  The concept of non-Hermiticity has expanded the understanding of band
topology leading to the emergence of counter-intuitive phenomena. One example
is the non-Hermitian skin effect (NHSE), which involves the concentration of
eigenstates at the boundary. However, despite the potential insights that can
be gained from high-dimensional non-Hermitian quantum systems in areas like
curved space, high-order topological phases, and black holes, the realization
of this effect in high dimensions remains unexplored. Here, we create a
two-dimensional (2D) non-Hermitian topological band for ultracold fermions in
spin-orbit-coupled optical lattices with tunable dissipation, and
experimentally examine the spectral topology in the complex eigenenergy plane.
We experimentally demonstrate pronounced nonzero spectral winding numbers when
the dissipation is added to the system, which establishes the existence of 2D
skin effect. We also demonstrate that a pair of exceptional points (EPs) are
created in the momentum space, connected by an open-ended bulk Fermi arc, in
contrast to closed loops found in Hermitian systems. The associated EPs emerge
and shift with increasing dissipation, leading to the formation of the Fermi
arc. Our work sets the stage for further investigation into simulating
non-Hermitian physics in high dimensions and paves the way for understanding
the interplay of quantum statistics with NHSE.
