# Electron Theory of Metals

Mentor: | Sergei Mukhin |
---|---|

Revision: | 15 Dec 2013 |

## Course Summary

The course of lectures introduces into main methods and results of the electronic theory of metals, that are in the focus of contemporary studies of quantum properties of condensed matter. Description of normal metal properties exploits the quasi-particle concept and Landau Fermi-liquid theory. Description of physical phenomena in superconductors is based on the concept of spontaneous symmetry breaking with bose-condensation of the Cooper pairs in framework of the Bardeen-Cooper-Schrieffer theory, and makes use of the Ginzburg-Landau equations. The basics is introduced of the Green’s functions technique and its applications to predicting and interpreting experimental data of photon, neutron and muon scattering, and measurements of current-voltage characteristics of tunnel micro-contacts.

## Course Format

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

42 | 34 | 68 | 144 |

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

## Course Content

The plan is to work through the following topics:

- An electron in a crystal lattice (14 hours)
- Quantum theory as a basis for describing the physical properties of metals
- Drude and Sommerfeld theories.
- Comparison of theory with experiment.
- Bloch's theorem on the motion of an electron in a spatially periodic potential (crystal)
- The electronic energy spectra of metals and dielectrics.
- The concept of Landau Fermi liquid.
- Fermi surface in the metal.
- General view of the kinetic equation.
- Solution of the kinetic equation for isotropic metal in the approximation of elastic collisions
- Electrical and thermal conductivity.
- The kinetic equation in a magnetic field.
- Thermoelectric and thermomagnetic phenomena in metals.
- The processes of electron scattering.
- The basic mechanisms of electron scattering in metals
- Kondo effect in a metal with paramagnetic impurities.
- Kondo lattice in alloys with heavy fermions.

- Normal metal in an external magnetic field. Quantum oscillations (10 hours)
- Quantization of electron energy in a constant magnetic field: Landau levels.
- Pauli paramagnetism and Landau diamagnetism.
- The magnetic susceptibility of metals.
- Quantum oscillations of the magnetization of the metal in a magnetic field
- Quantum oscillations of the conductivity and thermal conductivity of the metal in a magnetic field.
- Quantum Hall effect (integer) in quasi two-dimensional electron gas.
- International standard for electrical resistance.
- Fractional quantum Hall effect in quasi two-dimensional strongly correlated electron gas

- Superconducting properties of metals (10 hours)
- Basic properties of the superconducting state.
- Thermodynamics of superconductors.Intermediate state.
- The Londons’ theory
- The main idea of the microscopic theory of superconductivity.
- Criterion of superfluidity
- Phonon attraction. Cooper pairing.
- The Little’s mechanism of high-temperature superconductivity in quasi one-dimensional molecular chains.
- Ginzburg and Landau theory.
- Quantization of magnetic flux.
- Surface Energy.
- Two kinds of superconductors.
- Abrikosov vortex lattice.
- Tunnel junctions
- Stationary and non-stationary Josephson effect
- International standard of volt.

- Green's functions method to describe the properties of metals (8 hours)
- The concept of Green's function.
- Theoretical basis of angle resolved photoemission spectroscopy(ARPES)
- Theoretical basis of measurements of the electron spectra of metals by microcontact spectroscopy.
- Spin precession in an external magnetic field.
- Theoretical Foundations of measurement of magnetic properties of metals by the muon and neutron scattering.

## Textbooks

Primary textbooks:

- A. A. Abrikosov.
*Fundamentals of the Theory of Metals*. North Holland, Amsterdam ; New York : New York, NY, USA, November 1988. - Charles Kittel.
*Quantum Theory of Solids*. Wiley, New York, 2nd revised edition edition edition, April 1987.

Additional textbooks:

- P. G. De Gennes.
*Superconductivity Of Metals And Alloys*. Westview Press, Reading, Mass, March 1999.

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. - Eugene M. Chudnovsky, Javier Tejada, Carlos Calero, and Ferran Macia.
*Problem Solutions to Lectures on Magnetism*. Rinton Pr Inc, Princeton, NJ, February 2007. - 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.

## Homework Assignments

Weekly, 12 problem sets in total, due at the beginning of the lecture. You may also submit via e-mail before the due date/time. It is of outmost importance that you invest your own effort into solving problems. Should you consult any sources, please provide references. Homework assignments should be typed. Legible handwritten assignments are acceptable.

## Grading

Class participation | 10% |

Homework assignments | 20% |

Midterm exam | 20% |

Final exam | 50% |