For any implant t osseointegrate successfully, we have to look at various parameters. Proper case selection, diagnosis and treatment planning is the key to success. Good implant system, pre-surgical and surgical protocols are to be practiced in order to achieve success.
The question is: What do you think is the minimal length required for the zirconia dental implant to osseointegrate successfully?
The answer is that the phenomenon of osseointegration is not an issue of length or width but more of a surface contact issue. Biologically the interface between bone and alloplastic material, in this case zirconia (zirconium oxide), may be very intimate, at a distance of 100-200 angstroms. This intimate contact is perceived as a very tight physical (probably not chemical) bond or osseointegration.
If you are asking about the minimum length needed to maintain integration of an implant to bone in the oral cavity I think that this is a different question and the answer to that question needs to include information on diameter, location in the arch, anticipated occlusal load, thread design, prosthetic connection, etc.
So the answer is that there is no one answer and even if you engineer the implant appropriately for initial performance this may be irrelevant 10 years down the road.
The problem with ceramic materials is that they fatigue over time so the number that you consider to be acceptable on day one might be inappropriate at day 3,650.