Spontaneous Symmetry Breaking and Dynamic Phase Transition in Monolayer Silicene

Abstract

The $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ honeycomb of silicene monolayer on Ag(111) was found to undergo a phase transition to two types of mirror-symmetric boundary-separated rhombic phases at temperatures below 40 K by scanning tunneling microscopy. The first-principles calculations reveal that weak interactions between silicene and Ag(111) drive the spontaneous unusual buckling in the monolayer silicene, forming two energy-degenerate and mirror-symmetric $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ rhombic phases, in which the linear band dispersion near the Dirac point and a significant gap opening (150 meV) at the Dirac point were induced. The low transition barrier between these two phases enables them to be interchangeable through dynamic flip-flop motion, resulting in the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ honeycomb structure observed at high temperature.