  Materials with a negative Poisson's ratio, also known as auxetic materials,
exhibit unusual and counterintuitive mechanical behavior - becoming fatter in
cross-section when stretched. Such behavior is mostly attributed to some
special reentrant or hinged geometric structures regardless the chemical
composition and electronic structure of a material. Here, using first
principles calculations, we report a new class of auxetic single-layer
two-dimensional (2D) materials, i.e., the 1T-type monolayer crystals of groups
6-7 transition-metal dichalcogenides, MX$_2$ (M = Mo, W, Tc, Re; X = S, Se,
Te). These materials have a crystal structure distinct from all other known
auxetic materials. They exhibit an intrinsic in-plane negative Poisson's ratio,
which is dominated by the electronic effects. We attribute the occurrence of
such auxetic behavior to the strong coupling between the chalcogen p orbitals
and the intermetal t$_{2g}$-bonding orbitals within the basic triangular
pyramid structure unit. The unusual auxetic behavior in combination with other
remarkable properties of monolayer 2D materials could lead to novel
multi-functionalities.
