Light propagates symmetrically in opposite directions in most materials and structures. This fact -- a consequence of the Lorentz reciprocity principle -- has tremendous implications for science and technology across the electromagnetic spectrum. Here, we investigate an emerging approach to break reciprocity that does not rely on magneto-optical effects or spacetime modulations, but is instead based on biasing a plasmonic material with a direct electric current. Using a 3D Green function formalism and microscopic considerations, we elucidate the propagation properties of surface plasmon-polaritons (SPPs) supported by a generic nonreciprocal platform of this type, revealing some previously overlooked, anomalous, wave-propagation effects. We show that SPPs can propagate in the form of steerable, slow-light, unidirectional beams associated with inflexion points in the modal dispersion. We also clarify the impact of dissipation (due to collisions and Landau damping) on nonreciprocal effects and shed light on the connections between inflexion points, exceptional points at band edges, and modal transitions in leaky-wave structures. We then apply these concepts to the important area of thermal photonics, and provide the first theoretical demonstration of drift-induced nonreciprocal radiative heat transfer between two planar bodies. Our findings may open new opportunities toward the development of nonreciprocal magnet-free devices that combine the benefits of plasmonics and nonreciprocal photonics for wave-guiding and energy applications.
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