Measurement of the Berry curvature of solids using high-harmonic spectroscopy

Tran Trung Luu,Hans Jakob Wörner

doi:10.1038/s41467-018-03397-4

Abstract

Berry phase and Berry curvature have become ubiquitous concepts in physics, relevant to a variety of phenomena, such as polarization, various Hall effects, etc. Studies of these phenomena call for characterization of Berry phase or curvature which is largely limited to theory, and a few measurements in optical lattices. In this work, we report polarimetry of high-harmonic emission from solids and exploit this novel capability to directly retrieve the Berry curvature of α-quartz. We show that the two manifestations of broken inversion symmetry in solids lead to perpendicular or parallel polarization of even harmonics with respect to the driving field. Using semiclassical transport theory, we retrieve the Berry curvature from spectra measured in perpendicular polarization, the results being supported by ab initio calculation. Our work demonstrates an approach for the direct measurement of Berry curvature in solids, which could serve as a benchmark for theoretical studies.

Highlights

Berry phase and Berry curvature have become ubiquitous concepts in physics, relevant to a variety of phenomena, such as polarization, various Hall effects, etc
The phase γn(C), later called Berry phase, can bRRe expressed in threedimensional (3D) space as γnðCÞ 1⁄4 À C dS Á ΩnðRÞ where Ωn(R) is a vectorial quantity known as Berry curvature
We introduce polarimetry of high-harmonic emission from solids and use it to perform a complete characterization of the vectorial properties of even- and oddharmonic emission

Summary

Introduction

Berry phase and Berry curvature have become ubiquitous concepts in physics, relevant to a variety of phenomena, such as polarization, various Hall effects, etc. Because both even and odd harmonics are linearly polarized and parallel to each other (Supplementary Note 2) and the incident electric field, even harmonics recorded in this direction can be assigned to quantum interference of direct and indirect excitation pathways included in the semiconductor Bloch equations (SBEs) for multiple bands[18] or asymmetric dipole element.

Results

Conclusion