1 / 19

Early History of Metal Theory 1900-1930 (Drude, Lorentz, Fermi, Dirac, Pauli, Sommerfeld, Bloch, …) The Basic Hamiltonia

Early History of Metal Theory 1900-1930 (Drude, Lorentz, Fermi, Dirac, Pauli, Sommerfeld, Bloch, …) The Basic Hamiltonian Approximations & Assumptions The Ground State ( T = 0) Wave-functions, allowed states, Fermi sphere, density of states Thermal Properties

selia
Download Presentation

Early History of Metal Theory 1900-1930 (Drude, Lorentz, Fermi, Dirac, Pauli, Sommerfeld, Bloch, …) The Basic Hamiltonia

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Early History of Metal Theory 1900-1930 (Drude, Lorentz, Fermi, Dirac, Pauli, Sommerfeld, Bloch, …) The Basic Hamiltonian Approximations & Assumptions The Ground State (T = 0) Wave-functions, allowed states, Fermi sphere, density of states Thermal Properties Expectation values, energy, specific heat Electrical Transport Properties DC and AC conductivities Magnetic Properties Classical Hall effect, Pauli paramagnetism, Landau quantization, the A-B phase, cyclotron resonance, the quantum Hall effect Chapter 1: The Free Electron Fermi Gas

  2. The Classical Hall Effect Pauli Paramagnetism Landau Quantization The Aharonov-Bohm Phase Cyclotron Resonance The Quantum Hall Effect Section 1.7: Magnetic Properties of a Free Electron Fermi Gas

  3. The Hall Effect z x y Lorentz force: Balance equation: RH is independent of t and m An excellent method for determining n

  4. The Hall Effect More formal derivation magneto-resistivity tensor magneto-conductivity tensor Jy = 0

  5. Density within the Drude Model rm [kg/m3]: mass density A [kg]: atomic mass (mass of one mole) rm/A moles atoms per m3 NArm/A atoms per m3, NA = 6.02 × 1023 n = NArmZ/A electrons per m3, Z: # of valence electrons For Li, rm = 0.542 × 103, A = 6.941 × 10-3, Z = 1 n = 4.70 × 1028 m-3

  6. Comparison with Experiments For Li, rm = 0.542 × 103, A = 6.941 × 10-3, Z = 1 n = 4.70 × 1028 m-3 RH= 1.33 × 10-10 m3/C good RH(exp)= 1.7 × 10-10 m3/C For Zn, rm = 7.13 × 103, A = 65.38 × 10-3, Z = 2 n = 1.31 × 1029 m-3 RH= 4.77× 10-11 m3/C bad RH(exp)= +3 × 10-11 m3/C Positive Hall coefficient!

  7. Cyclotron Frequency and the Hall Angle Newtonian equation of motion in E and B: steady state

  8. Deviation from the Classical Hall Effect

  9. How Difficult is wct > 1 ? me = 10000 cm2/Vs  B > 1 Tesla me = 1000 cm2/Vs  B > 10 Tesla me = 100 cm2/Vs  B > 100 Tesla

  10. The Classical Hall Effect Pauli Paramagnetism Landau quantization The Aharonov-Bohm Phase Cyclotron Resonance The Quantum Hall Effect Section 1.7: Magnetic Properties of a Free Electron Fermi Gas

  11. Pauli’s Spin Matrices Let’s concentrate on electronic spins

  12. Zeeman Effect B shifts the energy of each state by U ml: magnetic quantum number B = 0 B 0 quantization of angular momentum

  13. Electron Spin Anomalous Zeeman splitting Stern-Gerlach experiment (1922)  splitting into an even number of components (should be 2l +1) Goudsmidt and Uhlenbeck (1925): spinning on its axis Dirac’s theory (1928): existence of spin angular momentum B = 0 B 0

  14. Spin Angular Momentum ms: spin quantum number ms = +1/2: “spin up” and ms = -1/2 : “spin down”

  15. Gyromagnetic Ratio and the Electron g-factor : gyromagnetic ratio g-factor Quantum Electrodymanics (QED)

  16. Spin is Purely Quantum Mechanical Orbital angular momentum: As h 0, we can keep L non-zero by increasing the size of lto infinity Spin angular momentum: As h 0, S 0

  17. Magnetic Susceptibility Total field [T] or [Wb/m2] Applied field [A/m] Induced field [A/m] 4p× 10-7[T-m/A] : magnetization curve c > 0: paramagnetic c < 0: diamagnetic

  18. Calculate Spin c “Classically” spin “down” spin “up” Consider N electrons in volume V at temperature T in a magnetic field H, and calculate the total magnetic moment M Too large, and temperature dependent

  19. Pauli’s Spin Susceptibility g↓(e) 2mBm0H e spin imbalance magnetic moment per electron g↑(e) Net magnetic moment per m3:

More Related