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We consider a system of weakly coupled wires with quantum Hall effect (QHE)and in the presence of a spatially periodic modulation of the chemicalpotential along the wire, equivalent to a charge density wave (CDW). Weinvestigate the competition between the two effects which both open a gap. Weshow that by changing the ratio between the amplitudes of the CDW modulationand the tunneling between wires, one can switch between non-topologicalCDW-dominated phase to topological QHE-dominated phase. Both phases host edgestates of chiral and non-chiral nature robust to on-site disorder. However,only in the topological phase, the edge states are immune to disorder in thephase shifts of the CDWs. We provide analytical solutions for filling factor$\nu=1$ and study numerically effects of disorder as well as present numericalresults for higher filling factors.

Chiral and Non-Chiral Edge States in Quantum Hall Systems with Charge Density Modulation