  Superconductivity is realized by opening a gap in the superconducting state.
The gap symmetry is crucial in understanding the underlying superconductivity
mechanism. The magnitude and the phase are essential in fully characterizing
the superconducting gap. Angle-resolved photoemission spectroscopy (ARPES) has
played a key role in determining the gap symmetry in unconventional
superconductors. However, it has been considered so far that ARPES can only
measure the magnitude of the superconducting gap but not its phase; the phase
has to be detected by other phase-sensitive techniques. Here we propose a new
method to directly detect the superconducting gap sign by using ARPES. This
method is successfully validated in a cuprate superconductor with a well-known
$d$-wave gap symmetry. When two bands are nearby in momentum space and have a
strong interband interaction, the resulted electronic structures in the
superconducting state are sensitive to the relative gap sign between the two
bands which can be captured by ARPES measurements. Our present work provides a
new way to detect the gap sign and can be applied to various superconductors,
particularly those with multiple orbitals like the iron-based superconductors.
It also makes ARPES more powerful to determine both the gap magnitude and the
phase that are significant in understanding the superconductivity mechanism of
unconventional superconductors.
