Towards a spin dual of the fractional quantum Hall effect

Abstract

Electromagnetic duality between the Aharonov-Bohm and the Aharonov-Casher quantum mechanical phases predicts the existence of a new collective state of matter which can be regarded as a spin dual to the fractional quantum Hall effect. The state, induced by electric fields, is driven by effective spin-spin interactions. We derive experimental and materials conditions of spin-spin interactions and electric fields under which the new state may be observed.