1. 8/28/2015PHY 752 Fall 2015 -- Lecture 21 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 103 Plan for Lecture 2: Reading: Continue reading Chapter 1 in GGGPP; Electrons in one-dimensional periodic potentials 1.Review of Bloch’s Theorem 2.Kronig-Penny model potential from the viewpoint of scattering or tunneling

2. 8/28/2015PHY 752 Fall 2015 -- Lecture 22

3. 8/28/2015PHY 752 Fall 2015 -- Lecture 23

4. 8/28/2015PHY 752 Fall 2015 -- Lecture 24 Li 2 SnO 3

5. 8/28/2015PHY 752 Fall 2015 -- Lecture 25 Li 2 SnS 3

6. 8/28/2015PHY 752 Fall 2015 -- Lecture 26 Bloch theorem:

7. 8/28/2015PHY 752 Fall 2015 -- Lecture 27 Eigenvalue solutions to Kronig-Penny model

8. 8/28/2015PHY 752 Fall 2015 -- Lecture 28

9. 8/28/2015PHY 752 Fall 2015 -- Lecture 29 From wavefunction matching conditions: Condition for non-trivial solution: Simplified result:

10. 8/28/2015PHY 752 Fall 2015 -- Lecture 210

11. 8/28/2015PHY 752 Fall 2015 -- Lecture 211 v v Forbidden states f

12. 8/28/2015PHY 752 Fall 2015 -- Lecture 212 f ka/  Band gap

13. 8/28/2015PHY 752 Fall 2015 -- Lecture 213 Treatment of same problem in terms of transmission and reflection from a periodic barrier. First consider a single barrier: Matrix for determining coefficients:

14. 8/28/2015PHY 752 Fall 2015 -- Lecture 214 Matching conditions for wavefunction coefficients:

15. 8/28/2015PHY 752 Fall 2015 -- Lecture 215 Solving for transfer matrix elements:

16. 8/28/2015PHY 752 Fall 2015 -- Lecture 216 Transmittance

17. 8/28/2015PHY 752 Fall 2015 -- Lecture 217 After some algebra:

18. 8/28/2015PHY 752 Fall 2015 -- Lecture 218 Electron transmission through a one-dimensional periodic barrier Because of Bloch theorem:

19. 8/28/2015PHY 752 Fall 2015 -- Lecture 219 Bloch theorem & transmission coefficients: Condition for solution: