Transcript PY4007Lecture5

PY4007 – Quantum wires
Coulomb blockade worked example
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 R3 is much smaller than R1 or R2, and R1=R2.
(a)Assuming V2=0 V, sketch a graph of the current flowing between V1 and the 0V
ground terminal as a function of V1.
(b)V2 is set to +e/4C. Describe what happens to the current through junctions 1 and 2
as V1 is increased from 0 to +e/4C.
V1
C,R2
V2
C,R1
nanoparticle
C,R3
0V
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?
Roll up graphene sheets
Graphite
graphene sheets
Roll-up vectors
Types of SWNT
Nanotube diameter
Chirality angle
d
3

acc n  2nm  m
2
 3m 

  tan 

2
n

m


1
2

1
2
acc  0.14nm
Band structure and quantisation
metallic
semiconductor
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.
Quantum conductance
Conductance in a nanowire
Ballistic conductance with 2 contacts
E
subbands
DOS
Quantum well structure
Resonent tunnelling diode
Resonant tunnelling diode