Stability and electronic properties of two-dimensional indium iodide

Jizhang Wang, Baojuan Dong, Huaihong Guo, Teng Yang, Zhen Zhu, Gan Hu, Riichiro Saito, and Zhidong Zhang

Phys. Rev. B 95, 045404 – Published 3 January 2017

Abstract

Based on ab initio density functional calculations, we studied the stability and electronic properties of two-dimensional indium iodide (InI). The calculated results show that monolayer and few-layer InI can be as stable as its bulk counterpart. The stability of the monolayer structure is further supported by examining the electronic and dynamic stability. The interlayer interaction is found to be fairly weak ( $\sim 160$ meV/atom) and mechanical exfoliation to obtain monolayer and few-layer structures will be applicable. A direct band gap of 1.88 eV of the bulk structure is obtained from the hybrid functional method, and is comparable to the experimental one ( $\sim 2.00$ eV). The electronic structure can be tuned by layer stacking and external strain. The size of the gap is a linear function of an inverse number of layers, suggesting that we can design few-layer structures for optoelectronic applications in the visible optical range. In-plane tensile or hydrostatic compressive stress is found to be useful not only in varying the gap size to cover the whole visible optical range, but also in inducing a semiconductor-metal transition with an experimentally accessible stress. The present result strongly supports the strategy of broadening the scope of group-V semiconductors by looking for isoelectronic III-VII atomic-layered materials.

Received 6 October 2016

DOI:https://doi.org/10.1103/PhysRevB.95.045404

Physics Subject Headings (PhySH)

Band gap Electronic structure

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jizhang Wang¹, Baojuan Dong¹, Huaihong Guo^2,3, Teng Yang^1,3,*, Zhen Zhu^4,5, Gan Hu¹, Riichiro Saito³, and Zhidong Zhang¹

¹Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China
²College of Sciences, Liaoning Shihua University, Fushun 113001, China
³Department of Physics, Tohoku University, Sendai 980-8578, Japan
⁴Physics and Astronomy Department, Michigan State University, East Lansing, Michigan 48824, USA
⁵Materials Department, University of California, Santa Barbara, California 93106-5050, USA

^*yangteng@imr.ac.cn

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Vol. 95, Iss. 4 — 15 January 2017

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Images

Figure 1
Atomic structures and structural properties of InI crystal. (a) Bulk and monolayer InI, compared with black phosphorene (BP). (b) Cohesive energy $E_{c}$ ( $= E_{InI} - E_{I-atom} - E_{In-atom}$ ) as a function of lattice strain for both bulk and monolayer InI. (c) Upper: Interlayer interaction of bulk InI as a function of distance $d$ between two neighboring In layers. The reference energy at large distance $d$ is set to zero. Bottom: Interaction $Δ E_{L}$ as a function of the inverse of layer number $1 / N$ . Here, $Δ E_{L} = [E_{tot} (N) - E_{tot} (\infty)] / N$ , in which $N$ [ $= 2, 3, 4, ..., \infty$ (bulk)] is the number of layers. (d) Shear energy $E_{shear}$ of bulk InI as a function of tilting angle $θ$ along both $a$ and $b$ directions.
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Figure 2
(a) Total charge density $ρ$ and (b) interlayer charge density $Δ ρ$ of bulk InI. $Δ ρ = ρ (bulk) - ρ (two layers)$ . The cutting plane is chosen to go through the two nearest In atoms from both the upper and the lower layers. Isovalue contour lines with values are given to show the total and interlayer charge density distribution.
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Figure 3
Electronic and phonon band structure of InI. (a) Electronic band structure, density of states, and crystal orbital overlap population (COOP) of bulk and monolayer InI from the left to the right panel. Bulk and monolayer are shown as the black solid line and red circles, respectively. The high symmetry points of BZ are indicated in the inset. “+” and “ $-$ ” in COOP represent bonding and antibonding states, i.e., between In and I atoms (bulk as the black line and monolayer as the red circles) or between two neighboring In atoms (green line). (b) Phonon dispersion relation and zone-center Raman spectra of monolayer InI. Three Raman-active modes marked by blue dots in the dispersion relation are visualized and irreducible representations given in the inset.
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Figure 4
(a) Electronic structure evolving with layer number $N$ of InI crystals from bulk to few-layer to monolayer. (b) Electronic direct and indirect band gap ( $E_{g}^{d}$ and $E_{g}^{i}$ ) calculated from GGA-PBE as a function of the inverse layer number $1 / N$ . Direct band gaps for monolayer and bulk calculated from HSE calculations, as well as the experimental bulk band gap are also given for a comparison. (c) Electron structure of monolayer InI as a function of strain. (d) Stress dependence of HSE-corrected electronic band gap $E_{g}$ of monolayer InI. A visible optical range is marked by an arrow between two dashed lines. The inset shows the stress-strain curve of monolayer InI.
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