Concurrent inserts into a CCI can deadlock on a server with memory pressure.
If I kick off 3 sessions at the same time only the first one is able to insert rows.
Sessions 2 and 3 have a wait type of LCK_M_IX.
Once session 1 inserts all of its rows into a delta store it rolls them back.
After the rollback is complete a deadlock is reported to the client for session 1:
Msg 1205, Level 13, State 134, Line 1
Transaction (Process ID 57) was deadlocked on lock resources with another process and has been chosen as the deadlock victim. Rerun the transaction.
Sessions 2 and 3 are able to insert their rows concurrently into the CCI without issues after the session 1 is killed.