Physics – Condensed Matter – Materials Science
Scientific paper
2011-09-16
Phys. Rev. B 84, 125422 (2011)
Physics
Condensed Matter
Materials Science
12 pages and 8 figures
Scientific paper
10.1103/PhysRevB.84.125422
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.
Fedorov Alexei V.
Hwang Choongyu
Lanzara Alessandra
Louie Steven G.
Park Cheol-Hwan
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