Finite-temperature phase diagram and critical point of the Aubry pinned-sliding transition in a two-dimensional monolayer

The Aubry unpinned-pinned transition in the sliding of two incommensurate lattices occurs for increasing mutual interaction strength in one dimension and is of second order at $T=0$, turning into a crossover at nonzero temperatures. Yet, real incommensurate lattices come into contact in two dimensions, at finite temperature, generally developing a mutual Novaco-McTague misalignment, conditions in which the existence of a sharp transition is not clear. Using a model inspired by colloid monolayers in an optical lattice as a test two-dimensional (2D) case, simulations show a sharp Aubry transition between an unpinned and a pinned phase as a function of corrugation. Unlike one dimension, the 2D transition is now of first order, and, importantly, remains well defined at $T>0$. It is heavily structural, with a local rotation of moir\'e pattern domains from the nonzero initial Novaco-McTague equilibrium angle to nearly zero. In the temperature (T)-corrugation strength plane, the thermodynamical coexistence line between the unpinned and the pinned phases is strongly oblique, showing that the former has the largest entropy. This first-order Aubry line terminates with a novel critical point T=Tc, marked by a susceptibility peak. The expected static sliding friction upswing between the unpinned and the pinned phase decreases and disappears upon heating from $T=0$ to T=Tc. The experimental pursuit of this novel scenario is proposed.