Fractured Dental Implant? (photo)

There are a few concerning issues you bring up both in your description and photos. First of all I am not sure what brand of implants were used.  If a "knock off" brand was used, there is very little quality control. Name brand implants back their products and will replace free of charge, not the "knock offs." Second of all you use the term "implantologist." That is a a made up term used by practitioners who do not have an ADA recognized specialty. There is no such thing as an "implantologist." Oral and maxillofacial surgeons have the most training and experience with dental implants, some periodontist and prostodontists may have training as well.  Several dentists that have taken a weekend course in the placement of dental implants will call themselves implantologists.  Next, since this is an "all on 4" case the only reasons for the fracture of the implant are overtorque or "tightening" of the abutment screw or the framework did not have a "passive" fit when placed on the abutments so when tightened the lateral forces fractured the implant.  The other reson would be a problem with implant manufacture which is a very rare event unless a knock off brand was used.  Speak to your "implantologist" who should correct this.  If Nobel biocare implants were used and a Nobel Procera Bar was used, it is guaranteed an there should be no cost to you.  If knock off brands were used, good luck. 

The All-on-4 procedure is a fantastic solution for many patients. However, there are many complications that can accompany this procedure. The most common is screw loosening and also chipping of the material that the teeth are made out of. Several percautions can be taken to avoid these problems. 
Screw fracture is not very common. I have seen it in cases in which there was a small inaccuracy in the metal framework so the metal frame did not seat fully on the abutment or the abutment did not set fully on the implant. This problem can definitely cause a screw to break over time.
It can also be possible to damage the implant when attempting to retrieve a broken screw. 

Jess, it is unfortunate that you have to go through this but when implants fracture, a new prosthesis needs to be made.  Since you had an all on four prosthesis, I would recommend having a total of 6 if not 8 implants to support 12 or 14 upper teeth only because your present prothesis failed.  Implants, no matter what brand can fracture if they are under stress.  I have patients in my practice with 40 year old root form implants, placed by one of the original 3 US doctors that studied under Dr Branemark, the inventor of root form dental implants in Sweden.  The better implant companies such as Nobel/Branemark will have their implants replaced at no cost and if those recommended components are used, they are guaranteed for 10 years.  Good luck to you and please keep us informed.