This thesis presents a theory of electron-electron interaction effects and optical properties
of nanostructures of two-dimensional (2D) honeycomb crystals - graphene and transition metal dichalcogenides (TMDC). Graphene, a semimetallic hexagonal lattice of carbon atoms can be described by a massless Dirac fermion model, with the conduction band (CB) and valence band (VB) touching in the corners of a hexagonal Brillouin zone, valleys K and -K. TMDC crystals sites host either a transition metal atom or a chalcogen dimer, which opens the energy gap and allows for describing their low-energy nature with massive Dirac fermion (mDf) model. The metal atom in TMDC crystals causes strong spin-orbit (SO) coupling, resulting in large SO splitting in bands at both valleys. For TMDCs it is possible to excite carriers in each valley with oppositely circularly polarised light, which offers promising prospects for devices based on electrons valley index, i.e. valleytronic devices. Additionally, the optical response of TMDCs is enhanced by the presence of secondary CB minima, at Q-points.
The dimensionality of 2D crystals can be further reduced to form quantum dots (QDs) - nanostructures con ned in all dimensions. This thesis first discusses hexagonal graphene QDs, which exhibit energy gap oscillation as a function of size, due to the edge type: zigzag or armchair. These QDs are divided into concentric rings, analysed with tight-binding (TB) model. An armchair edged QD is built from a zigzag edged QD by adding a 1D Lieb lattice of carbon atoms on its edge. The energy gap is formed differently for both edges: from the outer ring states for zigzag edge and from the 1D Lieb lattice zero-energy states for armchair edge, which causes the energy gap. The remaining portion of the thesis focuses on TMDC materials. First a TB model is presented for a member of TMDC group, MoS2, using three d orbitals of Mo atom and three p orbitals of the S2 dimers. The tunneling matrix elements between nearest-neighbor and next-nearest-neighbour sites are explicitly derived at K and -K to form a six band TB Hamiltonian. Its solutions are fitted to the bands obtained from the density functional theory ab initio calculations to obtain the correct behaviour of bands around K and additional minima at Q-points, which explains the role of d orbitals in TMDCs. Close to K the TB model is reduced to mDf model, which
is then studied in response to light, yielding the valley-dependent selection rules for
absorption. The interaction of mDf with light is further studied in the presence of strong external magnetic eld, which leads to the formation of Landau levels (LLs), asymmetric
between both valleys, and valley Zeeman splitting. These LLs are populated with electrons
to form a Hartree-Fock ground state (GS), which can exhibit valley polarisation due to the LL asymmetry. Quasi-electron-hole excitations out of the GS are then formed and their self-energy, vertex corrections and scattering energy is calculated. The effect of electron-electron interactions on valley Zeeman splitting is demonstrated and the Bethe-Salpeter equation is numerically solved to give magnetoexciton spectrum for both valleys. The results include a valley-dependent absorption spectrum for mDf magnetoexcitons that vary with the valley polarisation.
The final part of this thesis discusses the single particle and interacting effects in gated MoS2 QDs. First, I perform a single electron atomistic calculation for a million-atom computational box with periodic boundary conditions based on a TB model developed from ab initio methods for bulk MoS2. Electrons are then con ned with a parabolic electrostatic potential from top metallic gates. They exhibit twofold degenerate harmonic oscillator energy spectrum with shell spacing ω associated with valleys K as well as a sixfold degenerate energy spectrum derived from the Q-points. The degeneracy of electronic shells is broken due to valley contrasting Berry curvature,which acts as an effective magnetic eld splitting opposite angular momentum states in both valleys. I populate up to ve K-derived harmonic oscillator shells with up to six electrons and turn on the electron-electron interactions. The resulting GS phases form two regimes dependent on ω, which are dominated each by a broken-symmetry phase, i.e. valley and spin polarised GS for low ω and valley and spin unpolarised but spin intervalley antiferromagnetic GS for higher ω. This behaviour is explained as an effect of the strong SO splitting, weak intervalley exchange interaction and strong correlations. Means of detecting these effects in experiment based on the spin and valley blockade are proposed. These results advance the understanding of interaction-driven breaking of symmetry for valley systems, crucial for designing of valleytronic devices in the future.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/40983 |
| Date | 11 September 2020 |
| Creators | Szulakowska, Ludmila |
| Contributors | Hawrylak, Pawel |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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