Bulk Pumping in 2D Topological Phases

TL;DR

This paper introduces a novel concept of bulk topological pumping in 2D topological phases, demonstrating its physical implications and unifying different phenomena like quantum Hall effects and topological superconductivity.

Contribution

It presents the idea of bulk flux-induced topological pumping, expanding the understanding of topological phenomena beyond edge-based mechanisms in 2D systems.

Findings

Bulk pumping links density variations and Josephson currents.

Demonstrates bulk pumping in quantum Hall and topological superconductors.

Unifies different topological effects through bulk flux control.

Abstract

The notion of topological (Thouless) pumping in topological phases is traditionally associated with Laughlin's pump argument for the quantization of the Hall conductance in two-dimensional (2D) quantum Hall systems. It relies on magnetic flux variations that thread the system of interest without penetrating its bulk, in the spirit of Aharonov-Bohm effects. Here we explore a different paradigm for topological pumping induced, instead, by magnetic flux variations $\delta\chi$ inserted through the bulk of topological phases. We show that $\delta\chi$ generically controls the analog of a topological pump, accompanied by robust physical phenomena. We demonstrate this concept of bulk pumping in two paradigmatic types of 2D topological phases: integer and fractional quantum Hall systems and topological superconductors. We show, in particular, that bulk pumping provides a unifying connection between seemingly distinct physical effects such as density variations described by Streda's formula in quantum Hall phases, and fractional Josephson currents in topological superconductors. We discuss the generalization of bulk pumping to other types of topological phases.