Geometrical phase shift in Friedel oscillations

TL;DR

This paper demonstrates that internal degrees of freedom in Bloch waves cause a geometrical phase shift in Friedel oscillations, linking local density of states interference patterns to the topological properties of band structures.

Contribution

It reveals the topological origin of phase shifts in Friedel oscillations due to internal wave degrees of freedom, providing a new way to probe band topology.

Findings

Internal degrees of freedom induce a geometrical phase shift.

Fourier analysis links phase shift to band topology.

Friedel oscillations serve as a probe for wave topological properties.

Abstract

This work addresses the problem of elastic scattering through a localized impurity in a one-dimensional crystal with sublattice freedom degrees. The impurity yields long-range interferences in the local density of states known as Friedel oscillations. Here, we show that the internal degrees of freedom of Bloch waves are responsible for a geometrical phase shift in Friedel oscillations. The Fourier transform of the energy-resolved interference pattern reveals a topological property of this phase shift, which is intrinsically related to the Bloch band structure topology in the absence of impurity. Therefore, Friedel oscillations in the local density of states can be regarded as a probe of wave topological properties in a broad class of classical and quantum systems, such as acoustic and photonic crystals, ultracold atomic gases in optical lattices, and electronic compounds.