School of Science Department of Physics 61 Quantum State Calculation of Two-dimensional Supramolecular Nanostructures Supervisor: LIN Nian / PHYS Student: CHUI Shek Hei / IRE Course: UROP1100, Summer The use of supramolecular nanostructures have been increasingly common in modern day technology, such as the improvement of drug efficacy, various electronic devices to the construction of modern semiconductors. As a result, more ways have been developed to aid the studying of its band structure, ranging from Quantum Monte Carlo methods, Density functional theory, scattering matrix method to free electron approximation. The objective of this project is to perform simulations on its band structures of different lattices, such as the Kagome and Lieb lattice, through adjusting different parameters in the MATLAB program. Trends relating different parameters were observed and the reasons behind were analyzed. Quantum State Calculation of Two-dimensional Supramolecular Nanostructures Supervisor: LIN Nian / PHYS Student: FAN Ka Cheuk / IRE Course: UROP1000, Summer Since the discovery of unique physical properties of band structure of 2D lattice, more researches focus on studying band structure of 2D materials. In this work, a 2D physical system of lieb lattice is simulated using MATLAB program. Through solving 2-dimensional Schrödinger Equation numerically in program, band structure and total density of states (TDOS) are plotted. By varying different parameters(including lattice constant, well potential and potential well radius), it shows that how the band structure and band width relate to different parameters. Quantum State Calculation of Two-dimensional Supramolecular Nanostructures Supervisor: LIN Nian / PHYS Student: WONG Yip Chun / IRE Course: UROP1000, Summer In this report, the physical system of kagome and lieb lattice formed by two-dimensional supramolecular nanomolecule is simulated, by numerically solving the 2-dimensional Schrödinger equation. This is performed by the construction of lattice geometry via potential wells or pillars in MATLAB, which then calculates the variables of the structure such as band structure, the total density of states (TDOS) and the local density of states (LDOS). The purpose of this research is to explore how different geometries and parameters affect the lattice’s physical properties and enhance the characters of the kagome and lieb lattice’s band structure.

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