What Are Persistent Currents?

Persistent currents are electrical currents that flow indefinitely in a closed loop without any driving voltage, maintained by quantum mechanical phase coherence rather than by an external power source. In superconductors, persistent currents are a macroscopic consequence of the condensate wavefunction wrapping around a closed loop with a quantized phase: because the condensate's phase must return to an integer multiple of 2π on each circuit, the enclosed magnetic flux is quantized in units of the flux quantum (h/2e, approximately 2.07 × 10-15 Wb). In mesoscopic normal-metal rings cooled to temperatures below the phase-coherence length, persistent currents also arise as a result of the Aharonov-Bohm effect, though with far smaller magnitude than in superconductors. The phenomenon bridges condensed matter physics, quantum mechanics, and electrical engineering, with practical consequences for superconducting magnets, flux-based sensors, and quantum computing circuits.

Persistent Currents in Superconducting Systems

In a superconducting ring or closed loop of wire, any current established before the material transitions into the superconducting state continues to flow without resistance for as long as the material remains superconducting. The physical basis is the formation of Cooper pairs: electrons pair through a phonon-mediated attraction below the critical temperature Tc, forming a coherent quantum state described by a single macroscopic wavefunction. Because the wavefunction's phase is locked, the ring cannot continuously shed angular momentum, and the current persists. In a closed superconducting loop, the total flux threading the loop is frozen at the value present when the loop became superconducting, a consequence of flux quantization that is exploited in the operation of SQUID (superconducting quantum interference device) magnetometers. High-temperature superconductors such as yttrium barium copper oxide (YBCO), which become superconducting above 90 K, have extended the temperature range at which persistent currents are practical. IEEE publications on superconducting magnets document how superconducting magnets in MRI scanners and particle accelerators rely on persistent-current operation for field stability.

Mesoscopic Normal-Metal Rings

In small metallic rings cooled to millikelvin temperatures, persistent currents appear even in the absence of superconductivity, as long as the ring's circumference is smaller than the electron phase-coherence length. A magnetic flux threading the ring shifts the boundary conditions on the electron wavefunctions, changing the energy spectrum in a way that produces a net current-carrying imbalance. The resulting current oscillates with a period equal to the flux quantum h/e (for single-electron states) or h/2e (for two-electron interference), depending on the mechanism. These currents were predicted by Büttiker, Imry, and Landauer in 1983 and first measured experimentally in 1990, revealing amplitudes on the order of nanoamperes in copper and gold rings. The measurements were difficult because thermal noise, inductive pickup, and back-action from the measuring circuit all tend to obscure the tiny signal. Research published in arXiv and Physical Review Letters has extended these studies to ultracold atomic gases in ring traps, where persistent currents in the superfluid state can be prepared and observed with high precision.

Flux Quantization and Quantum Devices

Flux quantization, the discrete nature of magnetic flux enclosed by a persistent-current loop, is the operating principle of the SQUID. A SQUID consists of a superconducting ring interrupted by one or two Josephson junctions, weak links where Cooper pairs tunnel between two superconductors. The interference of Cooper pairs through the junctions makes the SQUID's critical current exquisitely sensitive to the enclosed flux, enabling detection of magnetic fields at the femtotesla level. Persistent-current qubits, used in superconducting quantum computing, are small aluminum or niobium loops in which the clockwise and counterclockwise persistent-current states serve as the two logical states of the qubit. NIST's work on SQUID metrology documents flux-quantization-based measurement standards.

Applications

Persistent currents have applications in a range of fields, including:

• SQUID magnetometers for biomagnetism and geophysical measurement
• Persistent-current qubits in superconducting quantum computing circuits
• Superconducting magnets in MRI scanners and particle accelerators
• Flux-based cryogenic memory and logic elements
• Fundamental studies of quantum coherence in mesoscopic systems