Teaching

Our teaching focuses on graduate courses in Applied Physics and Materials Science: Structure and Bonding in Materials (MS 131), Computational Solid State Physics and Materials Science (APh/MS 256), and Introduction to Computational Methods for Science and Engineering (APh/MS 141). The syllabus for each course is given below.

MS 131. Introduction to Structure and Bonding in Materials

This course is a broad introduction to the electronic and crystal structures of materials. Course topics include: Electronic states in atoms and molecules. Born-Oppenheimer approximation. Crystal structure, including databases and visualization. Reciprocal space and Brillouin zone. Band theory using tight binding and plane waves. Introduction to density functional theory. Bonding and electronic structure in metals, semiconductors, ionic crystals, and complex oxides. Symmetry in materials: point groups, space groups, and time-reversal symmetry. Physical properties of crystals and their tensor representation. Introduction to correlated and topological quantum materials.

APh/MS 141. Introduction to Computational Methods for Science and Engineering

This course is a broad introduction to numerical methods for scientists and engineers. Course topics include: Introduction to scientific computing. The Python language and its packages Numpy, SciPy, and Matplotlib. Numerical precision and sources of error. Root-finding and optimization. Numerical differentiation and integration. Introduction to numerical methods for linear systems and eigenvalue problems. Numerical methods for ordinary differential equations. Finite-difference methods for partial differential equations. Discrete Fourier transform. Introduction to data-driven and machine learning methods, including deep learning using Keras and Tensorflow. Introduction to quantum computing using Qiskit and IBM-Q. Students develop numerical calculations in the homework and in midterm and final projects.

APh/MS 256. Computational Solid State Physics and Materials Science

The course covers first-principles computational methods to study the electronic structure and properties of materials. Topics include: Theory and practice of density functional theory (DFT) and plane-wave pseudopotential calculations. DFT calculations of total energy, structure, defects, charge density, bandstructures, density of states, ferroelectricity and magnetism. Lattice vibrations using the finite-difference and linear-response DFT methods. Electron-electron interactions, screening, and the GW method. GW bandstructure calculations. Optical properties, excitons, and the GW-Bethe Salpeter equation method. First-principles Boltzmann transport equation (BTE) for transport and dynamics of electrons and phonons. Computations of heat and charge transport in the BTE framework. Selected advanced topics will be covered, including methods to treat van der Waals bonds, spin-orbit coupling, correlated materials, band topology, and quantum dynamics. Lab sessions provide hands-on experience with first-principles calculations.