  This Letter identifies the physical mechanism for the quench of turbulent
resistivity in 2D MHD. Without an imposed, ordered magnetic field, a
multi-scale, blob-and-barrier structure of magnetic potential forms
spontaneously. Magnetic energy is concentrated in thin, linear barriers,
located at the interstices between blobs. The barriers quench the transport and
kinematic decay of magnetic energy. The local transport bifurcation underlying
barrier formation is linked to the inverse cascade of $\langle A^2\rangle$ and
negative resistivity, which induce local bistability. For small scale forcing,
spontaneous layering of the magnetic potential occurs, with barriers located at
the interstices between layers. This structure is effectively a magnetic
staircase.
