Criteria to Follow a Caliphate/Emir of an Islamic Emirate/Government

I am non-Muslim history major student. I would like to know the criteria to determine a Caliphate. I would give an example of the very recent/last Caliphate in the Islamic world, i.e. the leader of the Islamic Emirate of Afghanistan (Taliban), *Mullah Mohammed Omar Mujahid or Mullah Omar*. Mullah Omar called himself the Caliphate (Amir Al-Momenin) of all Muslims in the world. He ordered his followers to fully implement the Islamic Sharia laws, i.e. Quran and Hadith texts in almost 80% of Afghanistan from 1996 to 2001, longer than any other conservative Islamic group. Even famous and recent Islamic figures like Usama Bin Laden and his followers decided to choose Mullah Omar as their Caliphate. **Based on Quran/Hadith, what are the criteria to follow a Caliphate of an Islamic Emirate/Government like Mullah Omar?**