Terumah Bizman Hazeh

Rambam in Perek Alef of Hilchos Terumos Halacha 26:

כו] התרומה בזמן הזה, ואפילו במקום שהחזיקו עולי בבל, ואפילו בימי עזרא--אינה מן התורה, אלא מדבריהם: שאין לך
תרומה של תורה אלא בארץ ישראל, ובזמן שיהיו כל ישראל שם, שנאמר "כי תבואו" (ויקרא כה,ב), ביאת כולכם כשהיו בירושה ראשונה וכמו שהן עתידין לחזור בירושה שלישית; לא כשהיו בירושה שנייה שהייתה בימי עזרא, שהייתה ביאת מקצתן--ולפיכך לא חייבה אותן מן התורה. וכן ייראה לי שהוא הדין במעשרות, שאין חייבין בהן בזמן הזה אלא מדבריהם כתרומה.

The Rambam here is saying that terumah nowadays, and even in the times of Ezra is only D'Rabbanan because by terumah there is a requirement of "bias kulchem", meaning that all of Klal Yisroel need to be in Eretz Yisroel. This did not exist in the times of Ezra and therefore terumah, even at that time, was only mi'drabbanan.

The problem with this Rambam is that the gemara in Kesuvos on 25a clearly implies that the halacha of bial kulchem applies to challah, and not to terumah. The Rambam, in fact, in Hilchos Bikkurim 5:5 brings the halacha of bial kulchem by challah.

Another problem with the Rambam is that the pasuk of Ki Savou that the Rambam cites, is written by Shemittah, and not by terumah.

The Shu"t Bais HaLevi (Chelek 3 Siman Alef Os Daled) and Chiddushei HaGrach Al HaRambam (Shemittah V'Yovel 12:16) explain that by terumah there is no direct requirement of bias kulchem. However, terumah is dependent on Shemittah. Shemittah, in turn, is dependent on Kibbush and Chilluk. In order to have Chilluk one needs all of Klal Yisroel there. Mimeilah, it turns out that you need bias kulchem by terumah. By challah, on the other hand, there is a direct requirement of bias kulchem and no requirement of chilluk. The nafka minah would be during the years of after kibbush, but before chilluk. There would be a requirement for challah (because you have bias kulchem). However, there is no requirement for terumah, because there is no chilluk yet.

It is important to note that according to the Rambam Kedusha Shniyah is kidsha l'asid lavo. Meaning that the kedushas ha'aretz of Eretz Yisroel remains nowadays even after the second Bais Hamikdash was destroyed. Nevertheless, terumah is d'rabbanan because the kedushas haaretz (the second time around) never included terumos and maasros or shemittah.

The Raavad disputes the Rambam and holds that even nowadays terumah is d'orayssa. Finally, a third shittah - the sefer haterumos - holds that during the times of the second Bais Hamikdash terumah was d'orayssa. However, after the destruction the kedusha was batel and terumah is, therefore, no longer d'orayssa.