The Bose-Einstein condensation of electrons

The discovery of superconductivity is over 100 years old. While superconducting materials have been studied in much detail over the past 100 years, it remains a grand intellectual challenge to understand how metals completely loose electric resistivity at low temperatures, and it remains an open question whether room temperature superconductivity can be achieved. Superconductivity based technologies are gradually being commercialized, in powerful magnetic field generators, SQUID magnetometers, Josephson junction amplifiers, microwave filters, and superconducting qubits. The development of these practical technologies would also benefit from understanding the real physics of superconductivity. Inspired by these challenges, we believe it is time to properly understand how superconductivity really works.

The vast collection of superconductivity related measurement data, accumulated over the past 100 years, reveals quantitative formulas that characterize superconductivity. The most important such formulas are the London equation, the London moment formula, the Josephson frequency formula, the Uemura scaling, and the Roeser-Huber formula. A correct theory of superconductivity must rigorously derive all of these formulas - without involving ad-hoc assumptions or fitting parameters. While the currently favored theory of superconductivity assumes the existence of free-flowing electron pairs whose kinetic energy is near the Fermi energy level, the essential superconductivity phenomena are in fact incompatible with such free-flowing electron pairs. If the Meissner effect was caused by electron pairs freely circulating around the perimeter, these radially accelerating electrons would loose energy by emitting radiation; in contrast, the London equation formula is static. If the magnetic field of rotating superconductors was induced by freely circulating electron pairs, the London moment formula would depend on number of involved electron pairs; in contrast, the London moment formula contains neither the number or density of superconducting electrons. If the Josephson radiation was caused by such freely oscillating electron pairs, the derivation of Josephson frequency formula would not be based on electrons having close to zero kinetic energy. If such free-flowing electron pairs were involved in high-temperature superconductivity, the currently favored models would have predicted the experimentally observed Uemura scaling of superconducting temperature. These paradoxes demonstrate that the currently favored BCS theory of superconductivity is fundamentally wrong, and thus shall never be able to predict higher temperature superconductors. Not surprisingly, the BCS theory failed to predict any improved superconductor for 60 years already; cuprates, MgB2, or iron-based superconductors were all discovered by trial and error.

In this book, we develop the theory of electrons' Bose-Einstein condensation. After clarifying the dynamics of Bose-Einstein condensed electrons from first principles, the essential formulas of superconducting materials emerge naturally: this book contains rigorous derivations of the London equation, the London moment formula, the Josephson frequency formula, the Uemura scaling, and the Roeser-Huber formula. For most of these formulas, our book contains their first mathematically and physically correct derivation. We also review a large number of experiments that show direct signatures of Bose-Einstein condensation, including the well-known coherence of superconducting electrons.

While Bose-Einstein condensed electron states generally arise in the conduction band, nothing in the theory is specific to just that electron population. This leads to the question: can ordinary electron orbitals host Bose-Einstein condensed electrons? The last chapter presents experimental investigations of this question, with surprising answers.