Design monolayer iodinenes based on halogen bond and tiling theory

Xenes, two-dimensional (2D) monolayers composed of a single element, with graphene as a typical representative, have attracted widespread attention. Most of the previous Xenes, $X$ from group-IIIA to group-VIA elements, have bonding characteristics of covalent bonds. In this paper, we unveil the pivotal role of a halogen bond, which is a distinctive type of bonding with interaction strength between that of a covalent bond and a van der Waals interaction, in 2D group-VIIA monolayers. Combing the ingenious non-edge-to-edge tiling theory and state-of-the-art ab initio method with refined local density functional M06-L, we provide a precise and effective bottom-up construction of 2D iodine monolayer sheets, iodinenes, primarily governed by halogen bonds, and successfully design a category of stable iodinenes encompassing herringbone, Pythagorean, gyrated truncated hexagonal, i.e., diatomic kagome, and gyrated hexagonal tiling patterns. These iodinene structures exhibit a wealth of properties, such as nontrivial topology, flat bands and fascinating optical characteristics, offering valuable insights and guidance for future experimental investigations. Our paper not only unveils the unexplored halogen bonding mechanism in 2D materials but also opens an avenue for designing other noncovalent bonding 2D materials.

Figure 1

(a) 3D crystal structure (the upper panel) of bulk iodine and its monolayer (the lower panel). Black bold and red dashed lines indicate intramolecular covalent bonds and intermolecular halogen bonds (XBs), respectively. (b) Electrostatic potential (ESP) map on 0.015 a.u. charge density isosurface of monolayer herringbone iodinene. A $\sigma$ hole occurs at the blue tip on the isosurface with positive electrostatic potential. (c) Phonon spectra of monolayer herringbone iodinene. (d) Schematic diagram of XB between two iodine molecules. The iodine atoms, $p_y$ orbitals (lone pairs), ${\sigma }_{p_x}$ bond, and ${\sigma }_{p_x}^{*}$ antibond orbitals ($\sigma$ hole) are depicted as purple balls, green spindles, yellow ellipsoid, and blue ellipsoid, respectively. $p_z$ and $s$ orbitals are not shown here because $p_z$ sits out of plane and $s$ is the core orbital. The red dotted line signifies the presence of the XB, involving the transfer of electrons from a lone pair to a $\sigma$ hole through a donor-acceptor interaction. (e) Schematic diagram of XB angle.

Figure 2

(a1)–(a5) Five non-edge-to-edge tilings for mapping to desired monolayer iodinenes and (b1)–(b5) corresponding relaxed crystal structures. The nomenclature of those tilings is adopted in a visualized way. Herringbone: herringbone tiling; GTH: gyrated truncated hexagonal tiling, which is topologically equivalent to diatomic-kagome structures; GH: gyrated hexagonal tiling; TDT: truncated distorted trihexagonal tiling. In (b1)–(b5), the covalent bond and halogen bond are depicted by black and red lines, respectively. Grey dotted lines indicate the unit cell.

Figure 3

(a) Band structures of monolayer herringbone iodinene. (b) The Wilson loop along $k_{110}$ direction. Insets represent the enlarged Wilson loop around $\mathrm{\Theta }=\pi$, indicating the nontrivial higher-order topology with the nonzero second Stiefel-Whitney number. (c) Energy spectra in real space, with the energy of the two corner states highlighted in red. (d) The distribution of the two corner states (depicted in red) in real space.

Figure 4

(a) Band structures of GTH/diatomic-kagome iodinene. (b) Helical edge states of GTH/diatomic-kagome iodinene along the ($1\overline{1}$) edge. (c), (d) Band structures of Pythagorean and GH iodinenes respectively. Blue dashed lines and black lines are the band structures without and with spin-orbit coupling (SOC) respectively. Grey arrows indicate the band gap. Topological ${\mathrm{Z}}_2$ invariants are labeled above the occupied states defined.

Figure 5

Computed in-plane optical absorption coefficients of (a) herringbone and (b) Pythagorean iodinenes in a unit of ${10}^5{\mathrm{cm}}^{-1}$ as a function of photon energy. XX and YY indicate the directions along two primitive vectors of unit cell.