Electronic structure of MX2-type layered compounds

J. Phys. Chem. Solids Vol. 50, No. 8. pp. 801408. Printed in Great Britain.

1989

0022.3697189 $3.00 + 0.00 Maxwell Pergamon Macmillan plc

ELECTRONIC STRUCTURE OF MX,-TYPE LAYERED COMPOUNDS ERIC SANDRA, RAYMOND BREC and JEAN ROUXEL Institut de Physique et Chimie des Materiaux de Names, Laboratoire de Chimie des Solides U.A. C.N.R.S. 279, 2 rue de la Houssiniere 44072 Names Cedex 03, France (Received 30 May 1988; accepted in revised form 7 February 1989)

Abstract-From electronic photoemission spectra of Gage, the electronic structure of the transition metal dichalcogenides is considered and the general characteristics of layered compounds are stressed. More precisely, a new description of the Van der Waals gap is given that explains the cohesion of lowdimensional compounds. This study leads to a classification of the MX, polytypes according to the quantum nature of the frontier states and allows one to determine three families of layered MX, phases. These conclusions are in agreement with and explain previous Mossbauer studies on (2D) MPS,. The general conclusion underlines the importance of the electronic correlations in low-dimensional compounds and leads to three different electronic schemes for layered phases. Keywords: Layered transition metal dichalcogenides,

1. INTRODUCTION The unusual properties shown by layered compounds have been the subject of many studies by chemists as well as physicists during the past 15 years. Lowdimensional solids may exhibit charge density waves and oxidizing properties making them among the best host materials for intercalation by reducing agents. It is acknowledged that most of these properties are related to the strong anisotropy of the chemical bond, and this already appears in the crystal morphology. However, calling these structures two-dimensional, as is often done, may be quite exaggerated and probably does not correspond to reality. From many results published on layered materials, it is possible to suggest new interpretations of their structure leading to a better understanding of some of their chemical and physical properties. More precisely, GaSe (Ga,Se,) will be considered, as it provides a nice basis for a discussion of the 2D phases. It is to be pointed out that this article does not intend to calculate what experiments teach us, but rather aims at interpreting results using quantum models. 1.1. MX, crystal structure The basic MX, structure is an assembly of weakly linked layers. Inside a layer the iono-covalent or metallic bonding is fairly strong compared with that occurring between the slabs. In most cases, it is possible to obtain stoichiometric compounds, and only these phases will be considered here. The introduction of defects, as long as their concentration remains small enough, can be treated easily using a perturbation method. In a first approach, the MX, compounds may be classified according to the type of coordination pre-

MX, electronic structures, polytypes classification.

sented by the cations. If the MX, layers constituting the structure are built from a close packing of chalcogens, then the cations are octahedrally coordinated (Fig. 1). If the chalcogen layers are atop each other, then the cations are seated in trigonal prims as shown in Fig. 2. In both cases, the stacking of MX2 sheets is close packed. Superposition of the same types of layers and/or of different ones leads to a large variety of phases. Some of them are gathered in Fig. 3(a)-(c). The presentation of the structures in three different groups has to do with the interslab electronic interactions as explained below. All structural arrangements will be considered based on their hexagonal cell where the c-axis is perpendicular to the layers [I].

2. ELECTRONIC STRUCTURE OF MX, LAYERED

COMPOUNDS Many different studies of the MX2 electronic structures have already been made. In particular GaSe [ = (Gaz)Se,] has been the subject of many calculations in order to understand the chemical bond of these structures. The schematic crystal structure of this compound is given in Fig. 4 and we easily understand the relation between the GaSe structural type and the MX, one in which the M4+ cations are substituted by (Ga-Ca)4 + pairs. Clearly, the GaSe and MX, semiconductor electronic structures are expected to present close similarities that correspond to specific properties of layered compounds. Pointing these out will help in understanding how one goes from a semiconducting compound to a conducting one. 801

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(b) Set of transition metal dichalcogenides MX, structures represented as in (a), with M = Ta, Nb and Ti, Zr and Hf. One can notice that the cations are ordered in chains (underlined by a broken tine) along the c-axis. (c) Set of transition metal dichalcogenides MX, structures represented as in (a) with M = Nb and Ta. All the structures present a mixture of the features described in (a) and (b).

2.1. GaSe electronic structure:

molecular de-

scription Figure 5 shows a few results obtained by different calculational methods about the dispersion of energy states in the first Brillouin zone. The K point is defined by (a* + b *)/3 in reciprocal space. The structure of diagram 4 [5] is obtained using a tight-binding method and that of diagram 5 using semiempirical pseudo-potentials [5]. The tight binding interpretation of the different bands is given in Fig. 6 [5].

First of all, let us neglect the infinite dimension of as a molecule. This molecule is Ga,Se, (stoichiometry of the half unit cell). It possesses the symmetry of the Ga,Se, and SeGa, fragments (see Fig. 7). We suppose that the fundamental state can be correctly described using the reduced basis of 4p orbitals localized on Se and of 3s and 3p ones localized on Ga. Each atom in the structure exhibits a C,, local symmetry. Considering that symmetry, we can classify the different orbitals using group theory: ns orbitals the solid and consider the structure

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are a I; npz orbitals are a 1; and (npx, npy) orbitals are e. The more stabilized orbitals will be those which have the maximum overlap with others. As shown in Fig. 7, we qualitatively obtain the same results as Nagel et al. (Fig. 6 [S]). The description of the HOMO is now essential in understanding the structure. There states are mainly non-bonding and localized mostly on the 4pz orbitals of selenium. In fact these states are slightly antibonding as we observe a weak anti-bonding contribution of 3pz orbitals localized on gallium. In the structure, one can now consider a series of “electronic lone pairs” mostly located on selenium and pointing out of the layers along the trigonal axis. As these states are mostly made of one type of atomic orbital and are occupied by two electrons, we cannot neglect the correlation energy in the description of the valence state. If we consider a Hubbard type description, in the fundamental state, two electrons will be on approximately the same non-bonding orbital, and the energetic spectrum will then take a correlation

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energy U into account. In a molecular description, the energy of this two-electron state will be: E = 2E,,,,,, + U. The schematic representation in Fig. 8.

of this state is given

2.2. GaSe electronic struture: solid state description If we extend the molecular results to the solid state, it appears that the valence states cannot be described by a non-correlated monoelectronic wave function. The correlation in the movement of the electrons must be taken into account. Let us consider the states associated with the 4pz orbitals of selenium. First of all, if we neglect the correlation energy in Hubbard’s Hamiltonian and if we only retain the jump integrals between two adjacent 4pz orbitals belonging to the

‘I-TK Fig. 5. Calculated electronic structures of layered GaSe [2-61.

Electronic structure of MX,-type layered compounds

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same layer, this Hamiltonian reduces to a tight binding one. The only simple cases where one can solve the Schrodinger equation using Hubbard’s Hamiltonian is presented in Fig. 9 [7]. Considering an only-selenium plane network, (trigonal symmetry), the tight binding dispersion relation is reduced to: E(k) = 2t[cos(ka) + cos(kb) + cos(k(a + b))],

where t is the jump integral between two adjacent orbitals, u and b are the cell vectors in real space, and k is a wave vector in the reciprocal space. The correlation energy cannot be neglected because it seems that it is in the range of the energy difference between two different energetic states. In an electronic photoemission spectrum a state where electrons are strongly correlated must be associated to a wide band (unknown fine structure). The solutions of the Schrodinger’s equation using Hubbard’s Hamiltonian are not known. Using the momentum theorems we can have an idea of the dispersion of states diagram as shown in Fig. 10. When U is different from zero, we observe that the degeneracy of the two emission spectra associated with a two-electronic state disappears. As shown in Fig. 10, the lowest states correspond to noncorrelated ones. The degeneracy must remain from

_ slab 2

the bottom of the spectrum up to an energy U. The highest energy states correspond to strongly correlated states. (We must observe only one band at the peak of the spectrum.) The middle of the D.O.S. scheme corresponds to correlated and non-correlated states. This is in good agreement with the photoemission spectrum obtained by Leveque [5] and reproduced in Fig. 11. The A states correspond to the so-called correlated states and are mostly spatially localized on 4pz selenium orbitals. The B band corresponds to the gallium-gallium bonding state in which we can neglect the correlation energy since the two electrons are delocalized on two centers. The 4 C bands correspond to (px, py) bonding between gallium and selenium atoms, and the D band corresponds to gallium-gallium bonding through the 3s orbitals on gallium. A more quantitative assignment was given by Nagel (see Fig. 6). Up to now, we have only taken into account the interactions inside a layer, however we now have to consider the interactions between the different slabs. In the past, many electrostatic models were used but we suggest that inter-slab cohesion could be the result of second-order interaction between states associated with two adjacent layers. One can easily imagine an interaction between the full A state localized in the structure’s gap and an empty or partially filled state on an adjacent slab.

2.3. Model for the cohesion between slabs .-_--slab 1 -Ga

Fig. 8. Correlated electronic pair in the molecular description of GaSe.

If one considers a plane containing spherical or cylindrical states with a trigonal symmetry of the arrangement, it is clear that the extension of these localized states and their combination may create a metallic or a semiconducting state. In Fig. 12, we can see the evolution in the position of the electronic density in space when considering the variation of t/U. When the electronic density maximum is located

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Fig. 9. Simple cases when one can solve the Hubbard’s Hamiltonian. between the atomic positions, the state is conducting. On the contrary, when the density maximum remains on atomic positions, the state created is localized (insulating or semiconducting). Let us first consider the different observed polytypes that we classified in Fig. 3(a)-(c). The a group corresponds to the case in which every metal, in each layer, has a chalcogen as its first neighbor along the c-axis. The b group corresponds to the case in which every metal, in each layer, has another metal as its first neighbor along the c-axis. Finally the c group corresponds to cases in which both situations mentioned above coexist. If one now considers the elements M belonging to the three first transition metal columns of the Periodic Table, we observe that elements VI lead to the u-type dichalcogenides, elements IV to the b-type ones and elements V to a, b and a mixture (c) of both types [l].

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Fig. IO. Scheme representing a possible solution for a general Hubbard’s problem.

The difference in polytypes may be linked to the localized or delocalized character of the lowest unoccupied state (L.U.S.) located on the transition metal network. We assume that all specific properties of layered compounds are related to the interaction between the highest occupied states (H.O.S.) and the L.U.S. and also their nature. As far as the distance separating the different metals is concerned, elements belonging to group six cannot create a delocalized L.U.S. The maximum spatial density of states in that case remains, as in separate atoms, around the metallic centers, and then they are semiconductors. The maximum stabilization in the interaction between the layers occurs when the overlap between the electronic “lone paired” states located on pz chalcogen orbitals and the L.U.S. is a maximum. This is clearly observed for the u-type group. Elements of column four, on the contrary, create a delocalized L.U.S. The maximum density of state is then located at the center of a triangle formed by three metals within the 2D associated network. The maximum overlap for maximum stabilization occurs when the chalcogen pz orbital points through the metallic triangles along the c-axis direction, which corresponds to the b-type group. Elements belonging to column five are intermediary, constituting a frontier group. For these cations, the combination of the metallic states in the layers must create a L.U.S. state with a rather constant spatial density localization. That is why many polytypes are observed in thermodynamic conditions. If we take NbSez as an example, we notice that only a 2Hb polytype is stable at low temperature [9],

Electronic structure of MX,-type layered compounds

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proving that the maximum of the spatial density of

state in the L.U.S. is located at the centers of mass of a metallic triangle. The application to the GaSe case is immediate as it corresponds to the semiconducting case mentioned above. The anti-bonding state concerned is the first one localized mostly on gallium (anti-bonding GaGa). Let us consider this interaction as a perturbation at the center of the 1st Brillouin zone. The A state must now be described by a linear combination of: 4~2 orbitals on a slab; and 3pr orbitals on that slab and on adjacent ones. Some considerations concerning substituted MX, compounds (FePS,) by Fatseas et al. [lo] appear to sustain the above conclusions. In effect, the isomershift of FePS, [to be also written as Fe,,, (P,),,j Sd was interpreted by considering a 3d6 4~0.2 electronic configuration. From magnetic susceptibility measurements [ll], the paramagnetic behavior of the compound was perfectly fitted with a spin only formula (S = 2). The two results prove the diamagnetism of the 4s electrons. This can only be interpreted by considering the interaction between the layers as described in this article. 3. SEMICONDUCTING AND CONDUCTING MX2 COMPOUNDS

Let us now consider what is happening when looking at the energy dispersion of the electronic states in the directions parallel to the layers.

Let us look at the differences between conducting and semiconducting MX2 compounds. The layered compounds can only exist if the strongly correlated state A is stabilized enough to be less energetic than all empty or partially filled states of the compound. In a semiconducting compound only one type of band scheme exists: the A state is slightly anti-bonding because of the correlation energy that destabilizes it from non-bonding. This band must be separated from the empty or partially filled bands, as shown in Fig. 14. In a conducting compound, two band schemes are possible: (i) if the A band is below the conducting partially filled one, then we observe a normal metallic state and the gap width is mostly determined by the anionic radii of the chalcogen and is not very different from the width of an equivalent semiconductor [Fig. 14(a)]; (ii) if the A band is energetically around an empty conducting band in the structure, we observe a transfer and then the width of the Van der Waals gap must be narrower than what is observed in equivalent semiconductors. The band scheme is as shown in Fig. 14(b). The conductivity may appear as the result of a formal electronic exchange taking place between adjacent slabs, when building the structure from separated sheets. This must be the case of 2H NbSe, where the structures’s gap is 0.4 A narrower than in the corresponding semiconductor layered diselenides

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Fig. 12. Extended LCAO corresponding to a semiconducting (A) or conducting (B) case.

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and helped explain the various polytypes observed. The conductivity in the slabs may appear as a result of an electronic transfer between adjacent layers and the existence of the Van der Waals gap can be understood by considering a second-order interaction between two slabs. Correlation in the movement of the electrons localized in the gap must not be neglected, as proved experimentally. This fact seems to be very important in understanding properties such as superconductivity in layered compounds, a subject for further research.

REFERENCES 1. Lieth R. M. A and Terhell J. C. J. M., Physics and Chemistry of Materials with Layered Structures, Vol. I,

A correlated

slates

ib)

(a)

Fig. 14. (a), (b) Two different types of dispersion along the slabs for layered conductors. 4. CONCLUSION

Most of the properties of layered MX2 compounds are related to the strong anisotropy in the chemical bond. Taking into account that interaction, allowed us to classify the MX, phases in three main families

p. 141. Reidel, Dordrecht (1977). 2. Bassani M., Pastori G., Nuouo Cim. LB%, (1967). 3. Schiiltter M., Camassel J., Kohn S., Voitchovsky J. P., Shen Y. R. and Cohen M., Phys. Rev. B13, 3534 (1976). 4. Depeursinge Y., Nuouo Cim. 38B, 153 (1977). 5. Nagel S., Baldereschi A. and Maschke K., J. Phys. Cl2, 1625 (1979). 6. Doni E., Girlanda R., Grass0 V., Balzarotti A. and Piacentini M., Nuooo Cim. SlB, 154 (1979). I. Friedel J., Cours DEA de physique du Solide. Orsay (PXT), France (1986). 8. L%que G., Seminaire de Chimie du Solide, Galerne 87, Genolhac, 277 France, 21-25 Septembre (1987). 9. Vanderberg J. M., Physics and Chemistry of Materials with Layered Sfructure, Vol. IV, 423. Reidel, Dordrecht (1976). 10. Fatseas G., Evain M., Ouvrard G. and Brec R., Phys. Rev. 357,

3082 (1987).

11. Brec R., Solid St. Ionics 22, 3 (1986).