The Hall mobility of carriers hopping in an impurity band

Spin-Charge Conversion in Chiral Polymers with Hopping Conduction

Organic and biological materials are often chiral. Chiral polymers, as recent experiments indicate, facilitate spin-charge conversion: a charge current results in a spin polarization and vice versa, dubbed chirality-induced spin selectivity (CISS) and inverse CISS (ICISS). While CISS/ICISS in crystalline chiral systems such as tellurium can be understood in terms of their chirality- and spin-dependent band structure, such a picture becomes inapplicable to disordered chiral polymers, where carrier transport is via hopping rather than band conduction. Here, we develop a microscopic theory to describe CISS and ICISS in disordered chiral organics, in which chirality-induced geometric spin-orbit coupling leads to a purely geometric spin-dependent Berry phase in electron hops involving triads, whose orientations are dictated by the material's chirality. Our theory reveals a central role of spin-flip hopping, which suppresses CISS but enables ICISS.