Berry phase and spin quantum Hall effect in the vortex state of superfluid He3 in two dimensions

TL;DR

This paper demonstrates that the spin quantum Hall effect in the vortex state of 2D superfluid He3 can be understood through Berry phase and Chern number, linking it to adiabatic spin transport of quasiparticles.

Contribution

It introduces a theoretical framework connecting the spin quantum Hall effect in superfluid He3 to Berry phase and topological invariants, providing new insights into spin transport phenomena.

Findings

Spin Hall conductivity is expressed via Berry phase and Chern number.

The spin quantum Hall effect is described as adiabatic spin transport of quasiparticles.

Results draw parallels with adiabatic pumping and polarization in dielectrics.

Abstract

We show that the spin quantum Hall effect in the vortex state of two-dimensional rotating superfluid He3 can be described as an adiabatic spin transport of Bloch quasiparticles. We show that the spin Hall conductivity is written by the Berry phase as well as the Chern number. The results have similarity to the adiabatic pumping of Bloch electrons and the spontaneous polarization in crystalline dielectrics.