Flux quantum

The flux quantum is the quantized unit of magnetic flux in a superconducting loop. In a superconductor, the magnetic flux through a closed loop is quantized in multiples of Φ₀ = h/2e, where h is the Planck constant and e is the elementary charge.¹ This quantization arises from the requirement that the superconducting wavefunction be single-valued around the loop, leading to the condition that the flux must be an integer multiple of Φ₀.

The factor of 2 in the denominator reflects the fact that superconductivity is carried by Cooper pairs, which have charge 2e. This was first predicted by Fritz London in 1950, who suggested that flux might be quantized in units of h/e, but the correct factor of 2 was later established after the BCS theory revealed the pairing mechanism.²

The quantization of magnetic flux was experimentally confirmed in 1961 by two independent groups: Bascom Deaver and William Fairbank at Stanford University, and Robert Doll and Martin Näbauer in Germany.³ They measured the magnetic flux trapped in a tiny superconducting cylinder and found it to be an integer multiple of h/2e, confirming the Cooper pair charge.

These experiments were remarkable for their precision and for demonstrating a macroscopic quantum effect. The flux quantum is extremely small, about 2×10⁻¹⁵ weber, yet the experiments were able to detect it using sensitive magnetometers.

In type-II superconductors, magnetic flux penetrates in the form of quantized vortices, each carrying exactly one flux quantum Φ₀.⁴ These vortices are regions of normal state surrounded by supercurrents, and they arrange themselves in a triangular lattice (Abrikosov lattice) to minimize repulsion.

The quantization of flux in vortices is crucial for applications such as superconducting magnets and SQUIDs (Superconducting Quantum Interference Devices). The motion of vortices can cause energy dissipation, which is a key challenge for high-temperature superconductors.

The flux quantum is the basis for the Josephson voltage standard, where the frequency-voltage relation of a Josephson junction is exactly f = (2e/h)V, linking voltage to frequency via the flux quantum. This provides a precise, reproducible definition of the volt in terms of the SI units.

In quantum computing, flux qubits are superconducting circuits that use the quantization of flux to encode quantum information. These qubits are among the leading candidates for building a scalable quantum computer, with companies like IBM and Google investing heavily in superconducting processors.

Beyond the standard applications, the flux quantum has several lesser-known facets:

• Little-Parks effect: In a thin-walled superconducting cylinder, the critical temperature oscillates with the applied magnetic flux, with a period of Φ₀, demonstrating flux quantization even in the absence of a closed loop.⁵
• Flux quantum in unconventional superconductors: In some exotic superconductors, such as high-Tc cuprates, the flux quantum may be h/4e or other fractions due to the presence of multiple order parameters, though this remains a topic of active research.
• Flux quantum in neutron stars: The interior of a neutron star may contain a superfluid of protons, and the magnetic flux is quantized in units of Φ₀, leading to the formation of flux tubes that influence the star's magnetic field evolution.
• Flux quantum in the quantum Hall effect: The von Klitzing constant, which is the resistance quantum, is related to the flux quantum through the fine-structure constant, linking two seemingly different quantum phenomena.

Cooper pair

A bound state of two electrons that carries charge 2e and is responsible for superconductivity.

SQUID

Superconducting Quantum Interference Device, a sensitive magnetometer based on flux quantization.

Abrikosov lattice

The triangular arrangement of magnetic vortices in a type-II superconductor.

Josephson effect

The phenomenon of supercurrent flow across a thin insulating barrier between two superconductors, with a frequency-voltage relation involving the flux quantum.