School of Science Department of Physics 63 First-principles Calculations for Real Materials Supervisor: LIU Junwei / PHYS Student: HEUNG Tsz Fung / IRE Course: UROP1100, Summer Tight Binding model is a modelling method for calculating electronic band structure of crystalline solids. It assumes that electrons can only hop from one atom to nearest-neighbor (NN) or next-nearest-neighbor (NNN), making the calculation simpler. This assumption can be justified when the Coulumb potential of the solid is strong. In this report, the band structures of graphene and graphene nanoribbon will be discussed. Self-learning Monte Carlo with Deep Neural Networks Supervisor: LIU Junwei / PHYS Student: AU Kei Yin Eltis / PHYS Course: UROP1100, Summer Monte Carlo Simulation is a commonly used method to simulate different physical systems. In short, the theory is basically first to generate a set of possible outcomes or states underlining the law of physics, and those states can be further calculated as the physical quantities. In the simulation of the Ising model, those states will be the different spin configurations of a square lattice. With the given configuration, Thermodynamical quantities such as magnetization, energy, heat capacity, and susceptivity can be calculated. This paper has briefly review the different updating methods of the Markov chain Monte Carlo(Hastings, 1970) on the two-body spin system, which include the local update(Metropolis,Glauber)(Metropolis, Rosenbluth, Rosenbluth, Teller, & Teller, 1953), Global update(Wolff)(Wolff, 1989), and especially on Machine learning update(self-learning) (J. Liu, Qi, Meng, & Fu, 2017). The performance of different updates under the critical temperature has been discussed. Observational Phenomenology of Supermassive Black Hole Supervisor: LIU Tao / PHYS Student: TRAN Duc Huy / PHYS-IRE Course: UROP1100, Summer The recent success of the Event Horizon Telescope Collaboration (EHT) in imaging the supermassive black holes M87* and Sgr A* has opened up a new channel to extract information about Fundamental Physics. The image of a black hole observed on Earth, which follows the laws of General Relativity at zeroth order, may receive corrections from the physics phenomena beyond Standard Model. In this UROP project, we investigate the corrections to the image of a black hole that are induced by an axion cloud surrounding that black hole. Understanding these effects could lead to a potential method to detect axion, which is a popular dark matter candidate, using the images of supermassive black holes.