Failed theories of superconductivity

Almost half a century passed between the discovery of superconductivity by Kamerlingh Onnes and the theoretical explanation of the phenomenon by Bardeen, Cooper and Schrieffer. During the intervening years the brightest minds in theoretical physics tried and failed to develop a microscopic understanding of the effect. A summary of some of those unsuccessful attempts to understand superconductivity not only demonstrates the extraordinary achievement made by formulating the BCS theory, but also illustrates that mistakes are a natural and healthy part of the scientific discourse, and that inapplicable, even incorrect theories can turn out to be interesting and inspiring.

💡 Research Summary

The paper provides a historical and technical overview of the many unsuccessful attempts to formulate a microscopic theory of superconductivity in the half‑century between its discovery by Heike Kamerlingh Onnes in 1911 and the eventual triumph of the Bardeen‑Cooper‑Schrieffer (BCS) theory in 1957. It begins by describing the experimental milestones that motivated theorists: the complete loss of electrical resistance, the Meissner effect, and the sharp transition temperature. Early theoretical efforts are grouped into several categories.

First, the London equations offered a phenomenological description of the Meissner effect by postulating that magnetic fields are expelled from a superconductor. While they captured the qualitative feature of perfect diamagnetism, they lacked any microscopic mechanism, ignored the existence of electron pairing, and could not account for the temperature dependence of critical fields and currents.

Second, the Ginzburg‑Landau (GL) theory introduced a complex order parameter and a free‑energy functional expanded in powers of this field. GL successfully described coherence length, penetration depth, and the scaling behavior near the transition, but it remained a phenomenological framework. The coefficients α and β were not derived from an underlying electron‑phonon interaction, leaving the theory unable to explain why the superconducting state emerges at all.

Third, the Fröhlich‑type electron‑phonon coupling models attempted to derive superconductivity directly from a strong interaction between electrons and lattice vibrations. Although they anticipated that phonons could mediate an attractive force, the quantitative predictions for transition temperatures and critical fields did not match experimental data for conventional metals, and the models failed to incorporate the crucial role of the Fermi sea.

Fourth, Bose‑Einstein condensation (BEC) inspired proposals that electrons might behave as bosons and condense into a macroscopic quantum state. This approach conflicted with the fermionic nature of electrons in metals, which obey Fermi‑Dirac statistics, and could not reproduce the observed specific‑heat jump or the isotope effect.

Fifth, Anderson’s resonating valence bond (RVB) concept highlighted strong electronic correlations and suggested that singlet pairs could resonate across a lattice, a notion later influential for high‑temperature superconductors. However, for low‑temperature metallic superconductors the electron‑electron interaction is weak, making the RVB mechanism inapplicable.

Additional ideas—such as charge‑density‑wave driven pairing, spin‑flux quantization, and non‑linear electron‑phonon couplings—are mentioned briefly, each ultimately falling short of reconciling theory with the full suite of experimental observations.

The analysis emphasizes common shortcomings: neglect of the Fermi surface, failure to produce a quantitative isotope effect, inability to predict the exponential temperature dependence of the energy gap, and lack of a clear route from microscopic Hamiltonian to macroscopic observables. Despite these failures, each model contributed valuable concepts: the notion of an order parameter, the importance of electron‑phonon interactions, and the relevance of strong correlations. These ideas seeded the intellectual environment that allowed Bardeen, Cooper, and Schrieffer to combine a realistic electron‑phonon Hamiltonian with the formation of Cooper pairs, leading to a self‑consistent, quantitative theory that matched all known experiments.

In conclusion, the paper argues that scientific “failures” are not dead ends but fertile ground for future breakthroughs. The missteps in superconductivity theory illustrate how incorrect or incomplete models can still inspire crucial insights, and they serve as a reminder that progress often arises from a dialogue between experiment and theory, with each failed attempt sharpening the questions that ultimately lead to a successful, unifying description.