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Two-dimensional (2D) topological electronic insulators are known to give riseto gapless edge modes, which underlie low energy dynamics, including electricaland thermal transport. This has been thoroughly investigated in the context ofquantum Hall phases, and time-reversal invariant topological insulators. Herewe study the edge of a 2D, topologically trivial insulating phase, as afunction of the strength of the electronic interactions and the steepness ofthe confining potential. For sufficiently smooth confining potentials,alternating compressible and incompressible stripes appear at the edge. Ourfindings signal the emergence of gapless edge modes which may give rise tofinite conductance at the edge. This would suggest a novel scenario of anontopological metal-insulator transition in clean 2D systems. Theincompressible stripes appear at commensurate fillings and may exhibit brokentranslational invariance along the edge in the form of charge density waveordering. These are separated by structureless compressible stripes.

Edge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes