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From a Normal Insulator to a Topological Insulator in Plumbene

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From a Normal Insulator to a Topological Insulator in Plumbene From a normal insulator to a topological insulator in plumbene 1,2 1 1 Xiang-Long Yu , Li Huang , and Jiansheng Wu ∗ 1 Department of Physics, South University of Science and Technology of China, Shenzhen 518055, P.R. China and 2 School of Physics and Technology, Wuhan University, Wuhan 430072, P.R. China Plumbene, similar to silicene, has a buckled honeycomb structure with a large band gap ( 400 meV). All previous studies have shown that it is a normal insulator. Here, we perform first-principles∼ calculations and employ a sixteen-band tight-binding model with nearest-neighbor and next-nearest-neighbor hopping terms to investigate electronic structures and topological properties of the plumbene monolayer. We find that it can be- come a topological insulator with a large bulk gap ( 200 meV) through electron doping, and the nontrivial state is very robust with respect to external strain. Plumbene∼ can be an ideal candidate for realizing the quantum spin Hall effect at room temperature. By investigating effects of external electric and magnetic fields on electronic structures and transport properties of plumbene, we present two rich phase diagrams with and without electron doping, and propose a theoretical design for a four-state spin-valley filter. PACS numbers: 73.43.-f, 73.22.-f, 71.70.Ej I. INTRODUCTION lengable to prepare high-quality samples with chemical func- tionalizations, resulting in the unrealizable observation of the QSH effect in such experiments. For device applications it is In 2005, Kane and Mele first proposed the prototypicalcon- almost impossible. 1,2 cept of quantum spin Hall (QSH) insulator in graphene . Al- Therefore, to find QSH insulators with simple lattice struc- though the spin-orbit coupling (SOC) opens a band gap at the 3 3 tures and large bulk gaps has become our main purpose. Bi Dirac point, the associated gap is so small ( 10− meV ) monolayer film is a promising candidate, and theoretical stud- ff ∼ that the QSH e ect in graphene only appears at an unrealisti- ies have also shown that it is a topological insulator with cally low temperature. Subsequently, other group-IV materi- a large bulk gap ( 500 meV)20–24. But so far the QSH als with a honeycomb-like lattice and larger SOC interaction effect and topological∼ properties of Bi monolayer have not are reported to host the QSH effect with experimental accessi- 4–10 been reported experimentally. Our present research focuses ble gaps, such as silicene, germanene and stanene . How- on another large-gap insulator material, plumbene monolayer. ever, their gaps still are not large enough for the QSH effect Recently the stability of the buckled 2D Pb thin film was which can be realized easily at room temperature. Up to now, reported24–26. Previous theoretical works have given the same the quantized conductance through the QSH edge states have result that plumbene is a normal band insulator17,24. How- only been verified in several experiments10 (e.g. Bi bilayer 7 11 12 ever, we find that the system can become a topological insu- film , HgTe/CdTe , and InAs/GaSb quantum wells). These lator through electron doping, which is feasible using gating QSH experiments have various limitations, such as a small methods by electric fields in experiments27,28. In this paper, bulk gap, toxicity and technological difficulties during pro- we perform detailed first-principles and tight-binding calcula- cessing. The interference of thermally activated carriers in the tions to investigate band structures and topological properties bulk is the main question for realizing the QSH effect at room of plumbene. Our results show that the band structures of temperature. Therefore, it is urgent to find new topological gated plumbene harbour two spin-polarized Dirac cones with insulators with a large bulk energy gap that can stabilize the up to 96% ratio at the corner of the Brillouin zone, and that edge current. the system can change from a normal insulator with a large At present two-dimensional (2D) materials in groups IV gap of 400 meV to a topological insulator with a large bulk ∼ and V are promising candidates for the QSH effect. Theo- gap of 200 meV. The QSH state is very robust with respect ∼ retical calculations predict that a large bulk gap can be ob- to external strain. By investigating the effects of external per- tained through fluorination, hydrogenation, or other types of pendicular electric and magnetic fields on plumbene, two rich functionalizations13–18. The purpose of atom or molecule ab- phase diagrams are obtained and we further propose a design arXiv:1702.07447v1 [cond-mat.mtrl-sci] 24 Feb 2017 sorption is to saturate the pz orbital or dangling bond so that for a four-state spin-valley filter. Owing to the simple struc- a band gap can be opened at the Dirac point without SOC. ture, two large bulk gaps and various responses in external When the SOC is considered, a larger gap can be obtained in fields, plumbene can be a promising platform for topologi- the corresponding system. For example, first-principles calcu- cal phenomena and new quantum device applications at room lations predict a 2D QSH insulator in F-decorated plumbene temperature. monolayer with an extraordinarily giant bulk gap of 1.34 The remainder of the paper is organized as follows. In eV17. Unfortunately, a recent experiment has revealed that de- Sec. II, we describe the crystal structure of plumbene and our fects and disorders increase rapidly during plasma fluorination calculation methods, including first-principles methods and a and hydrogenation of materials and even under short plasma sixteen-band tight-binding model. In Sec. III, we study the exposures19. The systems with chemical functionalizations topological characteristics of plumbenewithout and with elec- may not be stable for long periods of time in air, especially tron doping; through investigating the effects of external elec- with hydrogenation15,19. Thus, it is rather difficult and chal- tric and magnetic fields on electronic structures of plumbene, 2 be 8.5. SOC is included in all the first-principles calculations unless stated otherwise. C. Tight-binding model In most of the previous works about 2D group-IV materi- als, only the NN hopping is considered in tight-binding mod- els, because the itineracy of electrons is bad and they focus on the band structure near the Fermi level6,26,34–36. There is no definitive strategy to fit the bands. In this study, both the NN and next-nearest-neighbor (NNN) hoppings are intro- duced into the total Hamiltonian so that the two bands above E can be fitted better. Three NN and six NNN translation FIG. 1: (Color online) Lattice structure of the buckled plumbene F vectors are from (a) the top view and (b) the side view. (c) The angle between the Pb-Pb bond and the z direction is defined as φ. (d) The first Bril- a √3 1 d1 = φ , louin zone with hight-symmetry points. Green and blue spheres cor- √3 2 2 cot a √3 1 respond to A and B sublattices, respectively. a1 and a1 are primitive d2 = cot φ , (1) √3 − 2 2 vectors. b1 and b1 are reciprocal lattice vectors. d = a 0 1 cot φ , 3 √3 − we present two rich phase diagrams and a theoretical design v = a 1 √3 , v = a 1 0 0 , for a four-state spin-valley filter is proposed; substrate effects 1 2 2 0 2 v = a 1 √3 , v = a 1 √3 , (2) on plumbene are also discussed. Finally, we conclude this 3 2 2 0 4 2 2 0 − 1− √3− work with a brief summary in Sec. IV. v5 = a 1 0 0 , v6 = a 0 , − − 2 2 where a is defined as the NNN distance. The total Hamilto- II. COMPUTATIONAL DETAILS nian read ′ ′ A. Crystal structure H = H00 + H0 + HA0 + HB0 + Hso, (3) where the five terms correspond to on-site energy, NN hop- Plumbene has a buckled honeycomb structure, as shown in ping, NNN hopping in A and B sublattices, and effective on- Fig. 1. The lattice constant a = 4.93 Å and the nearest- 0 site SOC interaction, respectively. They reads neighbor (NN) Pb-Pb distance d = 3.00 Å are obtained through structural optimization, which agree with the previous H = ε c† c , (4) calculations26. Thespace groupis P3¯m1. Theangle φ, defined 00 X α Liασ Liασ as being between the Pb-Pb bond and the z direction in Fig. 1 L,i,α,σ (c), is 108.34◦. In comparison to graphene with φ = 90◦, the larger Pb-Pb bond length weakens the π π overlap. Mean- H = t c† c − 0 ABδαα′ A,i+δ,ασ Biα′σ σ π i,δ,α,αP ,σ while, the buckling can enhance the overlap between and ′ (5) + orbitals and stabilizes the system. The same mechanism also tBAηα′αc† + cAiασ, P B,i η,α′σ applies for other 2D materials in group IV which share the i,η,α,α′,σ similar buckled configuration. H′ = t c† c , A0 X AAvαα′ A,i+v,ασ Aiα′σ (6) B. First-principles calculations i,v,σ In this paper, our first-principles calculations for electronic ξ0 ξ0 ξ0 i 2 c†Aiz cAiy i 2 c†Aiy cAiz + i 2 c†Aiz cAiy ↑ ↓ − ↓ ↑ ↓ ↑ structures of plumbene were carried out using the WIEN2K ξ0 + ξ0 ξ0 29 i 2 c†Aiy cAiz i 2 c†Aiy cAix i 2 c†Aix cAiy package with a full-potential augmented plane wave , based − ↑ ↓ ↑ ↑ − ↑ ↑ ξ0 + ξ0 ξ0 on the Perdew-Burke-Ernzerhof generalized gradient approx- i 2 c†Aiy cAix i 2 c†Aix cAiy 2 c†Aiz cAix − ↓ ↓ ↓ ↓ − ↑ ↓ 30 ξ0 ξ0 ξ0 imation (PBE-GGA) .
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