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

2. Enrico Fermi 1901 - 1954 Paul Dirac 1902 - 1984

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

4. Ionisation Energy of Sodium 5.14 eV Band Theory of Metals

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

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

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

9. Band Theory of Metals

10. Fermi-Dirac Distribution electrons holes

11. Probability of Occupancy 1.0 0.0 T=0 T > 0

12. Probability of Occupancy

13. Energy in units Filling up the Fermi Sea In One Dimensional Box 10 20 30 ² F

14. 1-Dimensional Box

15. 1-Dimensional Fermi Gas Sum Over Spins

16. 1-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

17. 2-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

18. 3-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

20. 1-Dimensional Fermi Gas Single Spin Orientation Total Energy

21. 2-Dimensional Fermi Gas Single Spin Orientation Total Energy

22. 3-Dimensional Fermi Gas Single Spin Orientation Total Energy

24. 3-Dimensional Density of States

25. 2-Dimensional Density of States

26. http://upload.wikimedia.org/wikipedia/en/c/c5/DOS_multdim.jpg

27. 3-Dimensional Fermi Gas Density of States

28. 2-Dimensional Fermi Gas Density of States

29. 1-Dimensional Fermi Gas Density of States

30. Conduction Band Valence Band

36. Woodward Yang harvard lecture notes

37. CBO =conduction band offset

39. 2-Dimensional Density of States

42. Quantum Wire

43. http://boulder.research.yale.edu/Boulder- 2005/Lectures/Matveev/Boulder%20lecture.pdf

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

46. Ballistic Conductor

47. i i’ t’ t Landauer formula 1927 - 1999 Conductance

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

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

51. White dwarf as seen by Hubble Space Telescope

53. 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!