The goal of this course is to expose students to various aspects of modern solid state physics, including quantum phenomena in unconventional solids and atomic-sized objects. Apart from traditional areas, such as, for example, crystal structures, lattice excitations, semiconductors and magnetism, the course includes the following topics: quantum Hall effect, graphene and carbon nanotubes, quantum Landauer conduction in atomic-sized con-tacts, quantum magnetism (spin chains), strongly geometrically frustrated magnets, spin glasses, magnetic semiconductors, colossal magnetoresistance effect, quantum phase transitions, low-energy excitations in amorphous solids, disordered crystals and fractal structures, granular conductors, heavy-electron metals, Kondo semiconductors, incom-mensurately modulated crystals, composite crystals, quasicrystals and complex metal alloys. The course also describes the principles of operation of modern electronic devices, including magnetically-sensitive transistors and spin-polarized light emitting diodes and lasers.
Prerequisites for a course are a standard undergraduate background in electrodynamics, thermodynamics, theoretical mechanics, quantum mechanics and statistical physics is assumed.
Hours of lecture
Hours of discussion
Hours of independent study
Please note that students are expected to study outside of class for three hours for every hour in class.
The class will cover following topics:
Types of solids
Other types of solids
Classification of Bravais lattices and crystal structures
The reciprocal lattice
Experimental determination of crystal structure by X-ray diffraction
Solids with complex structures
Aperiodic crystals: incommensurately modulated crystals, composite crystals and quasicrystals
Complex metal alloys
Liquid crystals and polymers
Aerogels and opals
Classical theory of the harmonic crystal
Normal modes of a Bravais lattice
Normal modes of a lattice with a basis
Relation to the theory of elasticity
The number of independent elastic constants
Elastic isotropy and transverse elastic isotropy
Quantum theory of the harmonic crystal
Lattice specific heat
The Einstein and Debye models
Vibrational density of states, van Hove singularities
Quasi-localized vibrational modes
Localized vibrational modes
Examples of the Einstein solids
The Phonon dispersion relation
Inelastic neutron scattering
Inelastic X-ray scattering
Optical methods: Brillouin and Raman scattering
The Grüneisen parameter
Lattice thermal conductivity
Lattice Excitations in Complex Structures
Amorphous solids—thermal and elastic anomalies at low temperatures
Umklapp processes in heterostructures and quasicrystals
Structural scattering of the lattice excitations in quasicrystals
Transport of heat in aerogels and opals
Semiconductors—general properties and examples
Typical band structures
Carrier densities in thermal equilibrium
Degenerate and nondegenerate semiconductors
Intrinsic and extrinsic semiconductors
Population of impurity levels
Carrier densities of impure semiconductors
Conduction in energy “bands” arising from the impurities
Marius Grundmann. The Physics of Semiconductors: An Introduction Including Devices and Nanophysics. Springer, Berlin; New York, 1 edition edition, May 2006.
Problems and solutions textbooks:
László Mihály and Michael C. Martin. Solid State Physics: Problems and Solutions. Wiley-VCH, Weinheim; Chichester, 2 edition edition, February 2009.
Chung-Kuo K’O Hsueh Chi Shu Ta Hsueh Physics Coaching Class, Lim Yung-kuo, Zhou You-yum, Zhang Shi-ling, and Zhang Jia-lu. Problems and Solutions on Solid State Physics, Relativity and Miscellaneous Topics. World Scientific Pub Co Inc, Singapore ; River Edge, NJ, January 2003.
Eugene M. Chudnovsky, Javier Tejada, Carlos Calero, and Ferran Macia. Problem Solutions to Lectures on Magnetism. Rinton Pr Inc, Princeton, NJ, February 2007.
Homework will be assigned weekly and will become due at the beginning of next lecture (12 problem sets in total). Homework can be submitted via e-mail or in person. It is of outmost importance that you invest your own effort into solving problems. Should you con-sult any sources, please provide references. Typed homework assignments are preferred. Legible handwritten assignments are also acceptable.