Connectedness of the Balmer spectrum of the right bounded derived category

By virtue of Balmer's celebrated theorem, the classification of thick tensor ideals of a tensor triangulated category T is equivalent to the topological structure of its Balmer spectrum SpcT. Motivated by this theorem, we discuss connectedness, irreducibility, and Noetherianity of the Balmer spectrum of a right bounded derived category of finitely generated modules over a commutative ring.