Switching Chiral Solitons for Algebraic Operation of Topological Quaternary Digits

TL;DR

This paper demonstrates the experimental switching of chiral solitons with different topological numbers, enabling algebraic operations on topological quaternary digits, advancing topological information processing.

Contribution

It introduces the first experimental realization of algebraic operations on topological quaternary digits using chiral solitons in a $Z_4$ symmetric system.

Findings

Achiral solitons merge with chiral ones to switch their handedness.

Realization of algebraic operations of $Z_4$ topological numbers.

Potential for robust topological multi-digit information storage and processing.

Abstract

Chirality is ubiquitous in nature and chiral objects in condensed matter are often excited states protected by system's topology. The use of chiral topological excitations to carry information has been demonstrated, where the information is robust against external perturbations. For instance, reading, writing, and transfer of binary information are demonstrated with chiral topological excitations in magnetic systems, skyrmions, for spintronic devices. However, the next step, the logic or algebraic operation of such topological bits has not been realized yet. Here, we show experimentally the switching between solitons of different chirality in a one-dimensional electronic system with $Z_4$ topological symmetry. We found that a fast-moving achiral soliton merges with chiral solitons to switch their handedness. This corresponds to the realization of algebraic operation of $Z_4$ topological numbers. Chiral solitons could be exploited for storage and operation of robust topological multi-digit information.