Crystalline and correlated phases in two-dimensional transition metal dichalcogenides

This thesis is dedicated to the study of various aspects of the electronic structure of two-dimensional transition metal dichalcogenides (TMDs) of chemical composition MX $_2$ (where M is a transition metal atom and X= S, Se, Te), using a combination of \textit{ab inito} density-functional methods.

We first address the relative stability of the $1T$ and $1H$ phases of two-dimensional TMDs as a function of the column of the transition metal atom in the periodic table. Using a Wannier-function approach, we calculate crystal field and ligand field parameters for a broad range of members of this family of materials. Taking TaS $_2$ as an example, we show how the splitting of the $d$ electron states arises from an interplay of electrostatic effects and hybridization with the ligands' $s$ , $p$ and $d$ states. We show that the ligand field alone cannot explain the stabilization of the $1H$ polymorph for $d^1$ and $d^2$ TMDs, and that band structure effects are dominant. We present trends of the calculated parameters across the periodic table, and argue that these allow developing simple chemical intuition.

Secondly, we study the occurrence of charge density wave phases and periodic lattice distortion in metallic $1T$ transition metal dichalcogenides. The phonon dispersion and fermiology of representative examples with different $d$ electron counts are studied as a function of doping. Two qualitatively different behaviours are found as a function of the filling of the $t_{2g}$ subshell. We argue that away from half-filling, weak-coupling nesting arguments are a useful starting point for understanding, whereas closer to half-filling a strong-coupling real-space picture is more correct. Using Wannier functions, it is shown that strong metal-metal bonds are formed and that simple bond-counting arguments apply.

Thirdly, the recently synthesized $1T$ phase of NbSe $_2$ , in monolayer form, is investigated from first principles. We find that $1T$ -NbSe $_2$ is unstable towards the formation of an incommensurate charge density wave phase, whose periodicity can be understood from the Fermi surface topology. We investigate different scenarios for the experimentally observed superlattice and insulating behaviour, and conclude that the star-of-David phase is the most stable commensurate charge density wave phase. We study the electronic properties of the star-of-David phase at various levels of theory and confirm its Mott insulating character, as speculated and in analogy with TaS $_2$ . The Heisenberg exchange couplings are found to be ferromagnetic, which suggests a parallel with the so-called flat-band ferromagnetism in certain multiband Hubbard models.

Finally, we address the possibility of the occurrence of the excitonic insulator phase in single-layer TiSe $_2$ . The relative role of electron-electron and electron-phonon interactions in driving the charge density wave in layered and two-dimensional TiSe $_2$ has been disputed and is still unresolved. We calculate the electronic structure and finite-momentum exciton spectrum from hybrid density functional theory. We find that in a certain range of parameters, excitonic effects are strong and the material is close to a pure excitonic insulator instability. A possible necessary condition for the physical realization of a pure excitonic insulator is proposed.

Crystal field, ligand field, and interorbital effects in two-dimensional transition metal dichalcogenides across the periodic table

Diego José Pasquier, Oleg Yazyev

Two-dimensional (2D) transition metal dichalcogenides (TMDs) exist in two polymorphs, referred to as 1T and 1H, depending on the coordination sphere of the transition metal atom. The broken octahedral and trigonal prismatic symmetries lead to different crystal and ligand field splittings of the d electron states, resulting in distinct electronic properties. In this work, we quantify the crystal and ligand field parameters of 2D TMDs using a Wannier-function approach. We adopt the methodology proposed by Scaramucci et al (2015 J. Phys.: Condens. Matter 27 175503) that allows to separate various contributions to the ligand field by choosing different manifolds in the construction of the Wannier functions. We discuss the relevance of the crystal and ligand fields in determining the relative stability of the two polymorphs as a function of the filling of the d-shell. Based on the calculated parameters, we conclude that the ligand field, while leading to a small stabilizing factor for the 1H polymorph in the d(1) and d(2) TMDs, plays mostly an indirect role and that hybridization between different d orbitals is the dominant feature. We investigate trends across the periodic table and interpret the variations of the calculated crystal and ligand fields in terms of the change of charge-transfer energy, which allows developing simple chemical intuition.

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Structural and electronic properties of an abrupt 4H-SiC(0001)/SiO2 interface model: Classical molecular dynamics simulations and density functional calculations

Peter Broqvist, Fabien Devynck, Alfredo Pasquarello

Using a density functional approach, we study structural and electronic properties of the 4H(0001)-SiC/SiO2 interface. Through the sequential use of classical and ab initio simulation methods, we generate an abrupt model structure which describes the transition between crystalline SiC and amorphous SiO2 without showing any coordination defect. The first step in our generation procedure consists in identifying suitable interfacial bonding patterns which account for the bond density reduction across the interface. In the second step, the connection to amorphous SiO2 is achieved through classical molecular dynamics. The atomic positions are then relaxed within a generalized gradient approximation of density functional theory. The final model structure shows good structural parameters and an oxide density typical of amorphous SiO2. We investigate the electronic structure of the generated model interface through the local density of states obtained with hybrid density functionals. In our atomically abrupt interface model, the full oxide band gap is recovered at a distance of similar to 5 A from the interface. This extent is in good agreement with estimates derived from internal photoemission measurements and provides support for the abrupt nature of the interface. We obtained band offsets through two different procedures: by evaluating the local density of states and by aligning the band extrema through the local electrostatic potential. Band offsets calculated with various functionals are compared to experimental values. The best agreement is achieved for a hybrid functional in which a screened Coulomb potential is used in the Hartree-Fock exchange term. For this case, the calculated band offsets underestimate the experimental values by similar to 25%, but agree with experiment within a few percent when expressed with respect to the oxide band gap.

2007

Band-edge problem in the theoretical determination of defect energy levels: The O vacancy in ZnO as a benchmark case

Audrius Alkauskas, Alfredo Pasquarello

Calculations of formation energies and charge transition levels of defects routinely rely on density functional theory (DFT) for describing the electronic structure. Since bulk band gaps of semiconductors and insulators are not well described in semilocal approximations to DFT, band-gap correction schemes or advanced theoretical models, which properly describe band gaps, need to be employed. However, it has become apparent that different methods that reproduce the experimental band gap can yield substantially different results regarding charge transition levels of point defects. We investigate this problem in the case of the (+2/0) charge transition level of the O vacancy in ZnO, which has attracted considerable attention as a benchmark case. For this purpose, we first perform calculations based on nonscreened hybrid density functionals, and then compare our results with those of other methods. While our results agree very well with those obtained with screened hybrid functionals, they are strikingly different compared to those obtained with other band-gap-corrected schemes. Nevertheless, we show that all the different methods agree well with each other and with our calculations when a suitable alignment procedure is adopted. The proposed procedure consists in aligning the electron band structure through an external potential, such as the vacuum level. When the electron densities are well reproduced, this procedure is equivalent to an alignment through the average electrostatic potential in a calculation subject to periodic boundary conditions. We stress that, in order to give accurate defect levels, a theoretical scheme is required to yield not only band gaps in agreement with experiment, but also band edges correctly positioned with respect to such a reference potential.

2011

Structural and electronic properties of an abrupt 4H-SiC(0001)/SiO2 interface model: Classical molecular dynamics simulations and density functional calculations

Peter Broqvist, Fabien Devynck, Alfredo Pasquarello

2007