CL600 Captain reported after landing; the aircraft would not steer to the right due to the nose landing gear door jammed against the torque link.

Narrative

On approach into ZZZ runway XXR; landing gear was extended; after which a series of loud noises could be heard coming from the nose gear area of the aircraft; right below the flight deck. All gear indications were normal; the approach was continued and a normal landing was executed. After rollout; the aircraft was taxied off the runway at a high speed turnoff and on taxiway 1; running between the ZZZ parallel runways; and held short of runway XXL at taxiway 2. After receiving the runway crossing clearance; the aircraft was attempted to be taxied across the runway but both pilots quickly realized the aircraft would not steer to the right; only left. As we would later find out; this was caused by the nose gear door; which had become loose during the flight and jammed itself up against the side of the torque link during one of the taxi turns after landing; preventing the nose wheel from being turned to the right. Unable to straighten out the nose wheel to taxi across the runway; the aircraft became disabled with the nose not more than about 2 feet past the hold short bars at taxiway 2; which was beyond the usable portion of ZZZ's runway; at time of incident. A tug team was called to the scene; and in the meantime; some aircraft continued to depart XXL after the tower mentioned the aircraft was not on the usable part of the runway. When the tow team arrived; runway XXL was closed to departing aircraft for several minutes. Maintenance had to come out to the aircraft as the tow team could not connect to the aircraft with the gear door jammed. After maintenance released the door; the tug towed the aircraft to the gate without further incident.