1. PY4007 – Quantum wires nanoparticle V1V1 V2V2 0 V C,R 1 C,R 2 C,R 3 A small conductive nanoparticle is connected via 3 tunnelling junctions to voltage sources (see figure below). The capacitances, C, of the three tunnelling junctions are identical. The nanoparticle contains n excess electrons. (a)Write down an expression for the change in electrostatic energy of the nanoparticle when an electron tunnels onto or off the nanoparticle. (b)Derive three expressions for the work done by the voltage sources when an electron tunnels through one of the junctions 1,2 or 3. The tunnelling resistance R 3 is much smaller than R 1 or R 2, and R 1 =R 2. (a)Assuming V 2 =0 V, sketch a graph of the current flowing between V 1 and the 0V ground terminal as a function of V 1. (b)V 2 is set to +e/4C. Describe what happens to the current through junctions 1 and 2 as V 1 is increased from 0 to +e/4C. Coulomb blockade worked example

2. Carbon nanotubes Discovered by Sumio Iijima in 1991. –S. Iijima, Nature 354 (1991) 56. They can be metallic or semiconducting. They are mechanically extremely strong. –Use for composites?

3. Roll up graphene sheets graphene sheets Graphite

4. Roll-up vectors

5. Types of SWNT Nanotube diameter Chirality angle

6. Band structure and quantisation metallic semiconductor

7. DOS and STS data (A) and (B) STM image and corresponding STS spectrum of a discrete (8,8) SWNT (C) and (D) as for (A) and (B) but for an (8,8) SWNT located in a bundle. Ouyang M et al. Science 292 (2001) 702.

8. Quantum conductance

9. Conductance in a nanowire

10. Ballistic conductance with 2 contacts E DOS sub- bands

11. Quantum well structure

12. Resonent tunnelling diode

13. Resonant tunnelling diode