Electronic structure of two-dimensional materials: Effect of point defects and moiré patterns

Abstract

In the last two decades, research on two-dimensional (2D) materials has gained momentum due to their capability to host a wide range of novel phases of matter. These materials have also found applications in electronic, optoelectronic and sensor devices. The electronic structure of material forms a basic building block to understand its electronic phases. It can be altered by several external factors, for example, strain, defects, moiré patterns or electric field. In this thesis, we focus on two such external factors: point defects and moiré patterns. Using first-principle calculations, we study the influence of these factors on the electronic structure of phosphorene and transition metal dichalcogenides.

Defects appear spontaneously in a material at a finite temperature. We investigate native point defects: vacancy and self-interstitial in mono- and bilayer phosphorene. We have studied formation energies, quasiparticle energies of defect states, and charge transition levels of these defects using ab initio density functional theory and GW approximation to the electron self-energy. These defects have low formation energies of 0.9–1.6 eV in the neutral state. Furthermore, the vacancy in phosphorene behaves as an acceptor-like defect which can explain the p-type conductivity in phosphorene. On the other hand, interstitial can show both acceptor- and donor-like behaviour.

In homobilayers of transition metal dichalcogenides, a small twist can be introduced to form a moiré superlattice (MSL). Recently, there is experimental evidence of flat bands in such twisted bilayer structures. We study the flat bands in twisted WSe2 where strong spin-orbit interaction gives rise to novel and interesting phenomenon. Flat bands emerge at both the band edges in twisted bilayer WSe2. The flat bands at the valence band edge originate from the K point of the unit cell Brillouin zone, unlike other twisted transition metal dichalcogenide structures. For twist angle (θ) close to 0◦, the bands at the valence band edge also possess a non-trivial topology. Quantum spin Hall insulating state, which is a consequence of this non-trivial topology should be experimentally accessible for θ < 3.5◦. For θ close to 60◦, the flattening of the bands arising from the K point is a consequence of the atomic reconstructions of the individual layer. Our findings are in excellent agreement with spectroscopic measurements on this material.

Another way to generate a moiré pattern from the homobilayer is by applying strain to one of the layers. This induces a lattice constant mismatch between the two layers and causes the formation of an MSL. This strained MSL shows very different structural and electronic properties than the twisted ones. We show that the strained MSLs provide a platform to study the ionic Hubbard model on a honeycomb lattice and the Hubbard model on a triangular lattice.

Two different TMD layers can be rotated and stacked on top of each other to form a twisted heterostructure. We study the electronic structure and optical properties of a twisted MoS_2/MoSe_2 heterostructure. The electronic band structure of this system and its origin in the individual layer’s unit cell has been explored. Experimentally, it has been found that interlayer excitons in heterostructure are long-lived compared to the intralayer ones. We have studied both kinds of excitons in this system. Our calculations show that optically-dark-finite-centre-of-mass-momentum intralayer excitons in bilayers of MoS2 and MoSe2 become optically allowed in the heterostructure. This is due to the presence of the moiré potential. Furthermore, we clarify the nature of the interlayer excitons. Our calculations show that this heterostructure has a type II band alignment. This results in the lowest energy interlayer excitons as those arising from transitions between the valence band of MoSe2 to the conduction band of MoS2.