Modern Quantum Physics of Solids

Mentor:Mikhail Chernikov
Revision:2013 Dec 15

Course Summary

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.

Course Format

Hours of lectureHours of discussionHours of independent studyHours total
341769120

Please note that students are expected to study outside of class for three hours for every hour in class.

Course Content

The class will cover following topics:

  1. Types of solids
    • Periodically-ordered crystals
    • Amorphous solids
    • Other types of solids
  2. Crystal lattices
    • Classification of Bravais lattices and crystal structures
    • The reciprocal lattice
    • Experimental determination of crystal structure by X-ray diffraction
  3. Solids with complex structures
    • Aperiodic crystals: incommensurately modulated crystals, composite crystals and quasicrystals
    • Complex metal alloys
    • Liquid crystals and polymers
    • Amorphous solids
    • Aerogels and opals
  4. 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
  5. Quantum theory of the harmonic crystal
    • Phonons
    • 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
  6. The Phonon dispersion relation
    • Inelastic neutron scattering
    • Inelastic X-ray scattering
    • Optical methods: Brillouin and Raman scattering
    • Kohn anomalies
  7. Anharmonic effects
    • Thermal expansion
    • The Grüneisen parameter
    • Lattice thermal conductivity
    • Umklapp processes
  8. 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
  9. Homogeneous semiconductors
    • 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
    • Light absorption by semiconductors
  10. Inhomogeneous semiconductors
    • The p-n junction in equilibrium
    • Rectification by a p-n junction
    • The nonequilibrium p-n junction
    • The heterojunction
  11. The principles of some electronic devices
    • The bipolar (junction) transistor
    • The field-effect transistor
    • The charge-coupled device
    • Light-emitting diodes and lasers
    • Solar cells
    • Inversion Layers: heterostructures, quantum poin contacts, quantum dots
  12. Atomic magnetism
    • Larmor diamagnetism
    • The ground state of an ion, Hund’s rules
    • Van Vleck paramagnetism
    • Crystal field splitting
    • The quenching of the orbital angular momentum
    • The Kramers theorem
    • The Jahn—Teller effect
    • Curie’s law, adiabatic demagnetization
  13. Magnetism of the free-electron gas
    • Pauli paramagnetism
    • Landau levels
    • Landau diamagnetism
    • The Aharonov—Bohm effect
    • The integer quantum Hall effect
  14. Magnetic interactions
    • Magnetic dipolar interactions
    • Exchange interactions: direct exchange, superexchange—indirect exchange in insulators, indirect exchange in metals, double exchange
    • Localized moments in dilute magnetic alloys, the Kondo effect
  15. Magnetically ordered solids
    • Types of magnetic structure: ferromagnetism, antiferromagnetism, ferrimagnetism, helical order
    • Experimental observation of magnetic structures: magnetization, magnetic susceptibility, neutron scattering, nuclear magnetic resonance
    • Heisenberg and Ising models
    • Spin waves
    • Mean field theory, the Curie—Weiss law
    • Ferromagnetic domains
  16. Competing interactions
    • Frustration
    • Spin glasses
    • Strongly geometrically frustrated magnets
    • One-dimensional magnets, spin chains, the spin-Peierls transition
    • Two-dimensional magnets
    • Magnetism in heavy-electron metals
    • Kondo semiconductors
    • Quantum phase transitions
  17. Magnetic semiconductors
    • General properties and examples
    • Diluted Magnetic Semiconductors
    • Spin electronics: magnetically-sensitive transistors, spin-polarized light emitting diodes and lasers
  18. Miscelaneous topics
    • Graphene and carbon nanotubes
    • Quantum Landauer conduction in atomic-size contacts
    • Coulomb blockade, single electron transistor
    • Coulomb blockade and tunneling in granular conductors

Textbooks

Primary textbooks:

  1. Neil W. Ashcroft and N. David Mermin. Solid State Physics. Cengage Learning, New York, 1 edition edition, January 1976.
  2. Michael P. Marder. Condensed Matter Physics. Wiley, Hoboken, N.J, 2 edition edition, November 2010.

Additional textbooks:

  1. Stephen Blundell. Magnetism in Condensed Matter. Oxford University Press, Oxford; New York, 1 edition edition, December 2001.
  2. P. M. Chaikin and T. C. Lubensky. Principles of Condensed Matter Physics. Cambridge University Press, Cambridge; New York, NY, USA, reprint edition edition, October 2000.
  3. Eugene M. Chudnovsky and Javier Tejada. Lectures on Magnetism. Rinton Pr Inc, Princeton, NJ, April 2006.
  4. Harald Ibach and Hans Lüth. Solid-State Physics: An Introduction to Principles of Materials Science. Springer, Berlin; New York, 4th ed. 2009 edition edition, November 2009.
  5. C. Janot. Quasicrystals: A Primer. Oxford University Press, Oxford : New York, y first edition edition edition, November 1992.
  6. Charles Kittel. Introduction to Solid State Physics. Wiley, Hoboken, NJ, 8 edition edition, November 2004.
  7. Leonard M. Sander. Advanced Condensed Matter Physics. Cambridge University Press, Cambridge; New York, 1 edition edition, March 2009.
  8. 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:

  1. László Mihály and Michael C. Martin. Solid State Physics: Problems and Solutions. Wiley-VCH, Weinheim; Chichester, 2 edition edition, February 2009.
  2. 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.
  3. Eugene M. Chudnovsky, Javier Tejada, Carlos Calero, and Ferran Macia. Problem Solutions to Lectures on Magnetism. Rinton Pr Inc, Princeton, NJ, February 2007.

Homework Assignments

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.

Grading

Class participation10%
Homework assignments20%
Midterm exam20%
Final exam50%