Tunable electronic and magnetic properties in germanene by alkali, alkaline-earth, group III and 3d transition metal atom adsorption.

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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 15968

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Tunable electronic and magnetic properties in germanene by alkali, alkaline-earth, group III and 3d transition metal atom adsorption Sheng-shi Li,a Chang-wen Zhang,*a Wei-xiao Ji,a Feng Li,a Pei-ji Wang,a Shu-jun Hu,b Shi-shen Yanb and Yu-shen Liuc We performed first-principles calculations to study the adsorption characteristics of alkali, alkali-earth, group III, and 3d transition-metal (TM) adatoms on germanene. We find that the adsorption of alkali or alkali-earth adatoms on germanene has minimal effects on geometry of germanene. The significant charge transfer from alkali adatoms to germanene leads to metallization of germanene, whereas alkaliearth adatom adsorption, whose interaction is a mixture of ionic and covalent, results in semiconducting behavior with an energy gap of 17–29 meV. For group III adatoms, they also bind germanene with mixed covalent and ionic bonding character. Adsorption characteristics of the transition metals (TMs) are rather complicated, though all TM adsorptions on germanene exhibit strong covalent bonding with germanene.

Received 20th March 2014, Accepted 19th May 2014

The main contributions to the strong bonding are from the hybridization between the TM 3d and Ge pz

DOI: 10.1039/c4cp01211a

semiconducting behavior. Also, the variation trends of the dipole moment and work function with the adsorption energy across the different adatoms are discussed. These findings may provide a potential

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avenue to design new germanene-based devices in nanoelectronics.

orbitals. Depending on the induced-TM type, the adsorbed systems can exhibit metallic, half-metallic, or

I. Introduction Graphene, a two-dimensional (2D) honeycomb carbon network, has recently attracted much attention since its successful preparation in 2004.1 The unique symmetry of the honeycomb p-orbital network makes graphene exhibit peculiar electronic properties, which contain massless Dirac fermions, high thermal conductivity, half-integer Hall conductance, etc.2–4 It opens an approach for the minimization of electronic devices, therefore it is of interest to investigate this ultrathin 2D system. Nevertheless, the use of graphene faces many challenges such as toxicity, difficulty in processing, incompatibility with current Si-based electronic technology, and the growth of graphene over large areas. It is known that germanium (Ge) and silicon (Si) atoms belong to group IV of the Periodic Table, and they both have similar s2p2 valence electron configurations to the carbon (C) atom. Not so long ago, the marvelous electronic properties of 2D hexagonal lattices of Si, which was called silicene, were a

School of Physics and Technology, University of Jinan, Jinan, Shandong, 250022, People’s Republic of China. E-mail: [email protected] b School of Physics, State Key laboratory of Crystal Materials, Shandong University, Jinan, Shandong, 250100, People’s Republic of China c College of Physics and Engineering, Changshu Institute of Technology and Jiangsu Laboratory of Advanced Functional Materials, Changshu 215500, People’s Republic of China

15968 | Phys. Chem. Chem. Phys., 2014, 16, 15968--15978

theoretically predicted.5–7 Recently, evidence of epitaxial silicene on Ag(111),8 ZrB29 and Ir(111)10 substrates was reported. Unlike planar graphene, the most stable silicene prefers a low-buckled (LB) structure, which is attributed to mixing of its sp2/sp3 hybridized orbitals. The electronic structure of silicene is quite similar to that of graphene, showing semi-metallic character, in which the electrons at the Fermi level (EF) behave like massless Dirac fermions, leading to a higher carrier velocity. In comparison to Si, the Ge atom has a larger atomic radius and lower electronegativity. Ge-based materials may possess many distinct properties to their Si counterparts. Unlike graphene, the graphite-like Ge allotrope does not exist naturally, and thus much effort11–14 has been devoted to the investigation of graphene-like Ge nanosheets, referred to as germanene.15,16 Bianco et al.14 synthesized, for the first time, millimeter-scale crystals of a hydrogen-terminated germanene from the topochemical deintercalation of CaGe2. Interestingly, germanene also adopts the LB structure and the band character of germanene is similar to that of silicene, in which the p and p* bands cross linearly at EF of the Brillouin zone with a Fermi velocity of 1.7 106 m s1,10 a value comparable to that of silicene.17 Several remarkable features were also revealed, such as a large spin–orbit gap at the Dirac point,18,19 an experimentally accessible quantum spin Hall effect, as well as an electrically tunable band gap.20–24 Thus, germanene will be a possible graphene replacement

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not only due to its graphene-like features but also because of its compatibility with existing Si-based nanotechnology. The adsorption of metal atoms provides a route to modify the electronic properties of graphene for applications in nanoelectronics. Most reported works are focused on the alkali and simple-metal adsorption.25–31 TM adsorption on graphene has been studied by theoretical calculations and experiments extensively.22–36 It is found that the adsorption energies and diffusion barriers of TM adatoms on graphene depend significantly on the chemistry of the adatoms and they are generally larger than those of alkali or simple-metal adatoms.37,38 Also, graphene with adsorbed metal atoms were predicted to be promising host materials for hydrogen storage.39–41 Unfortunately, the binding energies of most metal adatoms on graphene are generally smaller than the cohesive energies of the bulk metals,32–45 suggesting that TM clustering is probably inevitable when depositing metal atoms on graphene with high coverage.46,47 To avoid these problems, the metal adatoms are generally proposed to substitute carbon atoms in graphene.48 However, the substitution of carbon by metal atoms always induces carbon defects, which cause severe damage to the complete geometry of graphene, unfavorable for practical applications in nanoelectronics.49–51 For silicene, the adsorption of metal adatoms also attracted attention theoretically when it was discovered.52–55 Nonmetal atoms on silicene can effectively adjust the band gap and alter the phonon spectrum of silicene, while for metal adatoms, silicene exhibits diverse adsorption characteristics as compared to graphene. Interestingly, the migration of metal atoms on the silicene lattice is found to be difficult and needs to overcome higher energy barriers, preventing metal clustering on silicene. Also, the adsorption of some metal atoms such as Li on silicene can result in effective hydrogen storage materials.56 In spite of the progress, understanding of the interaction between metal adatom and silicene is still far from complete. In this work, motivated by recent works on germanene, we systematically studied the characteristics of alkali, alkali-earth, group III, and TM adatom adsorption on germanene through first-principles density-functional theory (DFT). The corresponding adsorption energy, geometry, electric-dipole moment, work function, and magnetic moment are discussed correspondingly. In Section II, we describe the computational method used for the calculations in more detail. For the sake of comparison, we also present the geometric and electronic properties of free-standing germanene in Section III. Characteristics of metal atom adsorption on graphene and silicene are compared briefly with our calculated results on germanene, and the geometric and electronic properties of metal adatoms on germanene are also presented in Section III. Finally, the summary and conclusion are given in Section IV.

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modeled with projector augmented wave (PAW) potentials,61 while spin polarization and dipole moment corrections62,63 are also taken into account. To properly take into account the van der Waals (vdW) interactions in the structures, the DFT-D2 method64,65 is used throughout all the calculations. A planewave basis set with maximum plane-wave energy of 450 eV is used for the valence electron wave functions, and a set of (9 9 1) k-point sampling is used for Brillouin-zone (BZ) integration. The convergence criterion of our self-consistent calculations for the change in energy is less than 105 eV per cell. By using the conjugate gradient method, all atomic positions and the size of the unit cell are optimized until the atomic forces are less than 0.02 eV Å1. The adatom–germanene system is modeled in a 4 4 germanene supercell with periodic boundary conditions as shown in Fig. 1(b). The primitive cell of germanene is a parallelogram with two Ge atoms. We consider four different high symmetry adsorption sites of metal adatoms on germanene: the hollow (H) site at the center of a hexagon, the bridge (B) site at the midpoint of a Ge–Ge bond, the top (T) site directly above the upper Ge atom, and the valley (V) site directly above the low Ge atom. The adatom height (h) is defined as the difference in z coordinate of the adatom and nearest neighboring Ge atoms in germanene layer. We use a supercell length of 15 Å in the z direction to avoid the interactions between adatoms. Although the adatom–adatom interaction is not negligible, the distance between adatoms is large enough that the overlap of the electronic states of neighboring adatoms is small. All the calculations on the diffusion pathways of metal adatoms on germanene are using the nudged elastic band method. The adsorption energy of the adatom–germanene system can be defined by Eads = E(Ge) + E(M) E(M@Ge)

(1)

where E(Ge), E(M@Ge) and E(M) are energies of the freestanding germanene, and metal (M) adsorbed germanene

II. Computational details All the calculations are performed within DFT under the generalized gradient approximation (GGA) in the form of Perdew–Burke– Ernzerhof (PBE).57,58 The Vienna Ab-initio Simulation Package (VASP) is used to perform all calculations.59,60 Ion cores are


Fig. 1 (a) View of the honeycomb lattice of germanene. Structural parameters: the buckling h and Ge–Ge bond length are indicated. (b) Preferable adsorption sites, hollow, top, valley, and bridge, on the germanene lattice in a 4 4 supercell. (c) Electronic band dispersion of germanene and band decomposed charge densities of VBM and CBM at K symmetry points.

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systems, and free-atom impurity, respectively. Of the four adsorption sites considered, the site with the largest adsorption energy is referred to as the favored site. To better understand the different adsorption energies and lattice distortions for the metal adatoms on germanene, we introduce the charge density difference (CDD) distributions upon adsorption, as shown in Fig. 3. Here the CDD Dr(r) will be defined as: Dr(r) = r(M@Ge) r(Ge) r(M)

(2)

where r(M@Ge) is the charge density of adatoms–germanene, while r(Ge) and r(M) are the charge density of the isolated germanene and adatoms, respectively. The CDD demonstrates the charge redistribution in real space due to the interaction between adatoms and germanene. The region with the higher charge densities between the adatom and germanene indicates stronger covalent bond formation by metal atom adsorption.

III. Result and discussion A.

Free-standing germanene

Before moving to our results, we first present the electronic properties of free-standing germanene. The geometry of a 2D germanene monolayer can be viewed as a bipartite lattice composed of two interpenetrating triangular sublattices of Ge atoms [Fig. 1(a)], similar to that of a graphene lattice. Due to the weak overlapping of 4pz orbitals of the Ge, the p bonds between Ge atoms are weaker than in the case of the carbon atoms in graphene. Thus the planarity will be destabilized and Ge atoms are buckled in the germanene crystal. The optimized Ge–Ge bond length (d) and buckling distance (h) between two Ge planes are found to be 2.387 and 0.65 Å, respectively. By comparison, the buckled germanene monolayer is 0.12 eV per atom lower than the planar one. This demonstrates that the sp3 hybridization is more stable rather than sp2 hybridization in germanene, in agreement with the previous reports.11 Fig. 1(c) displays the calculated band structure of a 2D germanene monolayer. It is a semi-metal because the valence and conduction bands touch at EF. Analysis of the charge density demonstrates that the linear bonding p and anti-bonding p* bands which cross at the K symmetry point are responsible for the existence of massless Dirac fermions in germanene [see the insert of Fig. 1(c)]. Due to the degeneracy of the valence band maximum (VBM) and the conduction band minimum (CBM) at the K point, the corresponding states have the same ionization potential and electron affinity. So similar unique properties to those of graphene are expected in 2D germanene. B.

Table 1 The adsorption energies, the height of the adatom over the neighboring Ge atoms defined by the farthest atom, the bond length between the adatom and its nearest Ge atoms (dM–Ge), the in-plane displacement (din), the vertical distortions (dver), the electric-dipole moment p (D), the work function F (eV), and the charge transfer Q (for which plus and minus symbols represent obtaining and losing an electron, respectively)

Adatom Site h

Eads

dM–Ge din

dver

p

F

Q

Li Na K Be Mg Ca Al Ga In Ti V Cr Fe Co Ni

2.543 2.098 2.249 2.798 1.928 3.245 3.681 3.714 3.945 4.092 4.154 4.364 4.181 4.693 4.932

2.703 3.046 3.438 2.391 2.963 2.885 2.611 2.702 3.105 2.649 2.532 2.637 2.451 2.359 2.366

0.004 0.003 0.005 0.006 0.006 0.008 0.007 0.008 0.009 0.009 0.012 0.013 0.015 0.018 0.019

1.63 3.84 5.12 0.48 1.41 3.75 0.19 1.23 2.29 1.03 0.76 0.61 0.98 0.34 0.26

3.86 3.59 3.27 4.59 4.39 3.58 4.37 4.08 3.71 4.98 5.12 4.84 4.65 4.75 4.34

0.86 0.83 0.84 1.3 1.0 1.35 0.92 0.26 0.36 1.02 0.77 0.64 0.19 0.07 +0.03

H H H V V H V V H H H H V H H

1.66 1.94 2.88 0.54 1.57 1.27 1.31 1.18 1.21 1.14 1.02 0.81 0.66 0.58 0.46

0.002 0.001 0.002 0.002 0.002 0.006 0.006 0.008 0.011 0.011 0.015 0.018 0.021 0.026 0.026

as shown in Fig. 2(a). The optimized distance between the adatom and germanene monotonically increases with the chemical activity increasing from Li to Na to K. There is no trend in the adsorption energies of alkali metals on germanene (Table 1). In comparison to graphene,66 the adsorption energies

Energetics and geometric structures

We first study the characteristics of adsorption of alkali metals on a germanene layer. Table 1 lists the bonding character of Li, Na, and K, on germanene. Upon full geometry optimization, all alkali metals prefer the H site bonding to germanene. The adsorption of alkali metals causes very little distortion to the germanene lattice, nearly the in-plane distortion of germanene,


Fig. 2 Side and top views for characteristic adsorption geometries of (a) and (b) alkali metals and alkali-earth metals, (c) and (d) group III metals, as well as (e) and (f) TMs.


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Fig. 3 The charge density difference (CDD) in the vertical plane cutting though the structure. Red indicates an increase in electron density and blue means electron density loss.

of alkali metals on germanene are more than twice as high as in the case of graphene, suggesting that the bonding strength of the adatom to germanene is stronger. Taking the Na adatom as a representative example from Fig. 3(a), one can see that a Na adatom on germanene leads to a large amount of charge transfer from Na to germanene, suggesting the interaction between Na and germanene is purely ionic. The diffusion pathways of adsorbate atoms on the germanene lattice can also be predicted from the energy barrier between different sites. In Fig. 4, we present the trend of energy change for adatoms from top to hollow sites. As shown in Fig. 4(a), the different diffusion pathways of the alkali adatoms on germanene along the lines H–V, V–B, and B–T are presented. It is obvious that the most likely migration path between the most favorable H site passes through the neighboring V sites. With the atom radius increasing from Li to K, the energy barrier between the H and V sites becomes smaller, thus the diffusion of larger alkali

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atoms becomes relatively easier. Although the alkali metals can strongly bind to germanene, they may diffuse along H and V sites by overcoming the energy barrier of 0.15–0.23 eV at high temperature. Recently, a well-ordered K layer on graphite67 and a Cs layer on graphene66 have been realized in experiments. For the K adatoms on germanene, the diffusion barrier is larger than in the case of graphene. Considering the strong repulsive interaction between the positively charged adatoms, it is expected to be a possibility, which can achieve the formation of an alkali metal layer on germanene layer in experiments. Alkaline-earth adatoms have similar electronic structures, with one more s valence electrons in their outermost orbital in comparison to alkali metals. Considering their smaller atomic size and higher ionization energy, a strong interaction between the alkali-earth adatoms and germanene layer is obtained and the adsorption height of alkali-earth metals on germanene decreases clearly (Table 1). It is noticeable that the Ca atom binds to H sites like alkali metals, while both Be and Mg adatoms favor adsorption to the V site. The adsorption energies of both Be and Ca on germanene are significantly higher than those of alkali metals, whereas it decreases by 0.5 eV for Mg compared with the case of Na atoms, a second row alkali metal element. From Fig. 4(b), one can see that the Be atom has to overcome a quite large energy barrier B0.58 eV for migration from V to other adsorption sites. The possible reason can be attributed to the stretching of the germanene lattice induced by Be adsorption on the germanene layer, which is freed only in one direction perpendicular to the layer. According to Fig. 3(b) and the charge transfer data in Table 1, it can be seen that a mixture of ionic and covalent bond exists between the Be adatom and its nearest Ge atoms, in which the ionic bond plays the dominate role. For comparison, Ca atoms can migrate easily through V and H sites by overcoming the energy barrier of 0.25 eV at high temperature. We now discuss the adsorption characteristics of Al, a representative of the group III metals, on the V site. These adatoms have two s and one p valence electrons in the outermost shell.

Fig. 4 Diffusion pathways and barriers of (a) alkali metals, (b) alkali-earth metals, (c) group III metals, and (d) 3d TM adatoms through top, bridge, valley, and hollow sites.



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Compared with the alkali and alkali-earth metals, Al adsorption would affect the germanene electronic structures to a greater degree. As seen from Fig. 2(c), group III metal adsorption distorts the geometry of germanene clearly and the maximum in-plane displacement is in the range of 0.07–0.09% of the Ge–Ge bond length. The M–Ge bond lengths (dM–Ge) for Al, Ga, and In metals increase to 2.61, 2.72, to 2.95 Å, which are larger than those of alkali and alkali-earth metals on a germanene layer. As a result, it leads to larger binding energy values of 2.14–2.68 eV for Al, Ga, and In. For the Al and Ga atoms, the V site is more favorable in energy, whereas the In adatom prefers the H site (Table 1). The V site adsorption for the Al or Ga atom on germanene leads the Ge atom directly below the adatom to undergo significant displacement towards the outside of the plane of germanene, suggesting covalent bonding to neighboring Ge atoms, as shown in Fig. 3(c). Bader charge analysis shows that less than one electron is transferred from group III metals to germanene when they are adsorbed on germanene. So the bonding interaction between the Al or Ga atoms and germanene has mixed contributions from both covalent and ionic bonding. In comparison to the In atom at the H site, the bonding strength to the V site of the Al or Ga atoms is much stronger, in agreement with the variation of adsorption energy of group III metals on germanene. These are significantly different from the group III metals on graphene, in which only pure ionic bonding appears.19 It could be attributed mainly to the buckled structure of the germanene layer due to its mixed sp2/sp3 hybridization between the neighboring Ge atoms in germanene. Fig. 4(c) displays the different diffusion paths energetically for group III metals adsorption on germanene. For both Al and Ga atoms, the most likely migration path between the most favorable V site passes through the neighboring H sites, while the In atom can migrate via the B site easily at high temperature. It is also noticeable that the Al adatom has the largest diffusion barrier, B0.41 eV, thus the diffusion of larger alkali atoms becomes relatively easier. For both Ga and In adatoms, they may diffuse along H and V sites by overcoming the energy barrier of 0.18–0.21 eV at high temperature. Now, we focus on TM (Ti, V, Cr, Fe, Co, and Ni) adsorption on a germanene layer. Different from main group element adsorption, more electrons of TMs will participate in the chemical bonding due to their partially filled inner 3d orbitals. Along with the relatively large atomic radii of all TMs, a stronger interaction between the TMs and germanene results in the significant distortion of germanene. The in-plane distortion patterns in the germanene layer caused by the adsorption of Ti, V, Cr, Co, and Ni at H sites are very similar, and the maximum in-plane displacement is 1.2–1.8% of the Ge–Ge bond length which is much larger than that of group I–III metal adsorption on germanene. As a result, it binds strongly the six nearest Ge atoms covalently. However, the Fe adatom favors the V site, and only has an in-plane displacement of B0.05%, which is close to the Ge–Ge bond length (2.39 Å) in free-standing germanene. Comparing to the in-plane distortion of germanene, the vertical distortion (0.07 Å) on the germanene layer induced by the adatoms is similar to all the TMs (Table 1). The vertical distortions are mainly localized on Ge atoms next


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to the TM adatoms, resulting in a more reactive sp3-like character. As can be seen from Fig. 3(d), there is significant bonding charge between the 3d TM adatoms and their nearest-neighbor Ge atoms, suggesting stronger covalent bonding between them. The phenomena further lead to the larger adsorption energies of TM adatoms on germanene. The calculated adsorption energies of Ti, V, Cr, Fe, Co, and Ni are found to be 5.65, 5.85, 5.56, 5.38, 5.49, and 5.73 eV, which are significantly larger than in the cases of group I–III metals on germanene. Fig. 4(d) displays the different diffusion paths energetically for TM adsorption on germanene. One can see that the energy barrier between the most favorable and less favorable sites for Ti, V, Cr, Fe, and Co adatoms is in the range of 0.5–1.2 eV, larger than that of group I–III metals on germanene, suggesting that the TM cluster is hindered significantly and the TM layer can easily form on the germanene surface. The much larger diffusion barrier in these TM adatoms can be attributed to the strong orbital hybridization between the 3d orbitals of TMs and neighboring Ge pz states. However, the diffusion energetics of Ni atoms is relatively low (0.08 eV) due to the completely fulfilled 3d10 electronic structure on Ni atoms. The diffusion of Ti, V, Cr, Co and Ni atoms from a H site to another one may occur via a V site, while the Fe atom would move between the V sites via a B site. C.

Electronic structure and magnetic moments

In what follows, we turn to the electronic properties of alkali metal binding to the H site on a germanene layer. Fig. 5(a)–(c) display the energy band dispersions along the high symmetry points (G–K–M–G) for alkali metals on germanene. It is noticeable that the electronic states of germanene remain almost unaltered compared with the free-standing germanene. The Dirac point of germanene at the K point is well preserved upon adatom adsorption on germanene, but shifts down significantly away from EF, which is denoted as ED. The difference between EF and ED is about the same for the Li, Na, and K adatoms on germanene (B0.38 eV below EF), suggesting that almost the same amount of charge is transferred from Li, Na, and K adatoms to germanene. Since the electron density is lower at the center of the hexagonal network than at other adsorption sites, the adatom would stabilize closer to the layer by reducing the electrostatic energy. Thus the ionic bonding favors adsorption to the H site of germanene. Also, a small band-gap opening is found in the bands below EF, of 14, 21, and 28 meV for Li, Na, and K, respectively. Fig. 6(a) further displays the total density of states (DOS) near EF along with the projection of the DOS onto germanene of the K@H system as a representative example. One can see that the 4s peaks in spin-up and spin-down channels lie approximately 0.3 eV above EF and are unoccupied, while the CBM is mainly determined by Ge pz states. Since there is a small peak near the K 4s levels for germanene, weak hybridization between the K 4s peaks and Ge states is possible. By integrating the total DOS from ED to EF, we find that B0.85 electrons per adatom are transferred to germanene, in agreement with the results of Bader charge analysis. To check whether it is spin-polarized,


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Fig. 5

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Electronic band structures for alkali metal (a–c) and alkali-earth metal (d–f) adsorbed germanene. Fermi level is set to zero.

each initial alkali metal is set a net initial magnetic moment of 1.0 mB. However, the self-consistent calculations show that the spin-up and spin-down states are degenerate, suggesting nonmagnetic (NM) character. In previous works,28 it was reported that K adsorbed graphene exhibits magnetic behavior with a net magnetic moment of 0.17 mB; however, no spinpolarizations are obtained in K@H. Similar results are also observed in Li@H and Na@H systems. The isolated alkali-earth metals with fully filled two s electrons are less reactive by losing the outermost shell electrons comparing with alkali metals. As a result, the bond between the alkali-earth metal and its nearest Ge atoms exhibits covalent, as well as ionic components, when adsorbed on a germanene layer. Different from alkali@H, the adsorption of alkali-earth metals on germanene does not result in metallic states, while it yields energy gaps of 15, 29, and 17 meV for Be, Mg, and Ca, respectively [see the plots in Fig. 5(d)–(f)]. In Fig. 6(b), the total and partial DOS of Ca@H are displayed correspondingly. One can see that the adsorption of Ca at the H site does not yield the appearance of Ca s or d impurity states around EF. The states near VBM are mainly from the Ge p orbitals, while the CBM is composed of Ge p and Ca d states, with a slight contribution of Ca s states. However, the adsorption of Be at the


V site results in the hybridization of pz orbitals in Be and nearest Ge atoms at VBM, while the main contributions to VBM come from Mg s and Ge s and pz hybridization for Mg@V. For the CBM states of both Be@V and Mg@V systems, the main contributions come from the hybridization of pxy states of Be or Mg adatom with pxy and pz states of germanene layer. As for group III metal adsorption on germanene, Fig. 7(a) presents the total and partial DOS of Al@V as a representative example. It can be seen that the 3s state of Al appears to split and hybridize with germanene states below 4.0, 2.2 and 1.1 eV relative to EF. The Al 3p peak lies 0.2 eV above EF and is slightly broadened due to the Al and germanene interaction. Nevertheless, the Dirac point is still clearly visible [Fig. 8(a)]. The electron transfer from the Al atom to germanene shifts EF up B0.89 eV away from the Dirac point. The states between ED and EF are mostly from the pz states of Al adatom and germanene, suggesting the relatively strong orbital interaction between Al and its nearest-neighbor Ge atoms. Since both the spin-up and spin-down states are degenerate, there is no net magnetic moment in Al@V. All these features of the band structure for Al@V are qualitatively the same as for Ga@H and In@H structures. Interestingly, we find visible energy-gap


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Fig. 6 Total and partial DOS for K (a) and Ca adsorbates (b) and nearest germanium atoms. Fermi level is set to zero. DOS is broadened by Gaussian smearing with 0.2 eV.

Fig. 7 Total and partial DOS for Al adatom and its nearest Ge atoms. Fermi level is set to zero. DOS is broadened by Gaussian smearing with 0.2 eV.

openings of 153, 75, and 52 meV for Al, Ga, and In adatoms [Fig. 8(b) and (c)], which are as much as three times greater in the case of alkali metal adsorption on germanene. Adsorption characteristics of six TMs (Ti, V, Cr, Fe, Co, and Ni) are rather complicated. For Ti@H, the Ti 3d states hybridized with germanene are mainly localized around EF for both the spin-up and spin-down channels, and the Dirac point is still visible, as shown in Fig. 9(a). It is also spin-polarized with a 2.0 mB magnetic moment


per supercell. The net spin charge density [insert of Fig. 9(a)] clearly accumulates around the Ti atom, with a small contribution of neighboring Ge atoms, suggesting the ferromagnetic (FM) interaction between Ti and Ge atoms. Since the germanene lattice is significantly distorted [Fig. 2(e) and (f)], the degeneracy of Ti 3d states binding to six nearest Ge atoms is broken and the energy splitting between the main Ti 3d peaks of spin-up and spin-down is B0.94 eV. The spin-up channel is a semiconductor with an energy gap of 0.14 eV, which is contributed from the Ti dx2y2(m) orbitals mainly, while the spin-down one exhibits metallic properties. As a result, the Ti@H becomes a half-metal when Ti atoms adsorbed at the H site on the germanene layer. For V@H on germanene, the system is still half-metallic with a 1.0 mB magnetic moment per supercell, as shown in Fig. 9(b). However the energy-gap of the spin-up channel decreases to 0.09 eV, which is significantly smaller than the case of Ti@H. While only V dxy,yz(m) states have a significant contribution to VBM, the CBM is a combination of the effects of Ge p(k) and V dxy,xz(k) states. In comparison to Ti@H, the neighboring Ge atoms are antiferromagnetic (AFM) to V adatom on the germanene layer [see insert of Fig. 9(b)]. As for Cr@H, the spin-up bands near EF are composed of Cr dxy,yz,xz(k) and Cr dx2y2(k) mainly, whereas the spin-down channel is derived from the hybridization of Cr dxy,yz(k) and the Ge p(k) states mainly. Although it is spin-polarized with a 4.4 mB magnetic moment per supercell, both spin channels are metallic, as shown in Fig. 9(c). In the cases of Fe, Co, and Ni adatoms on germanene, Fe and Co atoms are magnetic with respect to different adsorption sites, while Ni is NM. In comparison to Ti@H and V@H structures, the interaction between Fe, Co, and Ni adatom and germanene is much stronger, thus the Dirac point cannot be identified. For Fe@V, the energy splitting between the main


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Fig. 8 Electronic band structures for Al, Ga, and In adsorbed on germanene. Fermi level is set to zero.

Fe 3d peaks of spin-up and spin-down states is very small (B0.33 eV), indicating metallic behavior with 2.1 mB net magnetic moment per supercell [Fig. 9(d)]. Also, the interaction above EF between the Fe 3d and germanene states is rather weaker for the spin-up state than that for the spin-down state. For adsorption of Co at the H site on germanene, the main peak of Co 3d lies just around EF, and spin split with a larger value of 0.89 eV. From spin-density distributions in the insert of Fig. 9(e), one can see AFM interactions between Co and neighboring Ge atoms. The spin-up channel is semiconducting with a band gap of 0.32 eV, mainly from the Co dx2y2(m) orbitals, while the spin-down one exhibits metallic properties, suggesting a half-metallic character. In the case of Ni adatom, one can see that the DOS peak around EF is contributed by the germanene states, slightly hybridized with the Ni d state, as shown in Fig. 9(f). The Ni 3d states in both spin-up and spin-down channels are almost symmetric, resulting in the NM character. The origin of the magnetic moment reduction upon adsorption in Ni@H can be attributed to the nearly filled Ni 3d8 orbitals due to the hybridization of s and d states on Ni adatoms. In addition, we also take account of the Cu adatom, whose 3d orbitals are filled completely, compared with the adsorption of Ni atom. The result indicates that the interaction between Cu atom and germanene is determined mainly by the 4s states rather than 3d states. Meanwhile, the consequence of Cu adsorption is consistent with the alkali metals. D.

Electric-dipole moment and work function

Generally, the interactions between the metal adatom and germanene layer can induce a strong dipole moment perpendicular to the layer in a 2D system. It can be used to describe the real-space charge rearrangement due to the interactions between adatom and germanene quantitatively. For adatoms with ionic bonds, the dipole moment has a large contribution from charge transfer between the adatom and the substrate, while the rearrangement of charge in covalent bonds also plays an important role. We define the electricdipole moment p in z direction for the adatom–germanene system as ð X p ¼ rðzÞzdz þ Zi ezi (3) i


where r(z) is the valence electron density integrated over the x–y plane, i indexes the ion, Zi is the net atomic number of ion i, e is the electronic charge, and zi is the z coordinate of ion i. The sum and integral are over the unit cell. As discussed above, the adatom adsorption on germanene can change EF and the dipole moment of the system. Therefore, adatoms generally alter the work function F through modification of the surface dipole and thus measurement of the work function changes F generally yields critical information on the degree of electronic charge reorganization upon adsorption. This simple model has been successfully employed to interpret a wide range of adsorption systems. As a result, we further investigate how the work function F changes relative to isolated germanene. Here, the work function can be expressed as F = Evac EF,

(4)

where Evac is the reference of vacuum energy, which is determined from the electrostatic potential in the vacuum region, far enough away from the adatom–germanene system in the z direction that the value is converged. Table 1 lists the calculated dipole moment per metal on germanene. For alkali metals, the remarkable dipole moment perpendicular to germanene appears because a large amount of charge transfers from the adatom to germanene: 0.28, 0.61, and 0.92 e Å1 for Li, Na and K adatoms, respectively. In comparison, the dipole moments are relatively smaller for TMs on germanene due to the formation of the stronger bonding between TM and germanene. The largest dipole moment for TM adsorption is found for Fe, where the induced dipole moment is 0.34 e Å1, while Ti, V, Cr, Co, and Ni adsorptions have dipole moments of 0.04–0.25 e Å1. In the case of group III metals, the induced dipole moment is large for Al, but much smaller than the value (0.29 e Å1) of an Al atom on a graphene layer. The induced dipole moment may cause long-range interactions between the adatoms and germanene. Hence, it will have important effects on the work function of metals on a germanene substrate.


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Fig. 9 Total and partial DOS for (a) Ti, (b) V, (c) Cr, (d) Co, (e) Fe, and (f) Ni adsorbates and nearest Ge atoms. Fermi level is set to zero. DOS is broadened by Gaussian smearing with 0.2 eV.

To reveal the correlations between the adsorption energy Ea, work functionF, and electric-dipole moment p, we also present the F–Ea and p–F plots, as shown in Fig. 10. It can be seen that for alkalis and alkaline-earth metals, there is no linear correlation between Ea and F, in comparison to the cases of graphene. However, the group III metal adsorption on germanene results in the work function linearly decreasing with increasing atomic size from Al to Ga to In atom, which may contribute to the mixed ionic and covalent bonding character between group III metals and the germanene layer. In the case of 3d TM adsorption on germanene, all TMs generate smaller dipole moments and larger F, but the large TM metal adsorption changes the free-standing germanene work function negligibly. It is also noted that the larger the adsorption energy, the higher the work function, which is different from the cases of TM adatom on graphene, where the TM adsorption on graphene has smaller work functions.25 While the TM adatoms do not exhibit a


particular trend in dipole moment p, for groups I–III, the work function F shows a linear decrease with increasing the dipole moment. As a result, it will result in significant effects on the magnetic properties for the adatom–germanene system.

IV. Conclusion In summary, we perform first-principles DFT study on the adsorption energy, geometry, charge transfer, and dipole moment of alkali, alkaline-earth, group III, and TM adsorption on germanene. In contrast to graphene, the interaction between the metal adatoms and germanene layer is quite strong due to its highly reactive buckled hexagonal structure. The adsorption of alkali (Li, Na, and K) is ideally ionic, and for alkali-earth (Be, Mg, and Ca) adatoms it is a mixture of ionic and covalent, both of which have minimal effects on the lattice of the germanene layer. The significant charge


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References

Fig. 10 (a) Plot of the adsorption energy Eads vs. work function F, and (b) the work function F vs. electric-dipole moment p.

transfer from alkali metals to germanene leads to metallization of the germanene sheet, whereas alkali-earth adatom adsorption on the germanene layer results in semiconducting behavior with an energy gap of B0.02 eV, which is different from their adsorption on graphene. For group III (Al, Ga, and In) atoms, they can bind most strongly to the germanene layer with mixed covalent and ionic bonding character. Adsorption characteristics of six TMs (Ti, V, Cr, Fe, Co, and Ni) are rather complicated. As a result of their partially occupied d orbital, TM adsorption on germanene exhibits strong covalent bonding with germanene, which causes the large lattice distortions of the germanene layer. The main contributions to the covalent bonds are from strong hybridization between the d orbitals of TM adatoms and the pz orbitals of Ge atoms. The diffusion energy barrier of the TMs is B0.5 eV due to their stronger covalent bonding to germanene, which is clearly larger than the cases of group I–III metal adatoms. Depending on the induced adatom type, the adatom–germanene systems can exhibit metallic, half-metallic, and semiconducting behavior. More importantly, the intriguing half-metallic nature of Ti, V, and Co-decorated germanene has great potential for Ge-based spintronic device applications.

Acknowledgements This work was supported by National Natural Science Foundation of China (Grant No. 1127414, 60471042 and 11304121).


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