Quantum effects in two-dimensional nanostructures

Abstract

Two-dimensional van der Waals semiconductors have emerged as one of the most promising class of materials in the field of nanoelectronics. Among them, InSe has excelled in providing all the requirements needed for technological applications, demonstrating superior flexibility, ambient stability and exceptional band gap tunability. In this thesis, we explore using k · p and tight-binding calculations, a plethora of quantum effects observed in few-layer InSe and we analyse transverse magnetic focusing data measured in twisted bilayer graphene. We studied the intersubband energy dependence on the number of layers and the applied electric field in the lowest conduction subband of multilayer InSe. From the subband energies, we extracted the intersubband optical absorption properties of n-doped InSe. Using a quantum well model, the intersubband energies in the conduction band were found to range in the infrared and far-infrared part of the optical spectrum. The dependence on the electric field was self-consistently calculated for the different number of layers and an analytical expression for the intersubband optical absorption coefficient was derived using the Fermi golden rule. Using the self-consistent algorithm previously developed to study the intersubband energy dependence on the applied electric field, the spin-orbit coupling (SOC) strength in the bottommost conduction subband was calculated at different applied displacement fields. The calculations performed were complemented with density functional theory (DFT) studies of ferroelectric charge transfer in InSe which indicated a very weak ferroelectric contribution to the overall SOC strength. Finally, our calculated SOC strengths were compared with those extracted from weak antilocalization measurements in a dual-gated device. We found a very good agreement between our theoretical predictions and the experimental data. We used the quantum harmonic oscillator basis to calculate the excitonic dispersion in InSe films ranging from the monolayer to the bulk limit. Both the excitonic dispersion and the binding energies in different film thicknesses were calculated taking into account the sombrero dispersion in the valence band. The effect of such band flatness was to generate a minimum in the excitonic dispersion at a finite centre of mass momentum which vanishes with an increasing number of layers. When the InSe film thickness surpasses the six-layer limit, a transition from a dark to a bright exciton was predicted. The proposed procedure was demonstrated to be effective to calculate the excitonic binding energies in any van der Waals heterostructure using an extension of the proposed procedure. Finally, we demonstrated how magnetic focusing can be used to probe the band structure of any 2D material. This technique was used to investigate the band structure profile of twisted bilayer graphene, where the application of an externally applied electric field generates a visible minivalley splitting.

Date of Award	17 May 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Vladimir Falko (Main Supervisor) & Francisco Guinea (Co Supervisor)