Typically dark circles are caused staining from broken vessels underneath skin under eyes. Toothpaste more often than not contains oil of ginger and peppermint. Apply a thin layer of the toothpaste under eyes and back rub a little could successfully help advance blood flow and evacuate blood stasis. You can apply some potato or cucumber cuts to help as well.
A few people even prescribe hemorrhoid cream as a solution for dark circles expulsion and it really works