Fig. 1: Orbital interactions of single-element monolayers.
From: Lone-pair activated ferroelectricity and stable charged domain wall in Bi monolayer
a Crystal structure of 2D ferroelectric single-element monolayers. Orange and purple spheres indicate the two non-equivalent atoms, labeled as M1 and M2, respectively. The partial charge density of pz is shown in both asymmetric and centrosymmetric environment. b Projected electronic density of states (DOS) for Bi1 pz and c crystal orbital Hamilton populations (COHP) for Bi1 pz and Bi2 px/py in asymmetric and centrosymmetric environment, respectively. Since the COHP of Bi1 pz–Bi2 px and Bi1 pz–Bi2 py are degenerate, only one of them is shown. The highest occupied state (Fermi level) is set to 0 eV. d The Bi1 px/py and Bi2 px/py interactions create filled bonding and empty antibonding combinations. The antibonding orbitals of P, As and Sb are also represented. e When the coordination environment of the Bi atom is asymmetric, the antibonding combination of px and py orbital is stabilized by the lone-pair of Bi1 pz coupling to form the upper valence band (VB). f When the coordination environment of Bi atom is centrosymmetric, this orbital interaction is suppressed due to destructive interference. In this case, the antibonding combination between Bi1 pz and Bi2 px/py mainly forms the upper VB without Bi1 pz orbital contribution. In e, f, the orange and purple balls represent Bi1 and Bi2, respectively. If adjacent orbitals are the same color, they represent symmetric wavefunctions, otherwise antisymmetric wavefunctions.
