Electronic properties of a π-conjugated Cairo pentagonal lattice: Direct band gap, ultrahigh carrier mobility, and slanted Dirac cones

Two-dimensional (2D) lattices composed exclusively of pentagons represent an\nexceptional structure of materials correlated to the famous pentagonal tiling\nproblem in mathematics, but their $\\pi$-conjugation and the related electronic\nproperties have never been reported. Here, we propose a tight-binding (TB)\nmodel for a 2D Cairo pentagonal lattice and demonstrate that $p$-$d$\n$\\pi$-conjugation in the unique framework leads to intriguing properties, such\nas an intrinsic direct band gap, ultra-high carrier mobility and even slant\nDirac cones. On the basis of first-principles calculations, we predict a\ncandidate material, 2D penta-NiP$_2$ monolayer, derivated from bulk NiP$_2$\ncrystal, to realize the predictions of the TB model. It has ultra-high carrier\nmobility ($\\sim$$10^5-10^6$ $cm^2V^{-1}s^{-1}$) comparable to that of graphene\nand an intrinsic direct band gap of 0.818 eV, which are long desired for\nhigh-speed electronic devices. The stability and possible synthetic routes of\npenta-NiP$_2$ monolayer are also discussed.\n