Aluminene as Highly Hole Doped Graphene C. Kamal,1 Aparna Chakrabarti,1 and Motohiko Ezawa2 1Indus Synchrotrons Utilization Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, India 2Department of Applied Physics, University of Tokyo, Hongo 7-3-1, 113-8656, Japan Monolayer structures made up of purely one kind of atoms are fascinating. Many kinds of honeycomb systems including carbon, silicon, germanium, tin, phosphorus and arsenic have been shown to be stable. However, so far the structures are restricted to group IV and V elements. In this letter, we systematically investigate the stability of monolayer structures made up of aluminium, in four different geometric configurations (planar, buckled, puckered and triangular), by employing density functional theory based electronic structure calculation. Our results on cohesive energy and phonon dispersion predict that only planar honeycomb structure made up of aluminium is stable. We call it ”aluminene” according to the standard naming convention. It is a metal. Results of electronic band structure suggest that it may be regarded as a highly hole doped graphene. We also present the tight-binding model and the Dirac theory to discuss the electronic properties of aluminene. PACS numbers: 68.65.-k, 61.46.-w, 81.07.-b, 31.15.E-, 71.15.Mb Monolayer structures made up of purely one kind of atoms graphene. We also report the geometric and electronic prop- possess many novel properties different from their bulk coun- erties of aluminene with alkali metal (M = Li and Na) adsorp- terparts. The best example is graphene, which is a hon- tion. Further, we construct an 8-band tight-binding model and eycomb monolayer of carbon[1, 2]. The other group IV the Dirac theory to discuss the electronic properties of alu- elements such as silicon, germanium and tin also form a minene. honeycomb monolayer known as silicene, germanene and We use QUANTUM ESPRESSO package[21] for perform- stanene, respectively[3–6]. Their geometric structures are ing a fully self-consistent DFT calculations[20] by solv- buckled, where we can control the band gap by applying ing the standard Kohn-Sham equations. For exchange- transverse electric field[7–10]. They are expected to be topo- correlation (XC) potential, the generalized gradient approx- logical insulators[4, 5]. Very recently, silicene is experi- imation given by Perdew-Burke-Ernzerhof[22] has been uti- mentally demonstrated to act as a field-effect transistor at lized. We use Rappe-Rabe-Kaxiras-Joannopoulos ultrasoft room temperature[11]. Phosphorene, honeycomb monolayer pseudopotentials[23] for Al, Li and Na atoms which include of phosphorus atoms, has experimentally been synthesized by the scalar-relativistic effect[24]. Kinetic energy cutoff of 50 exfoliating black phosphorus[12–14]. Its geometric structure Ry has been used for electronic wave functions. We adopt is puckered. It is a direct-band gap semiconductor and pos- Monkhorst-Pack scheme for k-point sampling of Brillouin sesses high hole mobility[15]. One can also tune the band gap zone integrations with 61 × 61 × 1, 51 × 51 × 1 and 51 × 41 by increasing the number of layers[15–17]. Another group V × 1 for the triangular / buckled, planar and puckered systems, honeycomb monolayer system (buckled and puckered struc- respectively. The convergence criteria for energy in SCF cy- tures) made up of arsenic atoms, called arsenene, has recently cles is chosen to be 10−10 Ry. The geometric structures are been predicted to be stable[18]. fully optimized by minimizing the forces on individual atoms It is note worthy that, so far there is no report available on with the criterion that the total force on each atom is below monolayer structure composed of purely group III elements. 10−3 Ry/Bohr. In order to mimic the two-dimensional sys- Though there exists a study on boron based finite triangular tem, we employ a super cell geometry with a vacuum of about structure with a hexagonal hole, it lacks translational invariant 18 A˚ in the direction perpendicular to the plane of monolayers symmetry to form a periodic system[19]. Thus, it is important so that the interaction between two adjacent unit cells in the to probe whether group III atom based monolayer systems are periodic arrangement is negligible. To calculate the phonon stable and then investigate the physical properties of the stable spectra, we employ the density functional perturbation theory ones. (DFPT)[25] implemented in PHonon code of the QUANTUM With this motivation, we investigate the stability of mono- ESPRESSO package. The dynamical matrix is estimated with layer structures made up of group III elements (B, Al, Ga and a 7 × 7 × 1 mesh of Q-points in the Brillouin zone. arXiv:1502.05874v1 [cond-mat.mes-hall] 20 Feb 2015 In) and then study the geometric, electronic and vibrational Stability: In order to study the stability of aluminene, we properties by employing density functional theory (DFT)[20] have carried out phonon dispersion calculations for all the ge- based calculations. We consider four different geometrical ometric configurations. The fully optimized geometric struc- configurations, namely, (a) planar, (b) buckled, (c) puckered tures and their corresponding phonon dispersion spectra are and (d) triangular geometries. Our DFT based phonon and co- given in Fig.1. Our calculations predict that planar aluminene hesive energy calculations predict that among the above men- with space group P 6=mmm forms a stable structure since tioned four configurations of group III elements, only the pla- it contains only positive frequencies for all the vibrational nar honeycomb monolayer made up of aluminium, as that of modes [Fig.1(a)]. On the other hand, the remaining geomet- graphene, is stable. We call it ”aluminene” in analogous to ric configurations possess structural instabilities in the trans- 2 (a) planar (b) buckled (c) puckered (d) triangular 400 400 400 400 ) -1 300 300 300 300 200 200 200 200 100 100 100 100 Frequency (cm 0 0 0 0 Γ K M Γ Γ K M Γ Γ K M Γ Γ K M Γ FIG. 1: Optimized geometries (top and side views) and phonon dispersion of aluminene in (a) planar, (b) buckled, (c) puckered and (d) triangular configurations. Planar aluminene is globally stable since the global minimum exists at the Γ point. There are negative phonons (corresponding to transverse acoustic modes) except for the planar configuration, indicating their instability. comb monolayer materials studied so far are either semimetal TABLE I: The results for optimized geometries of aluminene and K with alkali metals (M = Li and Na) are given below. or semiconductor. At the high symmetric point in Brillouin zone, two Dirac cones occur at energies 1:618 eV and −4:274 ˚ Structure Cohesive Lattice Bond length (A) eV. The former is due to the π bonds purely made up of the pz energy constant Al-Al Al-M M-M orbital and the latter is due to σ bonds which has strong con- (eV/atom) a (A)˚ tribution from the s orbital. At the Fermi energy, there exist Aluminene -1.956 4.486 2.590 - - two σ bands and we call them the σ1 and σ2 bands as shown Aluminene + Li -2.151 4.517 2.608 2.783 - in Fig.3(a). The σ2 band is purely made up of px and py or- Aluminene + Na -1.899 4.531 2.616 3.197 - bitals, while the mixing of the s orbital is not negligible in the Aluminene + 2 Li -2.218 4.420 2.552 2.908 2.790 σ1 band. Aluminene + 2 Na -1.846 4.554 2.629 3.217 3.709 The electronic band structure of aluminene closely resem- bles that of graphene[26], but the locations of Dirac points in these two systems are different. In the case of graphene, the Dirac point lies exactly at the Fermi level where the bands verse acoustic modes due to the presence of imaginary fre- due to the bonding orbitals (σ and π) are completely filled and quencies (shown as negative values). Cohesive energy for pla- those of anti-bonding orbitals are completely empty (σ∗ and nar aluminene is estimated to be -1.956 eV and the negative π∗). On the other hand, in aluminene, the bands due to the value indicates that this is a bound system. Our calculations bonding orbitals (σ and π) are not completely filled and thus yield 4.486 A˚ and 2.590 A˚ for lattice constant and Al-Al bond the Dirac point lies about 1.618 eV above the Fermi level. length for the planar structure, respectively (see Table I). After This is due to the fact that the number of valence electrons in the geometry optimization the buckled (puckered) structure Al (trivalent) is smaller than that of C (tetravalent). As a result, has become AB (AA) bilayer of triangular lattice [Fig.1(b) aluminene can be regarded as a highly hole doped graphene. and (c)]. The relative displacement between A and B layers is However, the important difference is that the Fermi energy is along the (1/3, 2/3, 0) direction. Since the aluminene in trian- highly shifted in aluminene. Here, we wish to point out a re- gular, buckled and puckered configurations are not stable, as markable feature of aluminene with respect to van-Hove sin- observed from their phonon spectra, we do not consider them gularities. The van-Hove singularity of the σ band exists very for further analysis. close to the Fermi energy at E = −0:212 eV. It may be possi- We have also carried out phonon dispersion calculations for ble to tune the Fermi energy around the van-Hove singularity the planar, buckled, puckered and triangular configurations and to make the electrical conductivity very large by applying made up of other group III elements (boron, gallium and in- gate voltage.