# Modern Quantum Physics of Solids

Mentor: | Mikhail Chernikov |
---|---|

Revision: | 15 Dec 2013 |

## 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 lecture | Hours of discussion | Hours of independent study | Hours total |
---|---|---|---|

34 | 17 | 69 | 120 |

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:

- Types of solids
- Periodically-ordered crystals
- Amorphous solids
- Other types of solids

- Crystal lattices
- 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
- Amorphous solids
- 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
- 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

- The Phonon dispersion relation
- Inelastic neutron scattering
- Inelastic X-ray scattering
- Optical methods: Brillouin and Raman scattering
- Kohn anomalies

- Anharmonic effects
- Thermal expansion
- The Grüneisen parameter
- Lattice thermal conductivity
- Umklapp processes

- 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

- 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

- Inhomogeneous semiconductors
- The p-n junction in equilibrium
- Rectification by a p-n junction
- The nonequilibrium p-n junction
- The heterojunction

- 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

- 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

- Magnetism of the free-electron gas
- Pauli paramagnetism
- Landau levels
- Landau diamagnetism
- The Aharonov–Bohm effect
- The integer quantum Hall effect

- 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

- 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

- 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

- Magnetic semiconductors
- General properties and examples
- Diluted Magnetic Semiconductors
- Spin electronics: magnetically-sensitive transistors, spin-polarized light emitting diodes and lasers

- 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:

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

Additional textbooks:

- Stephen Blundell.
*Magnetism in Condensed Matter*. Oxford University Press, Oxford; New York, 1 edition edition, December 2001. - 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. - Eugene M. Chudnovsky and Javier Tejada.
*Lectures on Magnetism*. Rinton Pr Inc, Princeton, NJ, April 2006. - 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. - C. Janot.
*Quasicrystals: A Primer*. Oxford University Press, Oxford : New York, y first edition edition edition, November 1992. - Charles Kittel.
*Introduction to Solid State Physics*. Wiley, Hoboken, NJ, 8 edition edition, November 2004. - Leonard M. Sander.
*Advanced Condensed Matter Physics*. Cambridge University Press, Cambridge; New York, 1 edition edition, March 2009. - 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 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 participation | 10% |

Homework assignments | 20% |

Midterm exam | 20% |

Final exam | 50% |