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It is good that you contrast the two elements that we need to consider:

Formal Pope = teaching/governing authority
Material Pope = physically holding onto the office

1983 Canon Law (1917 makes the same distinction using slightly different language):

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Can. 194

§1. The following are removed from an ecclesiastical office by the law itself [automatically]:
1/ a person who has lost the clerical state;
2/ a person who has publicly defected from the Catholic faith or from the communion of the Church;
3/ a cleric who has attempted marriage even if only civilly.

§2. The removal mentioned in nn. 2 and 3 can be enforced only if it is established by the declaration of a competent authority.

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So, the canon is clearly distinguishing between a de jure (formal) and a de facto (material) loss of office. The automatic/de jure/by-the-law-itself removal is what is referred to as the "formal Papacy." The declared/de facto/must-be-enforced-with-police removal is referred to as the "material Papacy."

A canonically-elected Pope loses his office (formally/de jure/by-the-law-itself) the moment he publicly defects from the Catholic Faith. No "declaration by a competent authority" is needed for anyone to recognize that fact and adjust their life accordingly. In that case, this canonically-elected Pope simply loses all of his authority and his dictates are binding on no one.

If that same canonically-elected Pope refuses to voluntarily vacate the physical office that he sits in, then his removal is only "enforced" by "the declaration of a competent authority." So a group of Cardinals would need to first recognize that 1) the former canonically-elected Pope has lost his office "formally." Then after that "formal loss" is acknowledged, those Cardinals can enforce the removal by calling in the Swiss Guard to physically kick the usurper to the curb.

P.S. Bergoglio is different from the papal claimants preceding him. He was not even canonically-elected, as you can read about at www.antipope.com. He was prophesied by St. Francis of Assisi: https://novusordowatch.org/saint-francis-assisi-prophecy-destroyer/. So none of the material/formal stuff is relevant to Bergoglio. He is simply a usurper and the Antichrist.

Ladislaus, of all people, I wish you could see the value of distinctions and consistency.

The whole point of sedeprivationism, or Fr Chazal's impoundism is the same...which you often advocate...that the spiritual office is impacted immediately by heresy...but the temporal/govt office needs temporal/govt action by the hierarchy. 

OK, if that's what you mean, I have no problem with it.  At the same time, it wouldn't be schismatic for someone to have a different opinion, where the "spiritual" office (formal aspect of office) would also cause the evacuation of the temporal office.  I think some the terms are a little bit confused, especially when you equate the power to govern somehow with the material aspect of the office.  If by "governing" you mean the ability to make appointments, etc., then I don't disagree.  If by governing you mean something closer to jurisdiction or the power to command, then I would have to disagree.  Perhaps that's the root of the misunderstanding, terms.

I hold that a Pope formally deprived of office can make appointments, but has no power / authority to teach or to command.  This Pope could also serve as a conduit for jurisdiction.  Thus, if a heretical non-Pope appoints a bishop, and the bishop himself has no impediments to exercising the office, the bishop would have ordinary jurisdiction and could formally exercise the office.