Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang Lecture 2 Fermi Gas

Enrico Fermi Paul Dirac

Ionisation Energy of Sodium 5.14 eV Band Theory of Metals Start with isolated Sodium Atom

Ionisation Energy of Sodium 5.14 eV Band Theory of Metals

Splitting of 3s level with 2 Sodium atoms Bring two Sodium Atoms together

Band Theory of Metals Splitting of 3s level with 6 Sodium atoms Bring six Sodium Atoms together

Band Theory of Metals Splitting of 3s levels with Sodium atoms in crystalline solid

Band Theory of Metals

Fermi-Dirac Distribution electrons holes

Probability of Occupancy T=0 T > 0

Probability of Occupancy

Energy in units Filling up the Fermi Sea In One Dimensional Box ² F

1-Dimensional Box

1-Dimensional Fermi Gas Sum Over Spins

1-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

2-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

3-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

1-Dimensional Fermi Gas Single Spin Orientation Total Energy

2-Dimensional Fermi Gas Single Spin Orientation Total Energy

3-Dimensional Fermi Gas Single Spin Orientation Total Energy

3-Dimensional Density of States

2-Dimensional Density of States

3-Dimensional Fermi Gas Density of States

2-Dimensional Fermi Gas Density of States

1-Dimensional Fermi Gas Density of States

Conduction Band Valence Band

Woodward Yang harvard lecture notes

CBO =conduction band offset

2-Dimensional Density of States

Quantum Wire

2005/Lectures/Matveev/Boulder%20lecture.pdf

A graphene nanoribbon field-effect transistor (GNRFET). Here contacts A and B are at two different Fermi levels E F1 and. E F2Fermi levels

Ballistic Conductor

i i’ t’ t Landauer formula Conductance

µ Gas Pressure on the Wall A cos θ v δ t A θ

Pressure due to Non-Relativistic Degenerate Fermi Gas Equation of state for Fermi Gas since at T = 0 We have for a metal

White dwarf as seen by Hubble Space Telescope

What's Inside a White Dwarf? To say that white dwarfs are strange is an understatement. An earth-sized white dwarf has a density ofdensity 1 x 10 9 kg/m 3. In comparison, the earth itself has an average density of only 5.4 x 10 3 kg/m 3. That means a white dwarf is 200,000 times as dense!