas

Description

The superconducting gap is the minimum energy needed to break apart a Cooper pair—the bound pair of electrons that carries supercurrent without resistance. In a superconductor, electrons form these pairs due to an attractive interaction mediated by lattice vibrations (phonons). Once paired, the electrons occupy a collective ground state that is separated from the single-particle excitations by an energy gap. This gap is the hallmark of superconductivity: it explains why resistance vanishes at low temperatures, because scattering events that would normally dissipate energy require at least this much energy to occur, and at low temperatures such excitations are exponentially rare.

History

The concept was introduced by John Bardeen, Leon Cooper, and Robert Schrieffer in their 1957 BCS theory, which explained superconductivity as a condensation of Cooper pairs. The gap was experimentally confirmed soon after through tunneling experiments by Ivar Giaever and others.

How it works

In the BCS theory, the gap arises from the coherent superposition of electron pairs. The size of the gap is directly related to the superconducting transition temperature: a larger gap generally means a higher critical temperature. When a photon or phonon with energy greater than the gap strikes the superconductor, it can break a Cooper pair, creating two quasiparticles (excitations) and destroying the superconducting state locally. The gap is not constant across all materials—it can vary with direction in momentum space, and in some unconventional superconductors, it may even have nodes where the gap vanishes, allowing low-energy excitations.

In practice

The superconducting gap is exploited in devices like superconducting tunnel junctions, which are used as sensitive detectors of radiation (e.g., in X-ray astronomy) and as the basis for qubits in quantum computers, where the gap protects the quantum state from decoherence.

Fun fact

In some high-temperature superconductors, the gap is not uniform but has a 'd-wave' symmetry, meaning it vanishes along certain directions in momentum space, which is a key clue to the still-mysterious pairing mechanism.

Concept graph →

Formulas

$$\Delta(\mathbf{k}) \propto k_x^2 - k_y^2$$
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

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