# Finite-temperature phase diagram and critical point of the Aubry pinned-sliding transition in a 2D monolayer

## TL;DR

This study investigates the finite-temperature phase diagram of the Aubry transition in a 2D monolayer, revealing a first-order transition with a critical point, differing from the 1D case, with implications for experimental observation.

## Contribution

The paper demonstrates that in two dimensions, the Aubry transition is first-order at finite temperature and identifies a novel critical point, contrasting with the second-order transition in 1D.

## Key findings

- Aubry transition in 2D is first-order at finite T.
- A thermodynamic coexistence line with a critical point is identified.
- Sliding friction behavior changes with temperature, disappearing at the critical point.

## Abstract

The Aubry unpinned--pinned transition in the sliding of two incommensurate lattices occurs for increasing mutual interaction strength in one dimension ($1D$) 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 ($2D$), 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 $2D$ case, simulations show a sharp Aubry transition between an unpinned and a pinned phase as a function of corrugation. Unlike $1D$, 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 ($W_0$) 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 $T=T_c$, 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 $T=T_c$. The experimental pursuit of this novel scenario is proposed.