  Coexisting orders are key features of strongly correlated materials and
underlie many intriguing phenomena from unconventional superconductivity to
topological orders. Here, we report the coexistence of two interacting
charge-density-wave (CDW) orders in EuTe4, a layered crystal that has drawn
considerable attention owing to its anomalous thermal hysteresis and a
semiconducting CDW state despite the absence of perfect FS nesting. By
accessing unoccupied conduction bands with time- and angle-resolved
photoemission measurements, we find that mono- and bi-layers of Te in the unit
cell host different CDWs that are associated with distinct energy gaps. The two
gaps display dichotomous evolutions following photoexcitation, where the larger
bilayer CDW gap exhibits less renormalization and faster recovery.
Surprisingly, the CDW in the Te monolayer displays an additional
momentum-dependent gap renormalization that cannot be captured by
density-functional theory calculations. This phenomenon is attributed to
interlayer interactions between the two CDW orders, which account for the
semiconducting nature of the equilibrium state. Our findings not only offer
microscopic insights into the correlated ground state of EuTe4 but also provide
a general non-equilibrium approach to understand coexisting, layer-dependent
orders in a complex system.
