There are at least two bands with this name:

1) Daybreak is an unsigned indie/rock band who perform in the American Midwest. The sounds the quintet makes are intended to be composed movements reflecting the go-with-the-flow attitude we wish we all could have (all of the time), along with image-driven lyrics and rather strange, but infectious melodies. The band is currently underground in Suburban Minnesota recording their first full length record tentatively called "influence/coincidence." They focus on creating songs with individual personalities; like humans, like nature.

myspace.com/daybreakrock | thisisdaybreak.com

2) Daybreak (데이브레이크) is also a korean pop/rock/electronic group with just one album release "Urban Life Style".