Let L be a finite extension of Qp, we prove Breuil's locally analytic socle conjecture for GL2(L), showing the existence of all the companion points on the definite (patched) eigenvariety. This work relies on infinitesimal "R=T" results for the patched eigenvariety, and the comparison bewteen (partially) de Rham families and (partially) Hodge-Tate families.