A-320 Captain reported an electrical power failure while starting APU and taxiing to the gate at night on one engine. The Captain stopped the aircraft and power was restored after the APU started; then requested a tow to the gate.

Narrative

After landing at night; we crossed Runway XXR and turned northbound on Bravo from taxiway to hold short of [another] taxiway while we figured out a gate due to ours being occupied. We received the gate change and that was open so we notified ATC and started taxing to the gate. During this taxi we shut down engine 2. Closer to entering the ramp the First Officer (FO) started the APU. As soon as he pressed the start button the aircraft went completely black. And when I say completely black; we lost everything in the cockpit; all screens were black and nothing worked; even the cockpit door locks failed and the door slammed open. The brakes worked thankfully; and I pressed those to stop the aircraft but the steering was completely gone. I then called for Flight Attendant stations.I set the parking brake and eventually was able to contact ATC to get fire trucks moving because we were completely blind not having any ECAMS or screen to help tell us what happened we were uncertain the safety of the aircraft. I could hear engine 1 picking up speed and getting louder. It eventually stayed at a higher RPM. When the APU came online the ECAM showed a generator one fault and avionics vent system fault. We had this avionics vent system fault at the gate the leg before and reported it prior to departure to Dispatch and Maintenance Control they signed off the log book for it after a reset. We followed the ECAM and reset the generator. Its very difficult to be dark in the cockpit and not have any indications or ideas as to what has happened to your aircraft. Fire trucks gave us all clear. So; we opted to be towed to the gate and did not want that to happen again we still had a avionics vent fault and was uncertain if that was the cause of the dark issue.