Sources of quantized excitations via dichotomic topological cycles

TL;DR

This paper uncovers a novel topological pumping mechanism in one-dimensional chains, linking bulk properties to edge electron transfer through a higher-order bulk-boundary correspondence, with theoretical and experimental implications.

Contribution

It introduces a new topological pumping phenomenon involving coupled chains and a higher-order bulk-boundary relation, expanding understanding of topological adiabatic cycles.

Findings

Derived a bulk-boundary correspondence relating Chern number and electron transfer.

Proven the relation using K-theoretic calculations.

Discussed experimental implementations with classical and quantum systems.

Abstract

We demonstrate the existence of a conceptually distinct topological pumping phenomenon in one-dimensional chains undergoing topological adiabatic cycles. Specifically, for a stack of two semi-infinite chains cycled in opposite directions and coupled at one edge by a gapping potential, we derive a higher-order bulk-boundary correspondence that relates the bulk Chern number associated with the adiabatic cycle of a single infinite chain and the number of electrons transferred between the semi-infinite chains. The relation is formulated using the relative index of two projections and proven using K-theoretic calculations. The phenomenon is exemplified using the Rice-Mele model and possible experimental implementations with classical and quantum degrees of freedom are discussed.