A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based on a pair of helical Luttinger liquids, which arise naturally at the edges of a quantum spin Hall insulator. Equipping each helical liquid with a beam splitter, current-current cross correlations can be used to construct a Bell inequality whose violation would indicate nonlocal orbital entanglement of the injected electrons and/or holes. Due to Luttinger-liquid correlations, however, the entanglement is exponentially suppressed at finite temperatures.
@article{arxiv.1402.6022,
title = {Detection of entanglement by helical Luttinger liquids},
author = {Koji Sato and Yaroslav Tserkovnyak},
journal= {arXiv preprint arXiv:1402.6022},
year = {2015}
}