Symmetry dictated universal helicity redistribution of Dirac fermions in transport

TL;DR

This paper reveals universal rules for how helicity, a fundamental property of Dirac fermions, redistributes during transport through electrostatic and mass potentials, linking it to Lorentz boosts and rotation groups.

Contribution

It introduces a unified theoretical framework describing helicity redistribution in Dirac fermion transport, connecting it to Lorentz transformations and abstract rotation groups.

Findings

Helicity changes are governed by Lorentz boosts in electrostatic potentials.

Helicity redistribution follows an abstract rotation group in mass-type potentials.

The results unify understanding of helicity transport in Dirac systems.

Abstract

Helicity is a fundamental property of Dirac fermions. Yet, the general rule of how it changes in transport is still lacking. We uncover, theoretically, the universal spinor state transformation and consequently helicity redistribution rule in two cases of transport through potentials of electrostatic and mass types, respectively. The former is dictated by Lorentz boost and its complex counterpart in Klein tunneling regime, which establishes miraculously a unified yet latent connection between helicity, Klein tunneling, and Lorentz boost. The latter is governed by an abstract rotation group we construct, which reduces to SO(2) when acting on the plane of effective mass and momentum. They generate invariant submanifolds, i.e., leaves, that foliate the Hilbert space of Dirac spinors. Our results provide a basis for unified understanding of helicity transport, and may open a new window for exotic helicity-based physics and applications in mesoscopic systems.