Study-Unit Description

Study-Unit Description


CODE PHY3155

 
TITLE Solid State Physics

 
LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course

 
ECTS CREDITS 5

 
DEPARTMENT Physics

 
DESCRIPTION One of the main pillars of the unit is the investigation electric conduction in metals. We will follow a historic perspective which has the added value of being very didactic. In this approach, the students develop physical intuition as subsequent layer of complexity are added one by one. In the first step, the Drude model, the electrons are treated as classical particles moving freely until they undergo random instantaneous collisions. In the second step, the Sommerfeld model, the electrons still propagate as classical particles but, immediately after a collision, are described by a quantum distribution. In the third step, the band theory, the electronic spectra are calculated using a full-fledged quantum mechanical description that treats the electrons in the periodic potential created by the ions as probability waves. This approach resolves several inconsistencies of the Drude and Sommerfeld models and is able to explain the different behavior of conducting and insulating materials. In this setting, the main theoretical concepts and methods related to the dynamics of waves in the presence of discrete translational invariance are introduced. These include the crystal lattice, the reciprocal lattice, Bloch's theorem and the tight-binding approximation. We will supplement the band theory with a semiclassical description of the electrons dynamics in an external electric or magnetic field. We will apply the theoretical understanding acquired in the study of electrons in metal to a related wave phenomenon, the propagation of mechanical waves in the crystal structure. This is the second pillar of the course. We will initially focus on the classical theory of harmonic vibrations. We will then discuss the quantum theory of lattice vibrations and tie it to the quantum harmonic oscillator.

In addition, we will discuss semiconductors including inhomogeneous semiconductors, in particular, p-n junctions. We will give a brief introduction to magnetism introducing the mean field approach. If time permits we will discuss the Ginzburg-Landau theory of superconductivity.

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.

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);
- 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;
- describe the microscopic origin of diamagnetism, paramagnetism and ferromagnetism;
- explain how photons are converted into an electric current in a solar cell based on a p-n junction;
- explain the Meissner effect.

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;
- 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, e. g. appearance of Landau levels and of topologically protected edge states;
- tie the lattice thermal vibrations of a crystal to the Boltzman distribution of a set of harmonic oscillators (transferable to the blackbody radiation).

Main Text/s and any supplementary readings:

Main

- Neil W. Ashcroft, N. David Mermin, "Solid State Physics" (Holt, Rinehart and Winston).

Additional reading

- Richard P. Feynman, Robert B. Leighton, and Matthew Sands, "The Feynman Lectures on Physics" (Addison–Wesley).

 
STUDY-UNIT TYPE Lecture and Tutorial

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Resit Availability Weighting
5 Assignments SEM2 No 20%
Examination (3 Hours) SEM2 Yes 80%

 
LECTURER/S Tony John George Apollaro

 
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Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the study-unit description above applies to the academic year 2019/0, if study-unit is available during this academic year, and may be subject to change in subsequent years.

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