  We introduce and investigate material junctions as a generic and tuneable
electronic platform for the realization of exotic non-Hermitian (NH)
topological states of matter, where the NH character is induced by the surface
self-energy of a thermal reservoir. As a conceptually rich and immediately
experimentally realizable example, we consider a three-dimensional topological
insulator (TI) coupled to a ferromagnetic lead. Remarkably, the symmetry
protected TI is promoted in a dissipative fashion to a non-symmetry protected
NH Weyl phase with no direct Hermitian counterpart and which exhibits
robustness against any perturbation. The transition between a gapped phase and
the NH Weyl phase may be readily tuned experimentally with the magnetization
direction of the ferromagnetic lead. Given the robustness of this exotic nodal
phase, our general analysis also applies to, e.g., a two-dimensional electron
gas close to criticality in proximity to a ferromagnetic lead. There, the
predicted bulk Fermi arcs are directly amenable to surface spectroscopy methods
such as angle-resolved photoemission spectroscopy.
