Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases

Abstract

The bulk-boundary correspondence relates quantized edge states to bulk topological invariants in topological phases of matter. In one-dimensional symmetry-protected topological systems (SPTs), quantized topological Thouless pumps directly reveal this principle and provide a sound mathematical foundation. Symmetry-protected higher-order topological phases of matter (HOSPTs) also feature a bulk-boundary correspondence, but its connection to quantized charge transport remains elusive. Here we show that quantized Thouless pumps connecting $C_4$-symmetric HOSPTs can be described by a tuple of four Chern numbers that measure quantized bulk charge transport in a direction-dependent fashion. Moreover, this tuple of Chern numbers allows to predict the sign and value of fractional corner charges in the HOSPTs. We show that the topologically non-trivial phase can be characterized by both quadrupole and dipole configurations, shedding new light on current debates about the multi-pole nature of the HOSPT bulk. By employing corner-periodic boundary conditions, we generalize Restas's theory to HOSPTs. Our approach provides a simple framework for understanding topological invariants of general HOSPTs and paves the way for an in-depth description of future dynamical experiments.

4 pages, 4 figures plus supplements

References in corpus (3)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topolectrical-circuit octupole insulator with topologically protected corner states

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• High-order topological pumping on a superconducting quantum processor
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Many-body multipole index and bulk-boundary correspondence
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Finite-temperature topological invariant for higher-order topological insulators
• Floquet-Anderson localization in the Thouless pump and how to avoid it