We show that the inclusion of nonlocal correlation effects in a variational wave function for the ground state of a topological Anderson lattice Hamiltonian is capable of describing both topologically trivial insulating phases and nontrivial ones characterized by an indirect gap, as well as its closure at the transition into a metallic phase. The method, though applied to an oversimplified model, thus captures the metallic and insulating states that are indeed observed in a variety of Kondo semiconductors, while accounting for topologically nontrivial band structures. PACS numbers: 71.27.+a, 71.30.+h, 03.65.Vf Introduction. Phenomena at the crossroads of topological insulators and strongly correlated systems have recently gained a lot of attention, mainly stimulated by theoretical proposals that the inclusion of strong correlations in specific models with a nontrivial topological content may give rise to novel and interesting phenomena [1][2][3][4][5]. However, electronic correlations in most of the discovered topological insulators [6,7] seem to be relatively weak, and hence of minor importance. For that reason, the concept of topological Kondo insulators (TKIs) originally put forward in Refs.[8] and [9] is particularly appealing due to its possible realization in already known Kondo insulating compounds [10]. Notably, SmB 6 is convincingly confirmed to be a TKI [11][12][13][14][15][16][17][18][19] with strong evidence of the essential role played by many-body correlations [20,21].Theoretically, the main physical properties of TKI are frequently described in the framework of topological Anderson lattice models in which strong spin-orbit coupling is encoded into a spin-dependent hybridization with odd parity in momentum space [8,9,22]. Many-body correlations in these models have been mostly treated by the slave-boson approach or by the dynamical mean-field theory (DMFT), and predicted to induce quantum phase transitions between topologically distinct bulk insulating phases [22][23][24].The aim of this work is to demonstrate that accounting for nonlocal spatial correlations, beyond those already well captured by the mentioned techniques, plays an important role in modeling TKIs. Specifically, those nonlocal correlations supply the f electron self-energy with a momentum dependence, which is otherwise purely local within DMFT and at the saddle point of the slave-boson theory. Remarkably, such a momentum dependence allows one to describe, above a critical interaction strength, the emergence of a topological Kondo insulator with an indirect gap, and its subsequent closure at the transition into a metallic state, an intriguing result opposite to the conventional Mott phenomenon where increasing interaction instead favours the onset of an insulating state. We disclose this scenario in two dimensions by means of the diagrammatic expansion of the Gutzwiller wave function (GWF) technique [25,26]. CeIrSb [35]). Moreover, assuming that increasing pressure roughly corresponds to reducing the interaction strength, we can ...