Direct measurement of quantum phases in graphene via photoemission spectroscopy

TL;DR

This paper introduces a novel polarization-dependent ARPES technique to directly measure quantum phases, such as Berry's phase and matrix element signs, in graphene, overcoming previous observational challenges.

Contribution

The study presents a new method using polarization-dependent ARPES to directly access quantum phases and matrix element signs in two-dimensional materials like graphene.

Findings

Graphene with Berry's phase nπ shows ARPES intensity rotation by π/n.

The method directly measures the phase of the band wavefunction.

ARPES signals reveal the signs of matrix elements in graphene.

Abstract

Quantum phases provide us with important information for understanding the fundamental properties of a system. However, the observation of quantum phases, such as Berry's phase and the sign of the matrix element of the Hamiltonian between two non-equivalent localized orbitals in a tight-binding formalism, has been challenged by the presence of other factors, e.g., dynamic phases and spin/valley degeneracy, and the absence of methodology. Here, we report a new way to directly access these quantum phases, through polarization-dependent angle-resolved photoemission spectroscopy (ARPES), using graphene as a prototypical two-dimensional material. We show that the momentum- and polarization-dependent spectral intensity provides direct measurements of (i) the phase of the band wavefunction and (ii) the sign of matrix elements for non-equivalent orbitals. Upon rotating light polarization by \pi/2, we found that graphene with a Berry's phase of n\pi (n=1 for single- and n=2 for double-layer graphene for Bloch wavefunction in the commonly used form) exhibits the rotation of ARPES intensity by \pi/n, and that ARPES signals reveal the signs of the matrix elements in both single- and double-layer graphene. The method provides a new technique to directly extract fundamental quantum electronic information on a variety of materials.