| CODE | PHY3155 | ||||||||||||||||
| TITLE | Solid State Physics | ||||||||||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||||||||||
| MQF LEVEL | 6 | ||||||||||||||||
| ECTS CREDITS | 5 | ||||||||||||||||
| DEPARTMENT | Physics | ||||||||||||||||
| DESCRIPTION | This study-unit starts with the investigation of the crystal structure of solids, including the definition of the reciprocal lattice and the Brillouin zones. Building on, the specific heat of solids is investigated via the Einstein and the Debye modes of a solid. For this purpose, a thorough investigation of coupled harmonic oscillators is developed, with references to the formalism of second quantization giving rise to the acoustic and optical branches of the crystal vibrations, or phonons. There is next an investigation of the electric conduction in metals, starting with fully classical (Drude) and semi-classical (Sommerfeld) models. A full-fledged quantum description using Bloch’s Theorem (band theory) is then introduced, showing how this resolves inconsistencies in the simpler models. Both the quasi-free and the tight-binding approximation for determining the band structure of the metals are introduced, giving second-quantization expressions for the corresponding Hamiltonians. We will supplement the band theory with a semiclassical description of the electrons dynamics in an external electric or magnetic field. In addition, we will discuss semiconductors including inhomogeneous semiconductors, in particular, p-n junctions. We then introduce the phenomenological theory of superconductivity, explaining the Meissner effect, the isotope effect, and the zero resistance effect via London’s theory. We also briefly describe the BCS theory of superconductivity, introducing the Cooper pairs and the superconducting gap. If time permits, a brief introduction to magnetism via the mean field approach is given. Study-unit Aims: This unit aims to: - offer a broad overview on solid state physics, with a special focus on electron dynamics and lattice vibrations; - introduce the students to the basic techniques and methods of condensed matter physics; - tie the theoretical background acquired to modern applications such as graphene, photonic crystals, and the quantum Hall effect, and solid-state quantum information devices. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - enumerate the discrete rotational symmetries that are compatible with the crystal symmetry; - describe qualitatively the mechanism underlying crystal growth; - explain why electron at the bottom of a band, e.g. conduction electron in semi-conductors, can be treated as free electrons with an effective mass (that can be anisotropic); - understand the concept of Fermi energy and Fermi level; - give the definition of the density of states for a wave in a crystal; - describe how band theory explains the different linear response of metals and insulators to an applied voltage; - explain the phenomenon of screening; - calculate the specific heat of a crystal as a function of the density of states; - use the Debye and Einstein approaches to find an approximate analytical approximation for this quantity; - explain how photons are converted into an electric current in a solar cell based on a p-n junction; - explain the Meissner effect; - understand the phenomenological theory of superconductivity; - use the second quantization formalism to model elementary condensed matter systems. 2. Skills By the end of the study-unit the student will be able to: - calculate the conductance of an electrical wire in the Drude model; - given a lattice find its reciprocal lattice; - calculate the Fermi energy in the free-electron model; - define the quasi-momentum and give a proof of Bloch's theorem for a wave equation with discrete translational symmetry; - calculate analytically the bulk band structure of any wave (e.g. electrons, photons, phonons) in a given crystal structure when the tight-binding approximation applies, e.g. the graphene electronic band structure; - calculate numerically the band structure of an infinite strip; - use these techniques to demonstrate the effects of an external magnetic field in the electron's band structure; - tie the lattice thermal vibrations of a crystal to the Boltzmann distribution of a set of harmonic oscillators (transferable to the blackbody radiation); - determine the physical properties of a superconductor; - write condensed matter models in the second quantization formalism. Main Text/s and any supplementary readings: Main - Philip Hofmann, Solid State Physics: An Introduction, Wiley. Additional reading - Steve H. Simon, The Oxford Solid State Basics, Oxford University Press. - Charles Kittel, Introduction to Solid State Physics, Wiley. |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Tony John George Apollaro |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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