Berry phase and topological spin transport in the chiral d-density wave state

TL;DR

This paper explores how a chiral d-density wave state can support dissipationless spin transport driven by a Zeeman field gradient, linking it to Berry phase and topological invariants.

Contribution

It demonstrates the existence of quantized spin Hall conductance in a chiral d-density wave state, revealing its topological nature and relation to Berry phase.

Findings

Dissipationless spin currents can be induced by a uniform Zeeman field gradient.

Spin Hall conductance is related to Berry phase and becomes quantized at zero temperature and doping.

The quantized conductance acts as a topological invariant in the studied state.

Abstract

In this paper we demonstrate the possibility of dissipationless spin transport in the chiral d-density wave state, by the sole application of a uniform Zeeman field gradient. The occurrence of these spontaneous spin currents is attributed to the parity (${\cal P}$) and time-reversal (${\cal T}$) violation induced by the $d_{xy}+id_{x^2-y^2}$ density wave order parameter. We calculate the spin Hall conductance and reveal its intimate relation to the Berry phase which is generated when the Zeeman field is applied adiabatically. Finally, we demonstrate that in the zero temperature and doping case, the spin Hall conductance is quantized as it becomes a topological invariant.