Topological classification of adiabatic processes

TL;DR

This paper extends the classification of topological pumps, which enable quantized charge or spin transfer through adiabatic processes, to new symmetry classes using scattering matrix formalism, linking them to topological insulators.

Contribution

It introduces a scattering matrix-based topological index for classifying topological pumps in Dyson and chiral classes, connecting them to protected end states and quantized transport.

Findings

Topological pumps are characterized by protected gapless end states.

Quantized charge or spin can be pumped in the weak coupling limit.

The classification applies to Wigner Dyson and chiral symmetry classes.

Abstract

Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter upon rolling the insulator up to a cylinder and threading it with a time dependent flux. In this article we extend the classification of topological pumps to the Wigner Dyson and chiral classes, coupled to multi-channel leads. The topological index distinguishing different topological classes is formulated in terms of the scattering matrix of the system. We argue that similar to topologically non-trivial insulators, topological pumps are characterized by the appearance of protected gapless end states during the course of a pumping cycle. We show that this property allows for the pumping of quantized charge or spin in the weak coupling limit. Our results may also be applied to two dimensional topological insulators, where they give a physically transparent interpretation of the topologically non-trivial phases in terms of scattering matrices.