Higher Chern Number States in Curved Periodic Nanowires

TL;DR

This paper demonstrates that periodic curvature in nanowires with spin-orbit coupling can induce topological states characterized by higher Chern numbers, which can be controlled via external magnetization and phase modulation.

Contribution

It introduces a method to induce and control higher Chern number topological states in curved nanowires with intrinsic SOC through geometric curvature and external magnetization.

Findings

Periodic curvature induces topologically protected edge states.

Chern number can be modulated by external magnetization.

Charge pumping quantized by the Chern number.

Abstract

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