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The coupling between the spin and momentum degrees of freedom due tospin-orbit interactions (SOI) suggests that the strength of the latter can bemodified by controlling the motion of the charge carriers. In this paper, weinvestigate how the effective SOI can be modulated by constraining the motionof charge carriers to curved waveguides thereby introducing real-spacegeometric curvature in their motion. The change in the SOI can in turn inducetopological phase transitions in the system. Specifically, we study how theintroduction of periodic sinusoidal curvature in nanowires with intrinsic SOCcan induce the onset of mid-gap topologically protected edge states, which canbe characterized by a topological invariant or Chern number. The Chern numbercorresponds to the number of discrete charges that would be pumped across thelength of the nanowire when the phase of a sliding gate potential relative tothat of the sinusoidal curvature is varied adiabatically over a completeperiod. In addition, coupling to an external magnetization can be utilized asan experimental knob to modify the Chern number by changing the ordering of thenanowire energy bands. The magnetization can be tuned to achieve large discretejumps in the number of pump charges per phase period.

Higher Chern Number States in Curved Periodic Nanowires