$\newcommand{\Perf}{\operatorname{Perf}}$This is a toy example that I want to understand, I will be grateful for any help. Given a ring $R$ and $A=\Perf(R)$ the category of perfect complexes over $R$ . Suppose that $m\in\Perf(R)$ and $B$ the smallest thick subcategory generated by $ m $. Let $C$ be the verdier quotient $ C=\Perf(R)/B$.

I want to understand $C$ concretely up to equivalence of triangulated categories.

Is it correct that $C$ Is equivalent to a triangulated subcategory $ D$ of $A$ where $d\in D$ iff the graded abelian groups $$ \operatorname{Hom}_A^n(m,d)=0$$ for any integer $n.$