  We investigate experimentally an exotic state of electronic matter obtained
by fine-tuning to a quantum critical point (QCP), realized in a spin-polarized
resonant level coupled to strongly dissipative electrodes. Several transport
scaling laws near and far from equilibrium are measured, and then accounted for
theoretically. Our analysis reveals a splitting of the resonant level into two
quasi-independent Majorana modes, one strongly hybridized to the leads, and the
other tightly bound to the quantum dot. Residual interactions involving these
Majorana fermions result in the observation of a striking quasi-linear
non-Fermi liquid scattering rate at the QCP. Our devices constitute a viable
alternative to topological superconductors as a platform for studying strong
correlation effects within Majorana physics.
