Advanced Topics in Quantum Theory of Solids

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Department of Solid State Engineering

Synopsis:

The course focuses on advanced parts of quantum theory of solids, dealing in particular with the phenomena close to potential applications in quantum technology. It is assumed knowledge of the basics of quantum mechanics and theory of solids in the extend of the master's courses at FJFI. The graduate gains knowledge of the theoretical basis of the physical processes that determine the key properties of the currently developed quantum systems and devices.

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Syllabus of lectures:

1.Introductiom (Definitions of basic terms, repetitorium of the basic statements and results of quantum theory)2.First and second quantization (First quantization, single-particle systems, many-particle systems; Second quantization, basic concepts, specific operators, statistical mechanics of fermions and bosons)3.The electron gas (Non-interacting electron gas;Electron interactions in perturbation theory; Electron gases in 3, 2, 1, and0 dimensions)4.Phonons; coupling toelectrons (Jellium oscillations and Einstein phonons; Electron-phonon interaction and the sound velocity; Lattice vibrations and phonons in 1D; Acoustical and optical phonons in 3D; The specific heat of solids in the Debye model; Electron-phonon interaction in the lattice model; Electron-phonon interaction in the jellium model)5.Mean field theory (The art of mean field theory; Hartree–Fock approximation; Broken symmetry; Ferromagnetism, the Heisenberg model of ionic ferromagnets, the Stoner model of metallic ferromagnets; Superconductivity, breaking of global gauge symmetry and its consequences, microscopic theory)6.Time evolution models (The Schrodinger picture; The Heisenberg picture; The interaction picture; Time-evolution in linear response; Time dependent creation and annihilation operators)7.Linear response theory (The general Kubo formula; Kubo formula for conductivity; Kubo formula for conductance; Kubo formula for the dielectric function)8.Transport in mesoscopic systems (The S-matrix and scattering states; Conductance and transmission coefficients; Electron wave guides, quantum point contact and conductance quantization, Aharonov-Bohm effect; Disordered mesoscopic systems)9.Green’s functions (“Classical” Green’s functions; Green’s function for the one-particle Schrodinger equation; Single-particle Green’s functions of many-body systems; Measuring the single-particle spectral function, tunneling spectroscopy, optical spectroscopy; Two-particle correlation functions of many-body systems)10.Equation of motiontheory (The single-particle Green’s function; Anderson’s model for magnetic impurities; The two-particle correlation function, the Random Phase Approximation)11.The interacting electron gas (The self-energy in RPA; The renormalized Coulomb interaction in RPA; The ground state energy of the electron gas; The dielectric function and screening; Plasma oscillations and Landau damping)12.Fermi liquid theory (Adiabatic continuity; Semi-classical treatment of screening and plasmons; Semi-classical transport equation,finite life time of the quasiparticles; Microscopic basis of the Fermi liquid theory)13.Impurity scattering and conductivity (The conductivity in terms of a general vertex function; The conductivity in the first Born approximation; The weak localization correction to the conductivity; Combined RPA and Born approximation)

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Study materials:

Key references: [1] H. Bruus, K. Flensberg: Many-body quantum theory in condensed matter physics. Ørsted Laboratory, Niels Bohr Institute, University of Copenhagen, Mikroelektronik Centret, Technical University of Denmark. Copenhagen 2002.[2] C. Kittel,Kittel's Introduction to Solid State Physics, Wiley, 2018.Recommended references:[3] W.A. Harrison Solid State Theory, Courier Corporation, New York, 2012.[4] J.M. Zimman: Principles of theory f solids. 2nd ed. Cambridge University Press 1972.

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No time-table has been prepared for this course

The course is a part of the following study plans: