Physics 4340/7440 Solid-State Physics Spring 2001

Professor John Price, john.price@colorado.edu, 492-2484

Lectures: T,Th 9:30 -10:45 am, Duane G1B25

Office Hours: Duane F-635, time to be decided

Primary Text: Charles Kittel, Introduction to Solid State Physics, Seventh Edition

You are encouraged to also use the following books (reserved in the Math/Physics library):

H.M. Rosenberg, The Solid State (easier than Kittel)

J.S. Blakemore, Solid State Physics (same level as Kittel)

J. Richard Christman, Fundamentals of Solid State Physics (same level as Kittel)

N.W. Ashcroft and N. David Mermin, Solid State Physics (advanced)

G. Burns, Solid State Physics (advanced)

National Research Council, Condensed-Matter Physics (survey of current research)

Problem sets will be assigned on Tuesdays and will be due the following Tuesday in class, except there will be no problem set due the Tuesday after the midterm, and the first set will be due on Jan. 30. You may discuss the problems with others, but you should not receive written help.

Grading: There will be 12 problem sets, each worth 20 points. The midterm will be worth 60 points and the final will be worth 60 points. The total number of points possible is 360.

Note that the problem sets are worth 2/3 of the grade.

Graduate Students: After we see who is in the class we will discuss options for graduate students.

Jan. 16– Feb. 8 Introduction and Crystal Structure

Feb. 13–Mar. 6 Phonons

Mar. 8–20 Free Electron Fermi Gas

Mar. 22 Midterm (in class)

(Spring Break)

Apr. 3–12 Band Theory

Apr. 17–24 Semiconductors

Apr. 26–May 3 Magnetism

Physics 4340, Spring 2001

Foundations

I. Introduction and Crystal Structure

A. Introduction

1) What is a solid?

2) properties of solids

B. Crystal Structure and Symmetry

1) Why bother?

2) crystal lattice

a) Bravais lattice

b) structures

c) primitive lattice vectors

d) primitive unit cells

e) non-primitive unit cells

3) lattice types in 2-d

4) lattice types in 3-d

5) planes and directions

a) planes

b) directions

6) simple structures

a) NaCl

b) cubic ZnS

c) diamond

C. Reciprocal Lattice and Diffraction

1) Bragg law

2) Fourier analysis of lattice

a) 1-d Fourier series

b) 3-d Fourier series

c) condition on {G}

d) construction of {G}

3) diffraction conditions

a) scattering amplitude F

b) three forms of the Bragg law

4) Brillouin zones

a) construction

b) another form of Bragg law

5) Interpretation of the reciprocal lattice

a) G's are perpendicular to lattice planes

b) plane spacing

c) interpretation

d) Bragg law again

D. Crystal binding

1) Van der Waals bonds

a) correlated state

b) harmonic oscillator model

c) normal modes

d) ground state

e) Lennard-Jones potential

f) inert gas crystals

2) ionic bonds

a) ionic molecules

b) lattice energy

3) covalent crystals

4) metallic bonding

5) hydrogen bonds

II. Phonons

A. Crystal vibrations

1) properties influenced by phonons

2) typical numbers

a) sound velocity

b) thermal wavelength

3) linear monatomic chain in 1-d

a) dispersion relation

b) comments

4) vibrations of 3-d monatomic lattice

a) restrict k to first Brillouin zone

b) three branches

c) group velocity

d) example: copper

5) polyatomic basis

a) diatomic chain

b) general case

c) example: diamond

6) quantization of lattice waves

7) phonon scattering

a) conservation laws

b) examples: Brilloiun and Raman scattering

B. Thermal properties

1) phonon heat capacity

a) Planck distribution

b) general formula for heat capacity

c) density of states

d) Debye heat capacity

e) realistic density of states

2) thermal expansion

a) single oscillator

b) monatomic chain

3) thermal conductivity

a) phonons as particles

b) local thermal equilibrium

c) scattering mechanisms

d) phonon thermal conductivity

e) temperature dependence of thermal conductivity

III. Free-electron Fermi gas

A. Introduction to metals

1) basic properties

2) structure

3) idealizations

a) independent electrons

b) free electrons

c) band theory

B. Free-electron ground state

1) Schrödinger equation

2) orbitals

3) ground state

4) density of states

C. Free-electron heat capacity

1) Fermi-Dirac statistics

a) T=0

b) T>0

c) chemical potential

2) temperature dependence of chemical potential

a) Fermi-Dirac integrals

b) calculation

3) heat capacity

D. Electrical conductivity

1) Drude formula

a) equation of motion

b) scattering

c) result

2) temperature dependence of conductivity

a) Matthiessen's rule

b) residual resistivity ratio

c) typical behavior

3) Hall effect

E. Electronic thermal conductivity

1) formula

2) Wiedemann-Franz law

IV. Band theory

A. Introduction

B. Origin of band gap

C. Magnitude of gap

D. Bloch theorem

1) first form

2) second form

3) proof

a) lattice translation operator

b) composition law

c) eigenstates of translation operator

d) eigenvalues of translation operator

E. Extended, reduced, and repeated zone representations

1) extended

2) reduced

a) reassembling higher zones in the first zone

b) continuous bands in first zone

3) repeated

F. Empty lattice approximation

1) 1-d case

2) 2-d case: square lattice

3) 3-d case: fcc lattice

G. Band filling and classification of solids

1) number of k-vectors in first Brillouin zone

2) metals

3) insulators and semiconductors

4) band overlap

Applications

V. Semiconductor crystals

A. Introduction

1) simple picture at T=0

2) carriers for T>0

a) intrinsic

b) extrinsic

B. Bandgaps

C. Equation of motion for Bloch electrons

1) Bloch wave-packets

2) Lorentz equation

3) E=0, static and uniform B

4) effective mass

a) near conduction band minimum

b) near valence band maximum

D. Holes

1) definition

2) wavevector of a hole

3) energy of a hole

4) hole group velocity

5) hole equation of motion

VI. Metals and Fermi surfaces

A. Construction of Fermi surfaces

1) monovalent, Na-like

2) monovalent, Cu-like

3) multivalent

B. Orbit types

1) electron-like

2) hole-like

3) open

C. Tight binding approximation

VII. Superconductivity

A. Experimental facts

1) critical temperature

2) critical field

3) Meissner effect

4) critical current

5) energy gap

a) heat capacity

b) far-infrared absorption

c) tunneling

B. BCS theory

1) role of phonons

2) Cooper pairs

3) predictions of BCS theory

C. Boson gas model

1) the model

2) current

3) London equation

4) Meissner effect

D. Flux quantization

VIII. Magnetism

A. Overview

B. Independent moments

1) Langevin diamagnetism

a) H for an electron in a uniform B field

b) diamagnetic term

2) paramagnetism

a) paramagnetic part of the Hamiltonian

b) free atom

c) spin-1/2 in thermal equilibrium

C. Ferromagnetism

1) mean field theory, T>Tc

2) mean field theory, T<Tc

3) comments