  We consider a system of weakly coupled one-dimensional wires forming a
three-dimensional stack in the presence of a spatially periodic modulation of
the 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 CDW
and magnetic field, the system can support a second-order topological phase
characterized by the presence of chiral quasi-1D Quantum Hall Effect (QHE)
hinge modes. Interestingly, we demonstrate that direction of propagation of the
hinge modes depends on the phase of the CDW and can be reversed only by
electrical means without the need of changing the orientation of the magnetic
field. Furthermore, we show that the system can also support 2D chiral surface
QHE states, which can coexist with one-dimensional hinge modes, realizing a
scenario of a hybrid high-order topology. We show that the hinge modes are
robust against static disorder.
