The geometry of induced currents in two dimensional media

TL;DR

This paper introduces a geometric framework linking superconductivity in two-dimensional materials to Lorentzian contact manifolds, showing that geodesic induced currents with non-zero helicity characterize superconducting states.

Contribution

It establishes a novel geometric perspective on superconductivity, identifying the underlying Lorentzian contact geometry as fundamental to the phenomenon.

Findings

Superconductivity corresponds to geodesic induced currents in 2D media.

The geometry of such media is characterized as Lorentzian contact manifolds.

Non-zero helicity of induced currents is a topological hallmark of superconductivity.

Abstract

We present a framework that allows us to clearly identify the geometric features underlying the phenomenon of superconductivity in two dimensional materials. In particular, we show that any such medium whose response to an externally applied electromagnetic field is a geodesically flowing induced current, must be a superconductor. In this manner, we conclude that the underlying geometry of this type of media is that of a Lorentzian contact manifold. Moreover, we show that the macroscopic hallmark of their superconducting state is a purely topological condition equivalent to the geodesic nature of the induced current: the non-vanishing of its helicity.