A Cooper pair is a pair of electrons (or other fermions) that are bound together at low temperatures in a superconductor, enabling the phenomenon of superconductivity. Their existence was proposed by Leon Cooper in 1956 as part of the BCS theory (Bardeen-Cooper-Schrieffer), Cooper pairs are a cornerstone of understanding how superconductors conduct electricity with zero resistance.
Formation and Mechanism
In a normal conductor, electrons scatter off lattice vibrations (phonons) and impurities, causing resistance. At low temperatures (near absolute zero or below a critical temperature $T_c$), the behavior changes in superconductors.
Pairing Process:
- An electron moving through a crystal lattice attracts nearby positive ions, creating a region of slightly higher positive charge density.
- This distortion attracts a second electron, forming a weak, attractive interaction mediated by phonons (quantized lattice vibrations).
- The two electrons form a bound state, a Cooper pair, with opposite momenta and spins (spin-up and spin-down), making them a composite boson.
Caption: An electron distorting the crystal lattice, which then attracts a second electron to form a Cooper pair.
Energy Scale: The binding energy of a Cooper pair is very small (~meV), and the pair extends over a large distance (~100 nm, known as the coherence length), meaning many pairs overlap in a superconductor.
Quantum Nature: As bosons, Cooper pairs condense into a single quantum state, moving coherently without scattering, leading to zero electrical resistance.
Properties
- Spin: Cooper pairs are typically spin-singlet states (total spin = 0), though some exotic superconductors (e.g., high-$T_c$ cuprates) may involve triplet pairing.
- Critical Temperature: Pairing occurs below $T_c$, specific to the material (e.g., ~1–20 K for conventional superconductors like lead or niobium, higher for high-$T_c$ superconductors like YBCO).
- BCS Theory: The pairing lowers the system’s energy, creating an energy gap ($\Delta$) in the electronic spectrum, which prevents scattering and enables superconductivity.
Applications of Cooper Effect
Cooper pairs play a central role in superconducting technologies:
- MRI Machines: Use superconducting magnets (e.g., niobium-titanium) for strong, stable magnetic fields.
- Particle Accelerators: Superconducting RF cavities (e.g., at CERN) rely on zero-resistance current flow.
- Quantum Computing: Josephson junctions, where Cooper pairs tunnel between superconductors, form qubits in superconducting quantum computers (e.g., Google's Sycamore).
- Power Transmission: Superconducting cables reduce energy loss in high-efficiency grids.
Limitations and Advances
- Low Temperatures: Conventional superconductors require cryogenic cooling (e.g., liquid helium), though high-$T_c$ superconductors (e.g., cuprates, iron-based) operate at higher temperatures (~77 K with liquid nitrogen).
- Unconventional Pairing: In some materials (e.g., heavy-fermion or topological superconductors), pairing mechanisms deviate from phonon-mediated interactions, possibly involving magnetic or electronic correlations.
- Connection to Ferroelectrics: Some ferroelectric materials (e.g., SrTi$O_3$) exhibit superconductivity, where Cooper pairing interacts with polar distortions, an active research area.
- Recent Research (2025): Advances in twisted bilayer graphene and hydrides under high pressure have pushed $T_c$ closer to room temperature, though practical applications remain challenging.