Electronic properties of a \ensuremath{\pi}-conjugated Cairo pentagonal lattice: Direct band gap, ultrahigh carrier mobility, and slanted Dirac cones

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

Xiaofei Shao, Xiaobiao Liu, Xinrui Zhao, Junru Wang, Xiaoming Zhang, and Mingwen Zhao

Phys. Rev. B 98, 085437 – Published 30 August 2018

Abstract

Two-dimensional (2D) lattices composed exclusively of pentagons represent an exceptional structure of materials correlated to the famous pentagonal tiling problem in mathematics, but their π conjugation and the related electronic properties have never been reported. Here, we propose a tight-binding (TB) model for a 2D Cairo pentagonal lattice and demonstrate that p-d π conjugation in the unique framework leads to intriguing properties, such as an intrinsic direct band gap, ultrahigh carrier mobility, and even slant Dirac cones. On the basis of first-principles calculations, we predict a candidate material, 2D penta- $Ni P_{2}$ monolayer, derivated from bulk $Ni P_{2}$ crystal, to realize the predictions of the TB model. It has ultrahigh carrier mobility ( $\sim 10^{5} - 10^{6} c m^{2} V^{- 1} s^{- 1}$ ) comparable to that of graphene and an intrinsic direct band gap of 0.818 eV, properties which have long been desired for high-speed electronic devices. The stability and possible synthetic routes of penta- $Ni P_{2}$ monolayer are also discussed.

Received 27 March 2018
Revised 16 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.085437

Physics Subject Headings (PhySH)

Electrical conductivity Electronic structure

2-dimensional systems Narrow band gap systems

First-principles calculations Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiaofei Shao¹, Xiaobiao Liu¹, Xinrui Zhao², Junru Wang¹, Xiaoming Zhang¹, and Mingwen Zhao^1,*

¹School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, Shandong, China
²School of the Gifted Young, University of Science and Technology of China, Hefei 230026, Anhui, China

^*Corresponding author: zmw@sdu.edu.cn

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Vol. 98, Iss. 8 — 15 August 2018

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Figure 1
(a) Schematic representation of the TB model involving nearest-neighbor ( $t_{1}$ and $t_{2}$ ) and next-nearest-neighbor ( $t_{3}$ ) hoppings. Atomic orbitals in the unit cell are numbered by the blue numbers. ${\vec{a}}_{1}$ and ${\vec{a}}_{2}$ are the two basis vectors which are taken as $x$ and $y$ directions. (b) The energy-band diagram in the parameter space ( $ɛ / t_{0}$ , γ) of the TB model. The yellow line indicates the boundary between semimetals and semiconductors. (c)–(e) The TB band structures of (c) the semiconducting phase with $ɛ < (γ - 2 / γ) t_{0}$ and of semimetallic phases with (d) $ɛ = (γ - 2 / γ) t_{0}$ and (e) $ɛ > (γ - 2 / γ) t_{0}$ . The coordinates of the highly symmetric points in the square BZ are Γ (0,0), $M$ (π/ $a$ , 0), and $K$ (π/ $a$ , π/ $a$ ). The energy at the valence-band maximum is set to zero.
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Figure 2
(a) Top and side views of the atomic structure of 2D penta- $Ni P_{2}$ monolayer. (b)–(e) Electronic band structures of penta- $Ni P_{2}$ monolayer obtained by using (b) PBE and (c) HSE06 functionals, (d) penta- $Ni P_{2}$ bilayer, and (e) penta- $Ni P_{2}$ monolayer under tensile strain of 11%. The energy at the VBM is set to zero. (f) Variation of the band gap of penta- $Ni P_{2}$ monolayer as a functional tensile strain obtained by using the HSE06 functional.
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Figure 3
Orbital-resolved electron density of states (PDOS) projected onto (a) Ni(II) and (b) P atoms. The energy at the VBM is set to zero. (c) The isosurfaces of the Kohn-Sham electron wave functions of the (c) VBM and (d) CBM.
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Figure 4
(a) Schematic representation of the $d$ -orbital splitting and p-d π conjugation. (b) Electronic band structures of TB model (blue line) with the parameters of $t_{0} = 1.7 eV, γ = 1.6, γ^{'} = 0.6$ , and $ɛ = 0.34 eV$ . The band lines of penta- $Ni P_{2}$ monolayer nearest to the Fermi level obtained from DFT-HSE06 strategy are indicated by the red dots. The energy at the VBM is set to zero. (c) Three-dimensional plot of the highest valence band and the lowest conduction band near the Fermi level in the reciprocal space.
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Figure 5
Predicted carrier mobilities of typical 2D materials by using an acoustic phonon-limited scattering model on the basis of DFT-HSE06 calculations. Only the highest mobility (electron or hole) of the materials is presented for purpose of comparison.
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Figure 6
(a) Crystal structure of monoclinic $Ni P_{2}$ crystal. Ni and P atoms are represented by blue and red balls. (b) Top and side views of the atomic arrangement on the $(10 \bar{1})$ plane of monoclinic $Ni P_{2}$ crystal. (c) Phonon spectrum of penta- $Ni P_{2}$ monolayer. (d) Molecular dynamics simulations of penta- $Ni P_{2}$ monolayer at a temperature of 500 K for 5 ps. The configuration at the end of the simulation is plotted in the inset of this figure, which shows the small ripple of penta- $Ni P_{2}$ monolayer at high temperature.
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Physical Review B

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

Xiaofei Shao, Xiaobiao Liu, Xinrui Zhao, Junru Wang, Xiaoming Zhang, and Mingwen Zhao

Phys. Rev. B 98, 085437 – Published 30 August 2018

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Physical Review B

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

Xiaofei Shao, Xiaobiao Liu, Xinrui Zhao, Junru Wang, Xiaoming Zhang, and Mingwen Zhao

Phys. Rev. B 98, 085437 – Published 30 August 2018

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