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We consider a system of weakly coupled one-dimensional wires forming athree-dimensional stack in the presence of a spatially periodic modulation ofthe chemical potential along the wires, equivalent to a charge density wave(CDW). An external static magnetic field is applied parallel to the wire axes.We show that, for a certain parameter regime, due to interplay between the CDWand magnetic field, the system can support a second-order topological phasecharacterized by the presence of chiral quasi-1D Quantum Hall Effect (QHE)hinge modes. Interestingly, we demonstrate that direction of propagation of thehinge modes depends on the phase of the CDW and can be reversed only byelectrical means without the need of changing the orientation of the magneticfield. Furthermore, we show that the system can also support 2D chiral surfaceQHE states, which can coexist with one-dimensional hinge modes, realizing ascenario of a hybrid high-order topology. We show that the hinge modes arerobust against static disorder.

Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation