Multiple Dirac Points and Hydrogenation-Induced Magnetism of

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Multiple Dirac Points and Hydrogenation-Induced Magnetism of Germanene Layer on Al (111) Surface Gang Liu, Shi-Bing Liu, Bo Xu, Chuying Ouyang, Hai-Ying Song, Shan Guan, and Shengyuan A. Yang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02413 • Publication Date (Web): 25 Nov 2015 Downloaded from http://pubs.acs.org on November 26, 2015

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The Journal of Physical Chemistry Letters

Multiple Dirac Points and Hydrogenation-induced Magnetism of Germanene Layer on Al (111) Surface G. Liu1,2, S. B. Liu1*, B. Xu2, C. Y. Ouyang2, H. Y. Song1, S. Guan3,4, S. A. Yang3

1

Strong-field and Ultrafast Photonics Lab, Institute of Laser Engineering, Beijing University of Technology, Beijing 100124, China

2

College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China

3

Research Laboratory for Quantum Materials and EPD Pillar, Singapore University of Technology and Design, Singapore 487372, Singapore 4

School of Physics, Beijing Institute of Technology, Beijing 100081, China

S Supporting Information ○

Abstract: A continuous germanene layer grown on the Al (111) surface has recently been achieved in experiment. In this work, we investigate its structural, electronic, and hydrogenation-induced properties through first-principles calculations. We find that despite having a different lattice structure from its free-standing form, germanene on Al (111) still possesses Dirac points at high-symmetry K and K’ points. More importantly, there exist another three pairs of Dirac points on the K(K’)-M high-symmetry lines, which have highly anisotropic dispersions due to the reduced symmetry. These massless Dirac fermions become massive when spin-orbit coupling is included. Hydrogenation of the germanene layer strongly affects its structural and electronic properties. Particularly, when not fully hydrogenated, ferromagnetism can be induced due to unpaired local orbitals from the unsaturated Ge atoms. Remarkably, we discover that the one-side semi-hydrogenated germanene turns out to be a two-dimensional half-semimetal, representing a novel state of matter that is simultaneously a half-metal and a semimetal.

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Graphene has attracted tremendous attention in science and technology due to its novel properties and promising applications.1-6 The success in the research of graphene has motivated us to further pursue other two-dimensional (2D) layered materials composed of elements other than carbon. For example, germanene, the germanium equivalent of graphene, has recently attracted great interest both in theory and in experiment.7-15 Compared with graphene, germanene may have even better prospect of application because it is more easily incorporated into the existing semiconductor industry. Theoretically, free-standing germanene has been predicted to favor a low-buckled structure because germanium prefers sp3 hybridization instead of sp2. Similar to graphene, the most important characteristic of germanene is the presence of two Dirac points located at the K’ and K points in the hexagonal Brillouin zone. In the absence of spin-orbit coupling (SOC), the π and π * bands linearly cross at the Dirac points at Fermi level, making the low-energy carriers behave as massless Dirac fermions.16 This would lead to an extremely higher carrier mobility, which offers potential advantages for performance enhancement in high-speed electronic devices. Furthermore, SOC effect could open a gap ~23.9 meV at the Dirac points, which would drive the system into an interesting topological quantum spin Hall insulator phase.17 More theoretical researches focus on engineering the properties of germanene, e.g., by doping, hydriding, applying external strain or electrical field, adsorbing atoms or molecules and so on,18-25 aiming to tailor its physical and chemical properties for practical applications. Experimentally, germanane, the fully hydrogenated germanene, has been fabricated using a wet chemistry method in 2013.26 However, germanene, which was originally predicted to be stable, has remained elusive. Recently, the experiment by Dávila et al. showed that a two-dimensional germanium layer could be grown by dry deposition of germanium onto the Au (111) surface, similar to the formation of silicene on Ag (111).27 Bampoulis et al. also proposed that the outermost layer of the Ge2Pt nanocrystal is a germanene layer.13 Furthermore, Li et al. reported the fabrication of germanene sheets on a Pt (111) surface.14 The choice of Pt (111) 3 ACS Paragon Plus Environment


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substrate was based on several considerations, such as its hexagonal symmetry serving as a growth template and its weaker interfacial interaction with the adsorbed 2D honeycomb sheets compared with other metals. However, it was found that on the Pt (111) surface, due to surface reconstruction, the germanene lattice did not show honeycomb-like structures in the high-resolution STM images;14 while for the Au (111) substrate, the obtained 2D germanene layers actually showed multiple co-existing phases.27 Quite recently, Derivaz et al. reported the successful fabrication of a continuous germanene layer on the Al (111) surface.15 Aluminum is chosen as the substrate because it is a simple metal without surface reconstruction, and its surface electron density is dominated by s-type orbitals.15 Due to these advantageous characteristics, germanene on Al (111) seems to have a better prospect compared with other experimentally realized systems. It is also noted that while the primitive honeycomb lattice has not been observed for germanene on Au (111),27 Pt (111),14 or Al (111),15 it was demonstrated in the high-resolution STM image for the germanene layer on Ge2Pt crystals.13 A review of these recent exciting experimental advances on germanene can be found in Ref. 28. So far, the properties of germanene on Pt (111),14 Ag (111) and some other substrates 19, 29-30 have been clarified through computational studies. However, the physical and chemical properties of germanene on Al (111), which are indispensable both for our fundamental understanding of these intriguing nanostructures and for their many potential applications, have yet to be explored. Motivated by the recent experimental progress and by the urgent need for theoretical understanding of the novel structures realized in experiment, in this letter, we investigate the structural, electronic, and hydrogenation-induced magnetic properties of germanene on Al (111) by using first-principles calculations. The germanene layer exhibits a superstructure different from its free-standing form. However, we find that the Dirac points at K and K’ still exist. More importantly, there appear extra three pairs of Dirac points located along the high-symmetry lines K(K’)-M, which show highly anisotropic dispersions due to the reduced symmetry at their locations. Such highly-anisotropic Dirac points on high-symmetry lines were 4 ACS Paragon Plus Environment

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previously proposed in a few predicted nanostructured materials.31-35 The co-existence of two types of Dirac points makes the current system an intriguing platform to explore the novel Dirac physics. The inclusion of SOC will turn the Dirac fermions from massless to massive. Furthermore, hydrogenation of the germanene layer strongly affects its structural and electronic properties. In particular, when not fully hydrogenated, ferromagnetism can be induced in the layer due to unpaired local orbital at the unsaturated Ge sites. Remarkably, we discover that the one-side semi-hydrogenated germanene turns out to be a half-metal and simultaneously a semimetal, hence corresponding to a new state of matter which we term as a half-semimetal. Our first-principles calculations were based on the density functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package (VASP) 36 and with the projector augmented-wave (PAW) approach.37 The exchange-correlation interaction was treated within the generalized gradient approximations (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional.38 A plane-wave basis set with cutoff energy of 550 eV was used for the valence electron wave functions. Monkhorst-Pack k-point mesh 39 was used with a grid size of 5×5×1 and 9×9×1 for the structural relaxation and the density-of-states (DOS) calculation, respectively. The entire systems were relaxed by conjugate gradient method until the force on each atom was less than 0.01 eV/ Å. The Al (111) substrate was modeled by a five-layer slab. This number of Al layers was tested to limit the possible slab back face effect. According to the experimental result,15 the superstructure of genmanene/aluminium was modeled with a 2×2×1 supercell of germanene corresponding to a 3×3×1 supercell of the aluminium (111) surface. It contained 8 Ge atoms and 45 Al atoms. All the models had a 35Å vacuum layer in the z-direction to avoid the artificial interactions between periodic images. To simulate the superstructure of germanene on Al (111) surface, we start by first optimizing a free-standing germanene layer modeled with 2×2×1 supercell. The obtained low-buckled structure has a lattice parameter a=8.12Å and a buckling height 5 ACS Paragon Plus Environment


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∆ =0.69 Å, in agreement with previous reports.40 Based on the experiment results,15 a 3×3×1 Al (111) surface of a five-layer slab is cleaved from the bulk face centered cubic (fcc) aluminium. As the initial configuration, the 2×2×1 supercell of germanene is slightly stretched to match the 3×3×1 Al (111) substrate (i.e. the lattice constant 8.12 Å of germanene is stretched to 8.59 Å to compensate the lattice mismatch with the substrate). After structural relaxation, the superstructure of germanene on Al (111) is obtained, which is shown in Fig. 1. One clearly observes that the obtained structure is changed from the low-buckled structure of free-standing germanene. The unit cell contains eight Ge atoms arranged in a honeycomb network with six Ge atoms staying in the same atomic plane and two convex Ge atoms above this plane (marked with red circles in Fig. 1). With respect to the Al atoms of the first Al (111) layer, the two convex Ge atoms (denoted as Ge (up)) are located on top of the Al atoms, whereas the other six Ge atoms (denoted as Ge (down)) are located around the bridge sites between the Al atoms. In addition, it is worth noting that there are two (Ge+Al) pairs of atoms in each unit cell, which are slightly shifted upwards relative to other Ge or Al atoms (of the first Al (111) plane). The corresponding buckling heights are ∆z = 1.21 Å and ∆z’ = 0.45 Å, respectively (as indicated in Fig. 1(b)). The calculated in-plane Ge (down)-Ge (down) bond length is 2.67 Å, while the Ge (up)-Ge (down) bond length is 2.59 Å. The adsorption energy (defined as the energy difference per Ge atom between the total energy of the superstructure and the sum of the energies for each isolated component i.e. the substrate and the germanene layer) is -0.49 eV/atom. We further calculate the electron localization function (ELF), which is useful for the analysis of the degree of electron localization and the bonding character (shown in Fig. 2). One clearly observes that there is strong covalent bonding between the Ge atoms, which indicates the formation of a continuous germanene layer, while the interaction between germanene and the Al substrate is of electrostatic type. All these calculated results agree well with the previous experimental and simulation results.15 The results demonstrate that the structure of the germanene layer on Al (111) is changed from the low-buckled structure of its free-standing form. However, the germanene still maintains its original character as a strongly covalent-bonded continuous layer and its 6 ACS Paragon Plus Environment

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interaction with the substrate is relatively weak. The structural change is also expected to make the electronic properties of the germanene layer different from the free-standing germanene. DFT calculations have shown that the Dirac points get destroyed in silicene on Ag (111) surface.41 In comparison, the Dirac cones still exist for germanene on Ag (111) surface but their locations transfer from K and K’ points to the Г point for the superstructure.29 An interesting question here is whether the Dirac points are still maintained for the structure of germanene on Al (111). We have calculated the band structure of the superstructure combining both the germanene and the Al substrate (see Supporting Information). Evidently, the band structures of germanene are submerged in the bands from the Al substrate, similar to the cases of silicene/Ag 41 and germanene/Ag29 superstructures. In the following, to further illustrate the electronic properties associated with the modified lattice structure of the germanene layer, following similar treatment as in Ref. 42, we focus only on the germanene layer with the lattice structure determined above and remove the substrate in the following band structure calculations, if not explicitly stated otherwise. The calculated band structure of the germanene layer in the absence of SOC is shown in Fig. 3(a). One observes several interesting features. First, the linear band crossing at K (K’) point can be clearly seen. Hence, although the structure is distorted from the low-buckled structure of free-standing germanene, the Dirac points at K/K’ are still maintained. This is similar to the case of germanene on Ag (111),29 and is in contrast to the case of silicene on Ag (111).41 More interestingly, there is an additional linear band crossing at a point D between K point and M point. We further check the energy dispersion around this point and confirm that it is indeed a Dirac point with linear dispersion along all directions in the 2D plane (see Figs. 3(e), 3(g), and 3(h)). Figure 3(e) explicitly shows the Dirac cone around D. And from symmetry, there are in fact 3 pairs of such Dirac points in the Brillouin zone, as indicated in Fig. 3(c). Plus the one pair of Dirac points at K and K’, we have 8 Dirac points in total for this system. The possibility of a Dirac cone not at high-symmetry point is very interesting. So far, it has only been proposed in a few nanostructured materials, such as graphynes, 7 ACS Paragon Plus Environment


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31-32

rectangular carbon and boron 2D allotropes, 33-34 and in gated phosphorene 43 as

well as some other 2D puckered lattices.35 Due to the reduced symmetry at point D, the energy dispersion should be anisotropic, which can be seen in Figs. 3(g) and 3(h). The Fermi velocity along K-M (~2.8×105 m/s) is almost twice as large as the velocity along the perpendicular direction (~1.6×105 m/s). In contrast, the dispersion at K is more or less isotropic at low-energy (see Fig. 3(d) and 3(f)), with a Fermi velocity ~2.4×105 m/s. We note that there are also usual quadratic bands crossing the Fermi level around Γ point, which would mix with the physical effects from the Dirac points. On the other hand, this may provide an interesting platform to study the interplay between multiple types of Dirac fermions and usual Schrodinger fermions. For example, due to suppression of backscattering for Dirac fermions, the mobility will be much higher for carriers around the Dirac points than for the quadratic bands. Using the Veselago lensing effect for Dirac fermions,44 one could even spatially separate the two types of carriers. SOC typically lifts the spin degeneracy of the energy bands. For free-standing germanene, it opens a small gap ~23.9 meV at the Dirac points at K and K’.17 In the modified germanene structure considered here, as shown in Fig. 3(b), we find that the SOC lifts the spin degeneracy of Dirac bands at both K and D points. For K and K’ points, the conduction band and the valence band still touch each other but with a quadratic dispersion around Fermi level. As for the D point, a small gap ~4 meV is opened at the original Dirac node. Therefore in general the SOC generates a finite mass for the massless Dirac fermions in the system. It has been found that for free-standing silicene and germanene, the effective SOC strength depends on the buckling and the bond length because they affect the overlap between π and σ orbitals.45 Similarly, for the current structure, we have checked that the effective SOC strength and the SOC gap would be enhanced when the buckling height is increased or the bond length is decreased. Hydrogenation can strongly affect the properties of 2D materials due to their large surface to volume ratio. In addition, since the hydrogenation process is reversible,46

it provides the flexibility to manipulate the adsorption coverage. 8 ACS Paragon Plus Environment

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Because of these, hydrogenation is considered to be an effective method to tune the properties of 2D materials. The hydrogenated germanene has been synthesized from the topochemical intercalation of CaGe2, which indeed shows distinct properties from the free-standing germanene, such as a large bandgap ~1.53 eV and a high mobility.26 In the following, we study the effect of hydrogenation on properties of germanene on Al (111). Due to the presence of substrate, we consider the hydrogenation from the top side while keeping the bottom side unhydrogenated.

First of all, the adsorption configurations for different hydrogenation ratio are constructed. A unit cell of germanene on Al (111) is used to study the favorable hydrogenated configuration. The unit cell (including the five layers of Al) is used to test the partial hydrogenation ratios ranging from 0% to 100% by comparing adsorption energies after geometry optimization. To make a quantitative comparison of the chemical adsorption of H atoms, we define the adsorption energy E ad - H (per H atom) as: E ad - H =

1 （E Al + Ge + N H E H − E Al + Ge + H） NH

where E Al + Ge is the total energy of the germanene on Al (111), E Al + Ge + H is the total energy of the hydrogenated germanene on Al (111), E H is the energy of a hydrogen atom in vacuum, and N H is the number of adsorbed hydrogen atoms. The adsorption energies per hydrogen atom on hydrogenated germanene on Al (111) versus hydrogenation percentage are shown in Fig. 4(a). It is found that the semi-hydrogenated

(50%)

germanene

corresponds

to

the

most

favorable

hydrogenation ratio. Next, the two typical configurations, namely the chair-like and the boat-like configurations for semi-hydrogenated germanene on Al (111) are considered. It is found that the energy of the chair-like configuration is lower than that of the boat-like configuration by about 15 meV/atom. Hence, the chair-like semi-hydrogenated configuration is used for our subsequent study of the electronic



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properties. The structure is shown in Fig. 4(b). One observes that due to hydrogenation, the original germanene structure is changed to be more like a low-buckled structure. The Ge-H bond length is 1.58 Å, in accordance with previous calculations for the free-standing case.10 The buckling height ∆ and the Ge-Ge bond length are 0.80 Å and 2.60 Å, respectively, which are slightly longer than the free-standing case due to the enlarged lattice constant of germanene on Al (111). One of the most striking effects induced by hydrogenation is the possibility of achieving magnetic orderings in a 2D system. The realization of magnetism without transition metal elements, known as d0-ferromagnetism,47 has attracted great interest in recent years. It has been proposed that the semi-hydrogenated free-standing germanene (from one side) is a direct bandgap ferromagnetic semiconductor.10 Will there be induced magnetism also in germanene on Al (111)? To answer this question, the magnetic property of one-side hydrogenated germanene on Al (111) is investigated. It is known that the overlap of pz orbital between Si-Si or Ge–Ge in free-standing silicene or germanene is much smaller than that of C–C in graphene.48 With respect to pristine germanene, three sp3-like orbitals form covalent bonds with its neighboring atoms while the last one forms a weak π bond with the adjacent atoms. Due to the saturation of orbitals for every Ge atoms, the system then exhibits a nonmagnetic state. When some of the Ge atoms are hydrogenated from one side of the sheet, bonds are formed between H atoms and the connected Ge atoms, leaving the electrons in unsaturated Ge atoms localized and unpaired. As a result, the system could possess a magnetic ground state. To verify this, taking semi-hydrogenated case as an example, we perform total energy calculations for various magnetic configurations to search for possible magnetic ground state. Indeed, we find that the ferromagnetic (FM) configuration has the lowest total energy, similar to the case for free-standing silicene or germanene, as predicted in Ref. 10. To illustrate the spatial distribution of spin polarization, the charge densities of spin-up and spin-down are plotted in the inset of Fig. 4(a). Apparently, it can be seen that the spin magnetic moments are localized on the unsaturated Ge atoms, while the H atoms carry very small spin polarization. It indicates that ferromagnetism in 10 ACS Paragon Plus Environment

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semi-hydrogenated germanene is indeed originated from the localized and unpaired electrons on the unhydrogenated Ge atoms. We further calculate the electronic band structure of the semi-hydrogenated germanene with the lattice structure determined above. The obtained band structure and projected density of states (PDOS) are shown in Fig. 5. In Figs. 5(a), one observes that an indirect bandgap is opened for the spin-up bands, with the valence band maximum (VBM) located at K point and the conduction band minimum (CBM) at Γ point. The gap size is about 0.50 eV. In contrast, for the spin-down bands, the gap is closed, and remarkably, the corresponding VBM and CBM just touch each other at

Γ point, forming a semimetal state. Furthermore, as shown in Fig. 5(c), only one type of spin carriers exist at the Fermi level, dominated with the p-orbital character, as originated from the unsaturated Ge atoms. This indicates that the system is also a half-metal. Therefore, this semi-hydrogenated germanene structure actually represents a new state of matter, a semimetal as well as a half-metal, which may be termed as a half-semimetal state. Finally, the magnetic properties corresponding to other hydrogenation ratios are also calculated. Results show that the system has no magnetism for the fully hydrogenated case. Indeed, as the hydrogenation ratio increases to 100%, there are no unsaturated Ge atoms hence no contribution to spin polarization. As the hydrogenation ratio increases from 0% to 50% then to 100%, the state of germanene on Al (111) could change from non-magnetic to ferromagnetic (FM) state then back to non-magnetic during the process. In summary, the structural, electronic and hydrogenation-induced magnetic properties of germanene on Al (111) are investigated by first-principles calculations. The analysis shows that the germanene grown on Al (111) surface forms a continuous layer. Compared with free-standing germanene, the germanene on Al (111) has a modified lattice structure, notably without an inversion center, resulting in some interesting and distinct properties. Like free-standing germanene, the π and π * bands linearly cross at Fermi level at K/K’ points, indicating that the Dirac cones are undestroyed. More importantly, there exist another type of Dirac points located on the



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high-symmetry lines between K (K’) and M. The dispersion around these new Dirac points is highly anisotropic. It is therefore an interesting system in which the Dirac cones at the high-symmetry points on high-symmetry lines can coexist in the Brillouin zone, which is distinct from the free-standing germanene and other 2D materials. The SOC lifts the spin degeneracy around the Dirac points and generates mass for the massless Dirac fermions. We further investigate the effect of hydrogenation. We find that hydrogenation could induce ferromagnetism in the germanene layer. The most striking result is that the semi-hydrogenated germanene on Al (111) is in a half-semimetal state, a novel state that is simultaneously a half-metal and a semimetal. Recently, a field effect transistor based on a single-layer silicene has been successfully fabricated by using a synthesis-transfer-fabrication technique.49 In view of the rapid progress of experimental technique, we expect the germanene structure studied here could also be fabricated onto other substrates and serve as building blocks for devices applications. The interesting results obtained in this work will facilitate the further experimental studies on this intriguing 2D material.

Associated Content s Supporting Information ○

Supporting Information Available: Description of germanene including the band structures of superstructure of germanene on Al (111) surface in a hexagonal primitive cell. This material is available free of charge via the Internet at http://pubs.acs.org.

Author Information *Corresponding Author E-mail: [email protected]

Acknowledgement This work is supported by the National Natural Science Foundation of China under Grant Nos. 51275012, 11264012 and 11564016. S. Guan and S. A. Yang are supported by SUTD-SRG-EPD2013062.

Reference 12 ACS Paragon Plus Environment

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Figure 1: Top view (a) and side view (b) of the superstructure of germanene on Al (111) surface. The red dashed line in (a) indicates the unit cell, and only the first Al atomic layer is displayed in (a). The two convex Ge atoms in a unit cell are marked by the red circles. In (b), only the first two Al atomic layers are displayed.


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Figure 2: (a) Top view of the overall electron localization function (ELF) of germanene on Al (111) with an isosurface with value of 0.7. (b-d) ELF profile maps of three vertical cross sections. (b), (c), and (d) correspond to the lines 1, 2, and 3 in (a), respectively.



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Figure 3: (a)-(b) Band structures of germanene without and with SOC. The inset in (b) shows the enlarged band structure at the K point around Fermi level (which is set to be zero). (c) Brillouin zone with the high symmetry points labeled. The Dirac points at K and K’ are marked by the blue dots, while the three pairs of Dirac points along K(K’)-M are marked by the red dots. The dashed lines indicate schematically the shape of constant energy contours around the Dirac points. (d) and (e) show the Dirac cones at K and D points respectively (without SOC). (f) Enlarged band structure from (a) around the K point. (g)-(h) Enlarged band structures from (a) around the D point along two perpendicular directions. (g) is along K-M, and (h) is along the direction perpendicular to K-M.


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Figure 4: (a) Adsorption energy per hydrogen atom for the hydrogenated germanene on Al (111) surface versus the hydrogenation percentage. The inset shows the spin polarization distribution (side view) corresponding to the semi-hydrogenated configuration. (b) Top view (left panel) and side view (right panel) of the one-side semi-hydrogenated germanene on Al (111).



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Figure 5: Spin-resolved band structures and projected density of states (DOS) of one side semi-hydrogenated germanene structure.


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50x50mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Figure 1: Top view (a) and side view (b) of the superstructure of germanene on Al (111) surface. The red dashed line in (a) indicates the unit cell, and only the first Al atomic layer is displayed in (a). The two convex Ge atoms in a unit cell are marked by the red circles. In (b), only the first two Al atomic layers are displayed. 153x241mm (96 x 96 DPI)


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Figure 2: (a) Top view of the overall electron localization function (ELF) of germanene on Al (111) with an isosurface with value of 0.7. (b-d) ELF profile maps of three vertical cross sections. (b), (c), and (d) correspond to the lines 1, 2, and 3 in (a), respectively. 259x287mm (96 x 96 DPI)



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Figure 3: (a)-(b) Band structures of germanene without and with SOC. The inset in (b) shows the enlarged band structure at the K point around Fermi level (which is set to be zero). (c) Brillouin zone with the high symmetry points labeled. The Dirac points at K and K’ are marked by the blue dots, while the three pairs of Dirac points along K(K’)-M are marked by the red dots. The dashed lines indicate schematically the shape of constant energy contours around the Dirac points. (d) and (e) show the Dirac cones at K and D points respectively (without SOC). (f) Enlarged band structure from (a) around the K point. (g)-(h) Enlarged band structures from (a) around the D point along two perpendicular directions. (g) is along K-M, and (h) is along the direction perpendicular to K-M. 400x517mm (96 x 96 DPI)


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Figure 4: (a) Adsorption energy per hydrogen atom for the hydrogenated germanene on Al (111) surface versus the hydrogenation percentage. The inset shows the spin polarization distribution (side view) corresponding to the semi-hydrogenated configuration. (b) Top view (left panel) and side view (right panel) of the one-side semi-hydrogenated germanene on Al (111). 169x217mm (96 x 96 DPI)



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Figure 5: Spin-resolved band structures and projected density of states (DOS) of one side semihydrogenated germanene structure. 275x389mm (96 x 96 DPI)


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Multiple Dirac Points and Hydrogenation-Induced Magnetism of

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