A Quantum Approach to Condensed Matter Physics

by Philip L. Taylor , Olle HeiUnknownn

• ISBN13: 9780521778275
• ISBN10: 0521778271
• Format: Paperback
• Copyright: 2002-03-18
• Publisher: Cambridge University Press

Summary

This textbook is an accessible introduction to the theory underlying the many fascinating properties of solids. Assuming only an elementary knowledge of quantum mechanics, it describes the methods by which one can perform calculations and make predictions of some of the many complex phenomena that occur in solids and quantum liquids. The emphasis is on reaching important results by direct and intuitive methods, and avoiding unnecessary mathematical complexity. Designed as a self-contained text that starts at an elementary level and proceeds to more advanced topics, this book is aimed primarily at advanced undergraduate and graduate students in physics, materials science, and electrical engineering. Problem sets are included at the end of each chapter, with solutions available to lecturers. The coverage of some of the most recent developments in condensed matter physics will also appeal to experienced scientists in industry and academia working on electrical properties of materials.

Table of Contents

Preface	ix
Semiclassical introduction	1	(25)
Elementary excitations	1	(3)
Phonons	4	(3)
Solitons	7	(3)
Magnons	10	(2)
Plasmons	12	(3)
Electron quasiparticles	15	(2)
The electron-phonon interaction	17	(2)
The quantum Hall effect	19	(7)
Problems	22	(4)
Second quantization and the electron gas	26	(52)
A single electron	26	(5)
Occupation numbers	31	(3)
Second quantization for fermions	34	(8)
The electron gas and the Hartree-Fock approximation	42	(8)
Perturbation theory	50	(6)
The density operator	56	(4)
The random phase approximation and screening	60	(11)
Spin waves in the electron gas	71	(7)
Problems	75	(3)
Boson systems	78	(47)
Second quantization for bosons	78	(2)
The harmonic oscillator	80	(2)
Quantum statistics at finite temperatures	82	(6)
Bogoliubov's theory of helium	88	(5)
Phonons in one dimension	93	(6)
Phonons in three dimensions	99	(3)
Acoustic and optical modes	102	(2)
Densities of states and the Debye model	104	(3)
Phonon interactions	107	(4)
Magnetic moments and spin	111	(6)
Magnons	117	(8)
Problems	122	(3)
One-electron theory	125	(57)
Bloch electrons	125	(7)
Metals, insulators, and semiconductors	132	(3)
Nearly free electrons	135	(8)
Core states and the pseudopotential	143	(7)
Exact calculations, relativistic effects, and the structure factor	150	(10)
Dynamics of Bloch electrons	160	(10)
Scattering by impurities	170	(4)
Quasicrystals and glasses	174	(8)
Problems	179	(3)
Density functional theory	182	(28)
The Hohenberg--Kohn theorem	182	(5)
The Kohn--Sham formulation	187	(4)
The local density approximation	191	(4)
Electronic structure calculations	195	(3)
The Generalized Gradient Approximation	198	(2)
More acronyms: TDDFT, CDFT, and EDFT	200	(10)
Problems	207	(3)
Electron-phonon interactions	210	(22)
The Frohlich Hamiltonian	210	(3)
Phonon frequencies and the Kohn anomaly	213	(3)
The Peierls transition	216	(3)
Polarons and mass enhancement	219	(3)
The attractive interaction between electrons	222	(4)
The Nakajima Hamiltonian	226	(6)
Problems	230	(2)
Superconductivity	232	(53)
The superconducting state	232	(3)
The BCS Hamiltonian	235	(2)
The Bogoliubov-Valatin transformation	237	(6)
The ground-state wave function and the energy gap	243	(4)
The transition temperature	247	(5)
Ultrasonic attenuation	252	(2)
The Meissner effect	254	(4)
Tunneling experiments	258	(7)
Flux quantization and the Josephson effect	265	(6)
The Ginzburg-Landau equations	271	(7)
High-temperature superconductivity	278	(7)
Problems	282	(3)
Semiclassical theory of conductivity in metals	285	(30)
The Boltzmann equation	285	(3)
Calculating the conductivity of metals	288	(7)
Effects in magnetic fields	295	(4)
Inelastic scattering and the temperature dependence of resistivity	299	(5)
Thermal conductivity in metals	304	(4)
Thermoelectric effects	308	(7)
Problems	313	(2)
Mesoscopic physics	315	(27)
Conductance quantization in quantum point contacts	315	(9)
Multi-terminal devices: the Landauer-Buttiker formalism	324	(5)
Noise in two-terminal systems	329	(3)
Weak localization	332	(4)
Coulomb blockade	336	(6)
Problems	339	(3)
The quantum Hall effect	342	(41)
Quantized resistance and dissipationless transport	342	(2)
Two-dimensional electron gas and the integer quantum Hall effect	344	(9)
Edge states	353	(4)
The fractional quantum Hall effect	357	(4)
Quasiparticle excitations from the Laughlin state	361	(6)
Collective excitations above the Laughlin state	367	(3)
Spins	370	(6)
Composite fermions	376	(7)
Problems	380	(3)
The Kondo effect and heavy fermions	383	(22)
Metals and magnetic impurities	383	(2)
The resistance minimum and the Kondo effect	385	(6)
Low-temperature limit of the Kondo problem	391	(6)
Heavy fermions	397	(8)
Problems	403	(2)
Bibliography	405	(6)
Index	411