  Two-dimensional (2D) topological insulator (TI) have been recognized as a new
class of quantum state of matter. They are distinguished from normal 2D
insulators with their nontrivial band-structure topology identified by the
$Z_2$ number as protected by time-reversal symmetry (TRS). 2D TIs have
intriguing spin-velocity locked conducting edge states and insulating
properties in the bulk. In the edge states, the electrons with opposite spins
propagate in opposite directions and the backscattering is fully prohibited
when the TRS is conserved. This leads to quantized dissipationless "two-lane
highway" for charge and spin transportation and promises potential
applications. Up to now, only very few 2D systems have been discovered to
possess this property. The lack of suitable material obstructs the further
study and application. Here, by using first-principles calculations, we propose
that the functionalized MXene with oxygen, M$_2$CO$_2$ (M=W, Mo and Cr), are 2D
TIs with the largest gap of 0.194 eV in W case. They are dynamically stable and
natively antioxidant. Most importantly, they are very likely to be easily
synthesized by recent developed selective chemical etching of transition-metal
carbides (MAX phase). This will pave the way to tremendous applications of 2D
TIs, such as "ideal" conducting wire, multifunctional spintronic device, and
the realization of topological superconductivity and Majorana modes for quantum
computing.
