The gemara says that an avel does not wear tefillin. We pasken like R' Yehoshua on 21a that he only abstains from Tefillin on the first day. This is paskened in Shulchan Aruch Y.D. 388 and O.C. 38:5. It is not clear from the gemara and Shulchan Aruch if this exemption only applies when the day of burial is the day of death (which is d'oraysa aveilus acc. to behag and rif), or even if the burial is a day or 2 later we still exempt the avel from tefillin on the day of the burial. The Pischei Teshuva in Y.D. brings 2 opinions about this, and the M.B. is machria that we always exempt the avel on the day of burial from wearing tefillin even if it is not the day of death. This is clear from the Rosh. The Behag and the Rif are of the opinion that aveilus is d'oraysa on the first day, when the burial and death occur on the same day. Based on this it could be that the exemption of tefillin would only apply on the first day if it is "d'oraysa" meaning the yom hamisa and yom hakevura. However, the Rosh writes (end of siman 3) that the exemption from tefillin is even for aveilus d'rabonon. The Rabbonon felt that it was inappropriate to wear the crown of Tefillin while in a state of depression, therefore they uprooted the mitzvas aseh of tefillin on the day of the kevurah. It is for this reason that until the burial the avel does not put on tefillin (or do any positive mitzvah) bec. he is an onen, but even after the burial he does not put on tefillin later that day.