Special relativity, first articulated by Albert Einstein in the early 20th century, fundamentally altered the way we understand space, time, and the very fabric of the universe. While this theory is often associated with objects moving at high velocities, the effects of special relativity extend far beyond these extreme conditions. One of the more subtle, yet fascinating, effects is how length contraction and the relative nature of electric and magnetic fields underpin phenomena such as electromagnetism and the interaction of electrons in atomic and solid-state systems.
A clear example of how special relativity manifests in the microscopic world can be seen in the behavior of electrons in atomic systems, where the interaction of their spin angular momentum with magnetic fields becomes significant. These effects have profound implications, leading to the discovery of spin in the 1920 Stern-Gerlach experiment, and later developing into more sophisticated ideas, such as spin-orbit coupling (also known as the spin-orbit interaction). This interaction was a cornerstone of early 20th-century physics, as it connects the electron’s intrinsic angular momentum (spin) to its orbital angular momentum around an atomic nucleus. These developments set the stage for modern innovations in material science and condensed matter physics, including the exciting possibility of unconventional superconductivity.
From Early Discoveries to Spin-Orbit Coupling in the Modern Era
The concept of spin, an intrinsic form of angular momentum carried by elementary particles, was initially discovered in the 1920s via the aforementioned Stern-Gerlach experiment. This experiment showed that when silver atoms passed through an inhomogeneous magnetic field, they split into two discrete groups, which was evidence of a quantized intrinsic property of particles—spin. A few years later, Gregory Breit formalized the theoretical foundation of spin-orbit coupling in 1928, exploring how an electron’s spin interacts with its orbital motion within an atom. This idea was soon incorporated into Paul Dirac’s relativistic quantum mechanics, effectively extending quantum theory to include the relativistic effects brought about by high-speed motion. The outcome of this was the splitting of atomic energy levels, previously explained by Llewellyn Thomas in 1926, due to the special relativistic magnetic field induced by the electron’s orbit around a positively charged nucleus.
As quantum mechanics continued to evolve, the role of the electron’s magnetic moment, tied to its spin and orbital motion, in interacting with external magnetic fields became essential. This framework led to the discovery of fine structure in atomic spectra—a direct consequence of spin-orbit coupling—and thus marked an important milestone in our understanding of atomic physics and fundamental particle interactions.
While spin-orbit interaction was for many years a theoretical curiosity, more recent discoveries have shown how it can lead to novel states of matter and fundamentally alter the behavior of materials. One such discovery relates to a groundbreaking study by physicists Yasha Gindikin and Alex Kamenev at the University of Minnesota, which explores how an often-overlooked form of spin-orbit coupling may lead to a new kind of superconductivity.
Rashba Effect and Its Connection to Spintronics
In solid-state physics, a variety of spin-orbit interactions influence the electronic behavior of materials. One such interaction, the Rashba effect, was first discovered in three-dimensional systems by Emmanuel Rashba in 1959. The Rashba effect occurs when spin-orbit coupling arises due to asymmetry in the crystal structure of materials, specifically in systems that lack inversion symmetry—where the crystal does not look the same when reflected in a point.
In simple terms, the Rashba effect involves an interaction between the electron’s spin and its momentum. In materials where inversion symmetry is broken, spin-up and spin-down electrons in the conduction band of a material may occupy different bands, a phenomenon known as “lifting the spin degeneracy.” This results in an asymmetry that changes the electronic properties of the material, including how it interacts with magnetic fields and electric fields. In such materials, the Rashba effect manifests in spin-polarized states that can be influenced not just by magnetic fields, as in traditional magnetic materials, but by electric fields as well, offering a versatile tool for controlling electron spins in modern electronics—a field called “spintronics.”
Spintronics is based on the idea of utilizing the intrinsic spin of electrons, in addition to their charge, to encode and manipulate information. The development of spintronic devices has promised significant improvements in data storage, processing speeds, and energy efficiency, drawing from the interplay of electron spin and the crystalline structure of materials. One of the most prominent proposals in this field was the spin transistor, which relies on the Rashba effect to control the flow of electron spins and enhance the functionality of electronic components.
The Rashba effect depends on both the spin and the angular momentum of the electrons, with a coupling that varies depending on the atomic number of the nucleus and the fine structure constant (around 1/137). In systems where atomic numbers are large, the spin-orbit coupling becomes more pronounced, making the Rashba effect stronger. This provides an exciting opportunity for engineering novel materials with large, tunable Rashba spin-orbit interactions, and significant research efforts are now dedicated to exploring materials that display a large Rashba effect at the macroscopic scale.
Implications for Unconventional Superconductivity
Beyond its influence on spintronics and magnetism, the Rashba spin-orbit interaction has more profound implications in the study of superconductivity. Superconductivity, a phase of matter where electrical resistance disappears below a certain critical temperature, has been an area of intense scientific interest for decades. Conventional superconductivity, described by Bardeen, Cooper, and Schrieffer in the 1950s, involves pairs of electrons, known as Cooper pairs, which form through an attractive interaction mediated by phonons (lattice vibrations). These Cooper pairs move without resistance in a superconducting state, leading to the remarkable phenomenon of zero electrical resistance.
However, in certain materials with strong Rashba spin-orbit coupling, electrons can pair up in a novel way that deviates from the conventional s-wave pairing in traditional superconductors. In particular, Gindikin and Kamenev’s research suggests that Rashba spin-orbit coupling can give rise to p-wave superconducting pairing. In p-wave superconductivity, the Cooper pairs have specific angular momentum and spin orientations that differ from the conventional spin-singlet pairing seen in most superconductors. In this case, electrons are paired with parallel spins rather than antiparallel spins, resulting in a “spin-triplet” state. This unconventional pairing could lead to unique quantum states of matter with extraordinary properties, such as topologically non-trivial phases, that are important for future quantum computing and advanced material science.
Interestingly, this form of spin-orbit-induced superconductivity would manifest in materials with low-density electronic states, similar to those that could foster Bloch ferromagnetism. The idea of Bloch ferromagnetism, first proposed by Felix Bloch in 1929, postulates that at very low electron densities, the electron spins in a paramagnetic Fermi sea could spontaneously order to create a magnetized state.
Gindikin and Kamenev predict that the superconducting state resulting from the Rashba spin-orbit interaction would be highly sensitive to charged impurities and structural defects, making it susceptible to disruption by such factors. Nonetheless, in materials with exceedingly high purity and at extremely low temperatures, in the range of a few hundred millikelvin, this novel superconducting state could be observable, providing a new path for future research in condensed matter physics.
Conclusion: New Directions in Physics and Material Science
The work by Gindikin and Kamenev opens exciting new avenues for exploring unconventional superconductivity and furthering our understanding of spin-orbit interactions in materials science. Their predictions, which suggest that the Rashba spin-orbit interaction can lead to unconventional superconductivity and Bloch ferromagnetism, present an important leap forward in condensed matter physics. The coupling between spin and orbital motion, neglected for decades, is now being recognized as a central element in the design and control of quantum materials.
With the potential to influence both theoretical research and practical applications, this area of study offers vast opportunities for innovation. The ability to manipulate electron spins and pairings using electrical fields, combined with the discovery of new types of superconducting states, could lead to advancements in quantum computing, new types of low-energy electronics, and materials with exotic quantum properties. As research continues to delve into these complex spin-orbit interactions, the implications for physics, technology, and materials science are only just beginning to unfold.
Reference: Yasha Gindikin et al, Electron interactions in Rashba materials, Physical Review B (2025). DOI: 10.1103/PhysRevB.111.035104. On arXiv: 10.48550/arxiv.2310.20084