What is the material of choice for a fresh furcation perforation of the 
size of 2 mm?
Perforation in the furcation area has the poor prognosis. Perforation occurring in mid root and apical part of root does not have communication with oral cavity and thus has good prognosis.
Commonly used materials for perforation repair include amalgam, calcium hydroxide, IRM, Super EBA, gutta-percha,MTA, and other materials tried for repair include dentin chips, hydroxyapatite, glass ionomer cements and plaster of Paris.
For perforation repair, hemostatics are needed to control the hemorrhage and make the area dry so that optimal placement of restorative material can be accomplished. 

Key notes 
MTA is ideal material with hemostatic and biocompatible property.
Textbook of ENDODONTICS
NISHA GARG 3rd edition.
Geristore
MTA
GIC
Amalgam