Direct Geometric Probe of Singularities in Band Structure

TL;DR

This paper introduces a direct method to probe band-structure singularities in optical lattices by transporting ultracold atoms through these points, revealing their topological properties and expanding the study of complex band touchings.

Contribution

It presents a novel experimental approach to directly measure non-Abelian transformations at band singularities in ultracold atoms, including quadratic band touching points.

Findings

Winding number of linear touching points is 1

Winding number of quadratic touching points is 2

Method enables direct study of band geometry singularities

Abstract

The band structure of a crystal may have points where two or more bands are degenerate in energy and where the geometry of the Bloch state manifold is singular, with consequences for material and transport properties. Ultracold atoms in optical lattices have been used to characterize such points only indirectly, e.g., by detection of an Abelian Berry phase, and only at singularities with linear dispersion (Dirac points). Here, we probe band-structure singularities through the non-Abelian transformation produced by transport directly through the singular points. We prepare atoms in one Bloch band, accelerate them along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic touching points of a honeycomb lattice. Measurements of the band populations after transport identify the winding numbers of these singularities to be 1 and 2, respectively. Our work opens the study of quadratic band touching points in ultracold-atom quantum simulators, and also provides a novel method for probing other band geometry singularities.