  We demonstrate for the first time a linear-zigzag phase transition induced
solely by temperature of the $^{40}$Ca$^{+}$ ion crystals in a
surface-electrode trap. In contrast to the previously observed counterparts
based on change of the mechanical equilibrium conditions of the ions, our
presented structural phase transition occurs due to controllable influence of
thermal fluctuation. The ions' temperature is well controlled by tuning the
cooling laser and the experimental observation could be fully understood by
classical Langevin equation in addition to the effects from thermal
fluctuation. Our experimental investigation indicates the fantastic role of
thermal fluctuation played in the thermodynamic process at atomic level, which
might bridge the thermodynamics from the macroscopic domain to the quantum
regime.
