I would like to know how to create a rough looking green emerald in Cycles.
It should look like that, but can be even rougher and doesn't have to be that translucent.
Maybe this will help get you started. You will still have a lot of work to do in order to refine the materials and lighting to get this to work.
Here's a link to the Fracture Modifier branch which was used to break up a model. https://www.dropbox.com/sh/xiuirkoo0rac5tw/AAB2XQbs9K5uTIYcbDPUDW1Ca