New Phases of Germanene V. Ongun Oz¸celik,¨ 1, 2 E. Durgun,1, 2 and S. Ciraci3 1UNAM-National Nanotechnology Research Center, Bilkent University, 06800 Ankara, Turkey 2Institute of Materials Science and Nanotechnology, Bilkent University, Ankara 06800, Turkey 3Department of Physics, Bilkent University, Ankara 06800, Turkey Germanene, a graphene like single layer structure of Ge, has been shown to be stable and recently grown on Pt and Au substrates. We show that a Ge adatom adsorbed to germanene pushes down the host Ge atom underneath and forms a dumbbell structure. This exothermic process occurs spon- taneously. The attractive dumbbell-dumbbell interaction favors high coverage of dumbbells. This letter heralds stable new phases of germanene, which are constructed from periodically repeating coverage of dumbbell structures and display diversity of electronic and magnetic properties. Three dimensional (3D) layered bulk phases, such as graphite,[1] BN[2] and MoS2[3] have led to the synthesis of single layer, honeycomb structures of those materi- als, which were initially conjectured to be unstable.[4{ 7] The existence of single layer, graphene like struc- tures of other Group IV elements, like Si and Ge, have been ruled out since these elements do not have lay- ered allotropes like graphite that would allow the syn- thesis of their single layer structures. Surprisingly, based on state of the art first-principles calculations, silicene,[8, 9] germanene,[10, 11] most of III-V and II-VI compounds[9, 11] and several transition metal dichalco- genides and oxides[12] have been shown to form stable, single layer honeycomb structures. Moreover, it has been also shown that silicene and germanene share several of FIG. 1: Electronic structure of monolayer germanene. The the exceptional properties of graphene, such as π- and splittings due to the spin-orbit coupling (SOC) are shown in the magnified insets. The Fermi level is set to the zero π∗-bands linearly crossing at the Fermi level and hence of energy and is indicated by the dashed-dotted line. The forming Dirac cones, the ambipolar effect and the fam- atomic structure of buckled germanene is illustrated by inset. ily behavior observed in nanoribbons.[10, 13] Advances in growth techniques have enabled the synthesis of some of these predicted single layer structures, in particular the growth of single and multilayer silicene on Ag(111) (PBE) functional.[22] The Brillouin zone (BZ) was sam- substrates[14{16] and the growth of germanene on Pt and pled in the Monkhorst-Pack scheme, where the conver- Au substrates[17{19] were recently succeeded. gence in energy as a function of the number of k-points was tested. The k-point sampling of (21×21×1) was In this letter, we find that a single Ge adatom ad- found to be suitable for the BZ corresponding to the sorbed to germanene constructs a dumbbell (DB) struc- primitive unit cell of germanene. For larger supercells ture. Even more remarkable is that new phases can be this sampling has been scaled accordingly. The number constructed by the periodic coverage of germanene with of k-points were further increased to (48×48×1) in the DBs. Depending on the coverage of DBs, these stable density of states calculation. Atomic positions were opti- phases can be metal or narrow band gap semiconductor mized using the conjugate gradient method, where the to- in magnetic or nonmagnetic states and hence they at- tal energy and atomic forces were minimized. The energy tribute diverse functionalities to germanene. We believe convergence value between two consecutive steps was that the intriguing stacking of these phases can pave the chosen as 10−5 eV. A maximum force of 0.002 eV/A˚ was arXiv:1407.4170v1 [cond-mat.mtrl-sci] 15 Jul 2014 way to the layered phase of bulk germanium, i.e. ger- allowed on each atom. Numerical calculations were car- manite. ried out using the VASP software.[23] Since the band Our predictions are obtained from the state of the art gaps are underestimated by DFT, we also carried out cal- first-principles pseudopotential calculations based on the culations using the HSE06 hybrid functional[24], which spin-polarized Density Functional Theory (DFT) within is constructed by mixing 25% of the Fock exchange with generalized gradient approximation(GGA) including van 75% of the PBE exchange and 100% of the PBE corre- der Waals corrections.[20] We used projector-augmented lation energy. The phonon dispersion curves were calcu- wave potentials (PAW)[21] and the exchange-correlation lated using small displacement method.[25] potential is approximated with Perdew-Burke-Ernzerhof It is known that the splitting of threefold valence band 2 the Ge atom underneath further down until the final DB forms as shown in 2 (a). As a concerted process, two Ge atoms above and below the germanene surface, named as D1 and D2, donate significant electronic charge to the three nearest Ge atoms of germanene and hence each forms three strong Ge-Ge bonds with a length of 2.58 A.˚ With these additional bonds with DB, these three Ge atoms of germanene become fourfold coordinated. D1 and D2 by themselves engage in a 3+1 coordination, since each has three nearest neighbor Ge atoms at a dis- tance of 2.58 A.˚ Whereas the D1 -D2 distance of 2.80 A˚ is slightly larger. At the end, the resulting DB cor- responds to a local minimum on the Born-Oppenheimer surface and remains stable. As for the DB decorated germanene, it is a structure between the fourfold coordi- nated cdGe and the three fold coordinated single layer, buckled germanene. Since moving a DB from one place to another by breaking three Ge-Ge bonds involves an FIG. 2: (a) Snapshots of conjugate gradient steps in the energy barrier, any pattern of DBs on germanene is ex- course of the formation of a dumbbell (DB) structure. The pected to remain stable. It is noted that DB has been external Ge adatom first approaches to the germanene layer found to be the second most energetic defect structure of from the top site, and eventually constructs the DB structure by pushing the host Ge atom down. (b) Top and side views carbon adatom on graphene.[12] Later, it has been found of DB formed on (4 × 4) germanene. Two Ge atoms of DB to be the most energetic defect structure of Si adatom on are highlighted by red. (c) The DB zoomed in along with the silicene,[28, 29] and has been demonstrated that it can total charge density isosurfaces. (d) Contour plots of the total form spontaneously without an energy barrier as long as charge density on planes passing through D1 − A − D2 and a Si adatom on silicene is available.[30] In the present pa- B − D2 − C atoms. Note that although the DB atoms make per, we demonstrated that Ge DB can form new phases bonds with nearest germanene atoms, there is no bonding (or derivatives) of germanene with novel electronic and between the DB atoms, D and D . 1 2 magnetic properties. Since the construction of a single DB is an exothermic process and hence does not involve any energy barrier, at the center of the Brillouin zone due to spin-orbit cou- the formation of DB structure is unavoidable as long as pling is significant (290 meV) for Ge crystal in cubic a free Ge adatom is present at the close proximity of diamond (cdGe) structure.[26] The extend of spin-orbit the surface. We define the associated binding energy as splitting in germanene is crucial as a starting point of Eb = ET [germanene] + ET [Ge] − ET [germanene + DB]; the present study. Despite 1 meV spin-orbit splitting in in terms of the total energies of germanene+DB, pristine silicene,[27] the spin-orbit splitting of germanene at Γ- germanene and free Ge adatom. The binding energies and K-points of the hexagonal Brillouin zone are calcu- are calculated for a single DB in the (n × n) hexagonal lated to be 70 meV and 23 meV. Accordingly, it is set 0 supercells with varying values of n. Accordingly, Eb is that at the K, K -points, where the linear bands cross the energy gained from the construction of a single DB at the Fermi level in the absence of spin-orbit coupling, through the adsorption of a single Ge adatom to ger- a gap of 23 meV is opened. This way the semimetallic manene and Eb >0 indicates an exothermic process. For state and massless Fermion behavior of electrons of pris- an isolated DB calculated in a large supercell with n=8, tine germanene are discarded as seen in 1. This result Eb ∼ 3.4 eV; but it increases with decreasing n or de- is critical for our study dealing with new derivatives of creasing DB-DB distance due to the attractive interac- pristine germanene. tion among DBs as discussed in the next paragraph. In Having clarified the effect of spin-orbit coupling on 2 (b) and (c), the atomic configurations of a single DB pristine germanene, we next examine the construction and its relevant structural parameters together with iso- of a single DB structure. In 2(a), we present various surfaces of charge density of Ge-Ge bonds around DB are stages of conjugate gradient calculations taking place in shown. The charge density counter plots calculated on the course of the adsorption of single Ge adatom. In various planes are presented in 2(d). The bonding of the presence of an external and free Ge adatom, the for- the DB atoms (D1 and D2) with the nearest Ge atoms of mation of DB structure on germanene is spontaneous.