A-321 Captain reported a loss of one of the hydraulic systems during climb. The flight returned to the departure airport and performed a safe overweight landing.

Narrative

Climbing through approximately FL200 we received a HYD Y ENG 2 PUMP LO PR warning. I observed yellow hydraulic quantity indicating zero; (empty); and pressure of 0 PSI. I was the pilot flying. After completion of the QRC I transferred control of the aircraft to the first officer with the command; 'Your aircraft; your radios.'; and completed the ECAM actions. I instructed the first officer to [request priority handling]; get a level off and return to the departure field. As the first officer was doing this; I performed the QRH procedures for the failure; the landing distance procedure; overweight landing and non-routine landing. I also notified Dispatch; the cabin crew and the passengers. We returned to the field and landed without incident. Mechanical failure.We landed without nose wheel steering and were towed in by a super-tug that followed an airport operations vehicle. The super-tug crew either did not have; or chose not to use a headset; so we had no choice but to use hand signals. It was unbelievable to me that the tug crew would meet an emergency aircraft; stopped on the runway; without a headset. The lack of headset seriously degraded safety. Separately; I must commend the First Officer. Although they were low-time in the aircraft and new to the company; you would never know it. Their performance was exemplary; and the entire scenario went as if it were a textbook example of how to handle this situation. ATC was also perfect; and provided us with exactly what we needed; when we needed it.