Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of quantum Hall phases, and time-reversal invariant topological insulators. Here we study the edge of a 2D, topologically trivial insulating phase, as a function of the strength of the electronic interactions and the steepness of the confining potential. For sufficiently smooth confining potentials, alternating compressible and incompressible stripes appear at the edge. Our findings signal the emergence of gapless edge modes which may give rise to finite conductance at the edge. This would suggest a novel scenario of a non-topological metal-insulator transition in clean 2D systems. The incompressible stripes appear at commensurate fillings and may exhibit broken translational invariance along the edge in the form of charge density wave ordering. These are separated by structureless compressible stripes.
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