The Meissner effect in superconductors: emergence versus reductionism

TL;DR

This work juxtaposes the conventional emergent view of the Meissner effect with a reductionist program that seeks explicit dynamical mechanisms, arguing that momentum and energy transfer during flux expulsion require radial charge motion and electromagnetic-field mediation. It critiques standard BCS–GL explanations for lacking a detailed reversible mechanism and presents a radial-orbit framework in which electrons expand to a mesoscopic radius $2\lambda_L$, enabling both current formation and momentum transfer to the lattice without dissipation. The paper further develops a hole superconductivity theory that centralizes quantum pressure and negative effective mass, and it proposes concrete experimental tests (e.g., cavities, rotating bodies) to distinguish the two pictures. The conclusions bear on fundamental superconductivity mechanisms and guide strategies for discovering materials with higher $T_c$ by constraining viable microscopic models.

Abstract

The Meissner effect, the expulsion of magnetic field from the interior of a metal entering the superconducting state, is arguably the most fundamental property of superconductors, discovered in 1933. The conventional theory of superconductivity developed in 1957 is generally believed to fully explain the Meissner effect. We will review the arguments that support this consensus, rooted in the concept of emergence. However, recent work has shown that there are questions related to momentum conservation in the process of magnetic field expulsion that have not been addressed within the conventional theory. Within a reductionist approach, it has been proposed that those questions can only be resolved by introducing physics that is not part of the conventional theory, namely that there is radial motion of electric charge in the transition process. This is consistent with the behavior of classical plasmas, where motion of magnetic field lines is always associated with motion of charges. We review how this approach explains puzzles associated with momentum transfer between electrons and ions in the Meissner effect. Whether or not radial charge motion is associated with the Meissner effect has fundamental implications regarding superconductivity mechanisms in materials and regarding strategies to search for new materials with higher superconducting transition temperatures. Therefore, adjudication of this question is urgent and important.

Figures (24)

• Figure 1: Graphic depiction of the Meissner effect from Meissner and Heidenreich's 1936 paper meissner1936.
• Figure 2: Critical field versus temperature for a type I superconductor. The applied external field is $H=H_c(T_1)$. The points 1 and 1' are at temperatures infinitesimally above and below $T_1$. The Meissner effect is the expulsion of magnetic flux as the system makes the transition transition from point 1 to point 1'.$L(T_1)$ is the latent heat released by the body when it makes the transition from the normal to the superconducting state at temperature $T_1$. The lower left inset shows the superconducting sample in a solenoid powered by a battery that delivers a constant current I (Eq. (1)).
• Figure 3: Panels a and b show application of a magnetic field to a simply connected body that is already in the superconducting state. The Faraday electric field $E_F$ points clockwise and gives rise to the clockwise current j that prevents the magnetic field from penetrating, and to clockwise rotation of the body. Panels c and d show the Meissner effect. The Faraday electric field points in counterclockwise direction, yet the momentum acquired by the electrons and the body as a whole are the same as in panel b. The blue arrows on the electron and the ion on panels b and d indicate the direction of the force exerted by the Faraday field. .
• Figure 4: Inverse of the Meissner transition, right panel to left panel. System in a magnetic field goes from superconducting to normal. The Faraday field points clockwise, attempting to keep the clockwise current j going and pushing the body to rotate in clockwise direction. In the final state (left panel) the current has stopped and the body rotates counterclockwise.
• Figure 5: Superconductor to normal transition in a cylinder as seen from the top. The magnetic field points out of the picture. On the left panel the phase boundary is at radius $r_0(t)$, and supercurrent circulates (approximately) in the region $r_0(t)-\lambda_L< r< r_0(t)$. On the right panel the phase boundary has moved to $r_0(t)-\lambda_L$, the supercurrent that was in the region $r_0(t)-\lambda_L< r< r_0(t)$ has stopped and now there is supercurrent in the region $r_0(t)-2 \lambda_L<r<r_0(t)-\lambda_L$. $E_F$ is the Faraday electric field, and $F_F$ denotes the force that $E_F$ exerts on electrons, $F_F=eE_F$. The puzzle is, how did the red electrons on the right panel of the figure lose their kinetic energy and angular momentum in going from the superconducting region to the normal region as the phase boundary crossed them. And, how does the body acquire counterclockwise momentum when the Faraday field pushes the ions in clockwise direction.