# Semiclassical conservation of spin and large transverse spin current in Dirac systems

## TL;DR

This paper reveals that in doped Dirac materials, a semiclassical approach shows a conserved spin and predicts a large transverse spin current, challenging the common belief of spin non-conservation due to strong spin-orbit coupling.

## Contribution

It introduces a new Boltzmann equation for doped Dirac systems and demonstrates a generalized spin conservation law and large transverse spin current.

## Key findings

- Spin conservation law is valid in doped Dirac materials.
- A large transverse spin current can be observed in nearly ballistic regimes.
- Softening of spin-momentum locking in the semiclassical regime.

## Abstract

In Dirac materials, the low energy excitations obey the relativistic Dirac equation. This dependence implies that the electrons are exposed to strong spin-orbit coupling. Hence, real spin conservation is believed to be violated in Dirac materials. We show that this point of view needs to be refined in the semiclassical picture which applies to the case of doped Dirac materials (away from the nodal point in the spectrum). We derive a novel type of Boltzmann equation for these systems if they are brought slightly out-of-equilibrium. Remarkably, spin-momentum locking is softened and a generalized spin conservation law can be formulated. The most striking observable consequence of our theory is a large transverse spin current in a nearly ballistic transport regime.