The　theories　of　gauge　potential　decomposition　and　topological　currents　proposed　by　Prof.　YiShi　Duan　et　al.　have　remarkable　significance　in　the　research　of　topological　inner　structures　of　gauge　fields,　with　wide　applications　in　the　analysis　of　topological　defects/excitations　in　various　physical　systems.　In　this　paper,　firstly,　a　brief　survey　for　these　theories　is　presented.　Secondly,　the　theories　are　applied　in　the　study　of　topological　insulators　in　two　dimensions.　Topological　insulators　are　at　the　cutting　edge　of　current　international　research　of　condensed　matter　physics,　where　topological　effects　stem　from　the　non-trivial　topological　numbers,　such　as　the　Chern　numbers.　In　this　paper　different　types　of　topological　defects　are　investigated　within　one　single　framework,　the　so-called　＇t　Hooft　monopole　model,　which　acts　as　a　U(1)　sub-field　theory　of　a　non-Abelian　gauge　field.