1. Computational Solid State Physics 計算物性学特論 第１０回 10. Transport properties II: Ballistic transport

2. Electron transport properties l e : electronic mean free path l φ : phase coherence length λ F : Fermi wavelength

3. Tunneling transport I L

4. Current in one-dimension T(k): transmission coefficient

5. Total current in one-dimension

6. Low bias limit : conductance at low temperatures

7. Landauer ’ s formula ： transmission coefficient ： Conductance ： Quantum conductance ： Quantum resistance I: current, V: bias

8. Two- and four- terminal measurements

9. Tow- and four- terminal measurement 2-terminal measurement 4-terminal measurement

10. Conductance of a quantum point contact

11. Only one channel (n=1) is open. for n=1 Conductance of a quantum point contact Quantization of transverse motion

12. Nanowire of Au

15. Mechanically Controllable Break Junction

16. Histogram of conductance of a relay junction

17. Conductance through a quantum dot

18. :Lorentzian broadening of resonant tunneling through quantized energy E N of a dot :Thermal broadening Tunneling current via quantum dot

19. A bound state and a resonant state

20. Transmission coefficient for resonant tunneling If T L =T R

21. Transmission coefficient of a resonant-tunneling structure

22. Characteristics of resonant tunneling diode

23. Resonant tunneling current :wave function :energy

24. Large bias and low temperature limit Total resonant tunneling current

25. Transmission coefficient for resonant tunneling If T L =T R

26. Profile through a three-dimensional resonant-tunnelling diode. The bias increases from (a) to (d), giving rise to the I(V) characteristic shown in (e). The shaded areas on the left and right are the Fermi seas of electrons. Profile through a three-dimensional resonant tunneling diode

27. Problems 10 Calculate the density of states for free electrons in one, two and three dimensions. Calculate the ballistic current in two dimensions. Calculate the transmission coefficient for a square barrier potential. Calculate the transmission coefficient for a double square barrier potential.