Structural phase transitions between semiconductors and topological insulators have rich applications in nanoelectronics but are rarely found in two-dimensional (2D) materials. In this work, by combining ab initio computations and evolutionary structure search, we investigate two stable 2D forms of gold(I) telluride (Au$_{2}$Te) with square symmetry, noted as s(I)- and s(II)-Au$_{2}$Te. s(II)-Au$_{2}$Te is the global minimum structure and is a room-temperature topological insulator. s(I)-Au$_{2}$Te is a direct-gap semiconductor with high carrier mobilities and unusual in-plane negative Poissons ratio. Both s(I) and s(II) phases have ultra-low Youngs modulus, implying high flexibility. By applying a small tensile strain, s(II)-Au$_{2}$Te can be transformed into s(I)-Au$_{2}$Te. Hence, a structural phase transition from a room-temperature topological insulator to an auxetic semiconductor is found in the 2D forms of Au$_{2}$Te, which enables potential applications in phase-change electronic devices. Moreover, we elucidate the mechanism of the phase transition with the help of phonon spectra and group theory analysis.
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