Electrodynamics of Solids: Optical Properties of Electrons in Matter

by Martin Dressel , George Grüner

• ISBN13: 9780521597265
• ISBN10: 0521597269
• Format: Paperback
• Copyright: 2002-01-28
• Publisher: Cambridge University Press

Summary

The authors of this book present a thorough discussion of the optical properties of solids, with a focus on electron states and their response to electrodynamic fields. A review of the fundamental aspects of the propagation of electromagnetic fields, and their interaction with condensed matter, is given. This is followed by a discussion of the optical properties of metals, semiconductors, and collective states of solids such as superconductors. Theoretical concepts, measurement techniques and experimental results are covered in three interrelated sections. Well-established, mature fields are discussed (for example, classical metals and semiconductors) together with modern topics at the focus of current interest. The substantial reference list included will also prove to be a valuable resource for those interested in the electronic properties of solids. The book is intended for use by advanced undergraduate and graduate students, and researchers active in the fields of condensed matter physics, materials science and optical engineering.

Table of Contents

Preface	xi
Introduction	1	(6)
PART ONE: CONCEPTS AND PROPERTIES	7	(198)
Introductory remarks	7	(1)
General books and monographs	8	(1)
The interaction of radiation with matter	9	(38)
Maxwell's equations for time-varying fields	9	(6)
Solution of Maxwell's equations in a vacuum	10	(3)
Wave equations in free space	13	(2)
Propagation of electromagnetic waves in the medium	15	(6)
Definitions of material parameters	15	(2)
Maxwell's equations in the presence of matter	17	(2)
Wave equations in the medium	19	(2)
Optical constants	21	(10)
Refractive index	21	(7)
Impedance	28	(3)
Changes of electromagnetic radiation at the interface	31	(16)
Fresnel's formulas for reflection and transmission	31	(3)
Reflectivity and transmissivity by normal incidence	34	(4)
Reflectivity and transmissivity for oblique incidence	38	(4)
Surface impedance	42	(2)
Relationship between the surface impedance and the reflectivity	44	(1)
References	45	(1)
Further reading	46	(1)
General properties of the optical constants	47	(24)
Longitudinal and transverse responses	47	(9)
General considerations	47	(2)
Material parameters	49	(3)
Response to longitudinal fields	52	(3)
Response to transverse fields	55	(1)
The anisotropic medium: dielectric tensor	55	(1)
Kramers---Kronig relations and sum rules	56	(15)
Kramers---Kronig relations	57	(8)
Sum rules	65	(4)
References	69	(1)
Further reading	70	(1)
The medium: correlation and response functions	71	(21)
Current---current correlation functions and conductivity	72	(7)
Transverse conductivity: the response to the vector potential	73	(5)
Longitudinal conductivity: the response to the scalar field	78	(1)
The semiclassical approach	79	(2)
Response function formalism and conductivity	81	(11)
Longitudinal response: the Lindhard function	81	(6)
Response function for the transverse conductivity	87	(4)
References	91	(1)
Further reading	91	(1)
Metals	92	(44)
The Drude and the Sommerfeld models	93	(13)
The relaxation time approximation	93	(2)
Optical properties of the Drude model	95	(10)
Derivation of the Drude expression from the Kubo formula	105	(1)
Boltzmann's transport theory	106	(9)
Liouville's theorem and the Boltzmann equation	107	(3)
The q = 0 limit	110	(1)
Small q limit	110	(2)
The Chambers formula	112	(1)
Anomalous skin effect	113	(2)
Transverse response for arbitrary q values	115	(5)
Longitudinal response	120	(12)
Thomas--Fermi approximation: the static limit for q < kF	120	(2)
Solution of the Boltzmann equation: the small q limit	122	(1)
Response functions for arbitrary q values	123	(7)
Single-particle and collective excitations	130	(2)
Summary of the ω dependent and q dependent response	132	(4)
References	133	(1)
Further reading	134	(2)
Semiconductors	136	(37)
The Lorentz model	137	(11)
Electronic transitions	137	(4)
Optical properties of the Lorentz model	141	(7)
Direct transitions	148	(5)
General considerations on energy bands	148	(2)
Transition rate and energy absorption for direct transitions	150	(3)
Band structure effects and van Hove singularities	153	(6)
The dielectric constant below the bandgap	154	(1)
Absorption near to the band edge	155	(4)
Indirect and forbidden transitions	159	(4)
Indirect transitions	159	(3)
Forbidden transitions	162	(1)
Excitons and impurity states	163	(6)
Excitons	163	(2)
Impurity states in semiconductors	165	(4)
The response for large ω and large q	169	(4)
References	171	(1)
Further reading	171	(2)
Broken symmetry states of metals	173	(32)
Superconducting and density wave states	173	(6)
The response of the condensates	179	(3)
London equations	180	(1)
Equation of motion for incommensurate density waves	181	(1)
Coherence factors and transition probabilities	182	(4)
Coherence factors	182	(2)
Transition probabilities	184	(2)
The electrodynamics of the superconducting state	186	(10)
Clean and dirty limit superconductors, and the spectral weight	187	(1)
The electrodynamics for q ≠ 0	188	(2)
Optical properties of the superconducting state: the Mattis---Bardeen formalism	190	(6)
The electrodynamics of density waves	196	(9)
The optical properties of charge density waves: the Lee-Rice--Anderson formalism	197	(1)
Spin density waves	198	(1)
Clean and dirty density waves and the spectral weight	199	(3)
References	202	(1)
Further reading	203	(2)
PART TWO: METHODS	205	(94)
Introductory remarks	205	(1)
General and monographs	206	(1)
Techniques: general considerations	207	(10)
Energy scales	207	(1)
Response to be explored	208	(2)
Sources	210	(2)
Detectors	212	(2)
Overview of relevant techniques	214	(3)
References	215	(1)
Further reading	216	(1)
Propagation and scattering of electromagnetic waves	217	(28)
Propagation of electromagnetic radiation	218	(12)
Circuit representation	218	(3)
Electromagnetic waves	221	(2)
Transmission line structures	223	(7)
Scattering at boundaries	230	(4)
Single bounce	231	(2)
Two interfaces	233	(1)
Resonant structures	234	(11)
Circuit representation	236	(2)
Resonant structure characteristics	238	(3)
Perturbation of resonant structures	241	(2)
References	243	(1)
Further reading	243	(2)
Spectroscopic principles	245	(24)
Frequency domain spectroscopy	246	(4)
Analysis	246	(1)
Methods	247	(3)
Time domain spectroscopy	250	(8)
Analysis	251	(2)
Methods	253	(5)
Fourier transform spectroscopy	258	(11)
Analysis	260	(4)
Methods	264	(3)
References	267	(1)
Further reading	267	(2)
Measurement configurations	269	(30)
Single-path methods	270	(11)
Radio frequency methods	271	(2)
Methods using transmission lines and waveguides	273	(2)
Free space: optical methods	275	(3)
Ellipsometry	278	(3)
Interferometric techniques	281	(5)
Radio frequency bridge methods	281	(1)
Transmission line bridge methods	282	(3)
Mach--Zehnder interferometer	285	(1)
Resonant techniques	286	(13)
Resonant circuits of discrete elements	288	(1)
Microstrip and stripline resonators	288	(2)
Enclosed cavities	290	(1)
Open resonators	291	(4)
References	295	(2)
Further reading	297	(2)
PART THREE: EXPERIMENTS	299	(98)
Introductory remarks	299	(1)
General books and monographs	300	(1)
Metals	301	(38)
Simple metals	301	(18)
Comparison with the Drude--Sommerfeld model	302	(10)
The anomalous skin effect	312	(4)
Band structure and anisotropy effects	316	(3)
Effects of interactions and disorder	319	(20)
Impurity effects	319	(2)
Electron--phonon and electron--electron interactions	321	(8)
Strongly disordered metals	329	(7)
References	336	(1)
Further reading	337	(2)
Semiconductors	339	(32)
Band semiconductors	339	(18)
Single-particle direct transitions	340	(13)
Forbidden and indirect transitions	353	(1)
Excitons	354	(3)
Effects of interactions and disorder	357	(14)
Optical response of impurity states of semiconductors	357	(4)
Electron--phonon and electron--electron interactions	361	(5)
Amorphous semiconductors	366	(2)
References	368	(2)
Further reading	370	(1)
Broken symmetry states of metals	371	(26)
Superconductors	371	(16)
BCS superconductors	372	(10)
Non-BCS superconductors	382	(5)
Density waves	387	(10)
The collective mode	387	(6)
Single-particle excitations	393	(1)
Frequency and electric field dependent transport	394	(1)
References	395	(1)
Further reading	396	(1)
PART FOUR: APPENDICES	397	(70)
Appendix A Fourier and Laplace transformations	399	(7)
Appendix B Medium of finite thickness	406	(15)
Appendix C k p perturbation theory	421	(2)
Appendix D Sum rules	423	(6)
Appendix E Non-local response	429	(16)
Appendix F Dielectric response in reduced dimensions	445	(16)
Appendix G Important constants and units	461	(6)
Index	467