Quantum Monte Carlo study of low dimensional materials

This thesis addresses several challenging problems in low-dimensional systems, which have rarely or never been studied using quantum Monte Carlo methods. It begins with an investigation into weak van der Waals-like interactions in bilayer graphene and extends to graphene placed on top of boron nitride at four different stacking configurations. The in-plane optical phonon frequencies for the latter heterostructure as well as the out-of-plane phonon frequencies for both structures are calculated. We find that the binding energies (BEs) of these structures are almost within the same range and are less than 20 meV/atom. Although the phonon vibrations are comparable within both the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT), DFT gives quantitatively wrong BEs for vdW structures. Next, the BEs of 2D biexcitons are studied at different mass ratios and a variety of screening lengths. Our exact DMC results show that the BEs of biexcitons in different kinds of transition-metal dichalcogenides are in the range 15 − 30 meV bound at room temperature. Besides 2D systems, the electronic properties of 1D hydrogen-terminated oligoynes and polyyne are studied by calculating their DMC quasiparticle and excitonic gaps. By minimising the DMC energy of free-standing polyyne with respect to the lattice constant and the bond-length alternation, DMC predicts geometry in agreement with that obtained by accurate quantum chemistry methods. The DMC longitudinal optical phonon is within the range of experimental values. Our results confirm that DMC is capable of accurately describing Peierls-distorted materials

Quantum Monte Carlo study of three-dimensional Coulomb complexes:Trions and biexcitons, hydrogen molecules and ions, helium hydride cations, and positronic and muonic complexes

Three-dimensional (3D) excitonic complexes influence the optoelectronic properties of bulk semiconductors. More generally, correlated few-particle molecules and ions, held together by pairwise Coulomb potentials, play a fundamental role in a variety of fields in physics and chemistry. Based on statistically exact diffusion quantum Monte Carlo calculations, we have studied excitonic three- and four-body complexes (trions and biexcitons) in bulk 3D semiconductors, as well as a range of small molecules and ions in which the nuclei are treated as quantum particles on an equal footing with the electrons. We present interpolation formulas that predict the binding energies of these complexes, either in bulk semiconductors or in free space. By evaluating pair distribution functions within quantum Monte Carlo simulations, we examine the importance of harmonic and anharmonic vibrational effects in small molecules

Quasiparticle and excitonic gaps of one-dimensional carbon chains

We report diffusion quantum Monte Carlo (DMC) calculations of the quasiparticle and excitonic gaps of hydrogen-terminated oligoynes and polyyne. The electronic gaps are found to be very sensitive to the atomic structure in these systems. We have therefore optimised the geometry of polyyne by directly minimising the DMC energy with respect to the lattice constant and the Peierls-induced carbon-carbon bond-length alternation. We find the bond-length alternation of polyyne to be 0.136(2) Å and the excitonic and quasiparticle gaps to be 3.30(7) and 3.4(1) eV, respectively. The DMC zone-centre longitudinal optical phonon frequency of polyyne is 2084(5) cm-1, which is consistent with Raman spectroscopic measurements for large oligoynes

Charge carrier complexes in monolayer semiconductors

The photoluminescence (PL) spectra of monolayer (1L) semiconductors feature peaks ascribed to different charge-carrier complexes. We perform diffusion quantum Monte Carlo simulations of the binding energies of these complexes and examine their response to electric and magnetic fields. We focus on quintons (charged biexcitons), since they are the largest free charge-carrier complexes in undoped and low doping transition-metal dichalcogenides (TMDs). We examine the accuracy of the Rytova-Keldysh interaction potential between charges by comparing the binding energies (BEs) of charge-carrier complexes in 1L-TMDs with results obtained using ab initio interaction potentials. Magnetic fields 8 T change BEs by ∼ 0.2 meV T − 1 , in agreement with experiments, with BE variations of different complexes being very similar. Our results will help identify charge complexes in the PL spectra of 1L semiconductors

Binding energies of two-dimensional materials

The binding energy curves of atomically thin layers are key quantities that enable the description of the interaction of two-dimensional (2D) materials with each other and with substrates. Here, the binding energy of bilayer graphene is calculated using highly accurate variational and diffusion quantum Monte Carlo (QMC) calculations[1] which are implemented in the CASINO code[2]. The results can be used in models of exfoliation and studies of the interaction of graphene and other layered materials. References [1] W.M.C. Foulkes et al., Rev. Mod. Phys. 73, 33 (2001). [2] R.J. Needs et al., J. Phys.: Condens. Matter 22, 023201 (2010)

Density of states of magnetic substitutional impurity-doped graphene in the paramagnetic and ferromagnetic phases

We reveal the effects of magnetic substitutional impurities on the density of states (DOS) of a graphene monolayer through the s–f model as well as coherent potential approximation. We show that the magnetic exchange interaction between the itinerant electrons in graphene and magnetic moments leads to ferromagnetic order and spin-splitting band below Curie temperature, which substantially affect the DOS. Furthermore, ferromagnetic graphene exhibits metallic behavior owing to the strong s–f exchange leading to the appearance of a sharp quasiparticle peak near the Fermi level. These phenomena, along with the gaps appearing in the DOS open prospects for new applications in pintronics and optics

Research data supporting "Charge-carrier complexes in monolayer semiconductors"

The data includes inputs and outputs used for calculating the binding energies of charge-carrier complexes in the presence of out-of-plane magnetic filed and uniform electric field in monolayer semiconductors. Part of the data is used for deriving the binding energy of quintons in monolayer semiconductors. Also, the data for examining the accuracy of Rytova-Keldysh interaction is included. README.txt file provides more information about each class of data.EPSRC Grant EP/P010180/1, EP/L01548X/1, EP/K01711X/1, EP/K017144/1, EP/N010345/1, EP/L016087/1, ERC grants Corr-NEQM, Hetero2D, GSYNCOR EU Graphene and Quantum Flagshi

Charge-tuneable biexciton complexes in monolayer WSe₂.

Multi-exciton states such as biexcitons, albeit theoretically predicted, have remained challenging to identify in atomically thin transition metal dichalcogenides so far. Here, we use excitation-power, electric-field and magnetic-field dependence of photoluminescence to report direct experimental evidence of two biexciton complexes in monolayer tungsten diselenide: the neutral and the negatively charged biexciton. We demonstrate bias-controlled switching between these two states, we determine their internal structure and we resolve a fine-structure splitting of 2.5 meV for the neutral biexciton. Our results unveil multi-particle exciton complexes in transition metal dichalcogenides and offer direct routes to their deterministic control in many-body quantum phenomena

Charge-tuneable biexciton complexes in monolayer WSe2.

Monolayer transition metal dichalcogenides have strong Coulomb-mediated many-body interactions. Theoretical studies have predicted the existence of numerous multi-particle excitonic states. Two-particle excitons and three-particle trions have been identified by their optical signatures. However, more complex states such as biexcitons have been elusive due to limited spectral quality of the optical emission. Here, we report direct evidence of two biexciton complexes in monolayer tungsten diselenide: the four-particle neutral biexciton and the five-particle negatively charged biexciton. We distinguish these states by power-dependent photoluminescence and demonstrate full electrical switching between them. We determine the band states of the elementary particles comprising the biexcitons through magneto-optical spectroscopy. We also resolve a splitting of 2.5 meV for the neutral biexciton, which we attribute to the fine structure, providing reference for subsequent studies. Our results unveil the nature of multi-exciton complexes in transitionmetal dichalcogenides and offer direct routes towards deterministic control in many-body quantum phenomena

Identification of Exciton Complexes in Charge-Tunable Janus WSeS Monolayers.

Janus transition-metal dichalcogenide monolayers are artificial materials, where one plane of chalcogen atoms is replaced by chalcogen atoms of a different type. Theory predicts an in-built out-of-plane electric field, giving rise to long-lived, dipolar excitons, while preserving direct-bandgap optical transitions in a uniform potential landscape. Previous Janus studies had broad photoluminescence (>18 meV) spectra obfuscating their specific excitonic origin. Here, we identify the neutral and the negatively charged inter- and intravalley exciton transitions in Janus WSeS monolayers with ∼6 meV optical line widths. We integrate Janus monolayers into vertical heterostructures, allowing doping control. Magneto-optic measurements indicate that monolayer WSeS has a direct bandgap at the K points. Our results pave the way for applications such as nanoscale sensing, which relies on resolving excitonic energy shifts, and the development of Janus-based optoelectronic devices, which requires charge-state control and integration into vertical heterostructures