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Quantum transport
in semiconductor nanostructures
Thomas Ihn
ETH Zürich
FS 15
Trajectory picture of electron transport
y
Conductance
quantum
Number of modes
Transmission
(0 or 1)
applied voltage
Directed current flow in resistors
Last week: (Semi)classical conductivity
Metal film resistors
Resistive metal wire
How small can a resistor be made?
Is there an "elementary" resistor?
Thales of Miletus, about 600 B.C.
rubbing amber with fur: the birth of electricity
Demokritus, about 460 B.C.
break a piece of matter in half, then in half again,
and so on: is there a smallest unit?
Idea dismissed by Aristotle, picked up again more than 2000 years later
in 1800 by Dalton
One-dimensional conductors:
the ultimate nanoresistors
Carbon nanotubes
One-dimensional conductors:
the ultimate nanoresistors
InAs
nanowires
Bi2Se3 nanoribbons:
topological insulators
One-dimensional conductors:
the ultimate nanoresistors
Graphene nanoribbons
One-dimensional conductors:
the ultimate nanoresistors
GaAs
quantum point contacts
GaAs quantum wires
by cleaved edge overgrowth
Conductance of graphene
nanoribbons
Susanne Dröscher, ETHZ, 2011
Irregular resonances
Conductance of GaAs nanowires
U. Meirav, M.A. Kastner, PRB 40, 5871 (1989)
Periodic resonances
Conductance of a constriction
in a GaAs 2D electron gas
Clemens Rössler, ETHZ, 2010
Step-like conductance increase in units of 2e2/h
dg/dVG
Conductance quantization
The pioneering work
Van Wees et al., 1988
Step-like increase of the conductance
Landauer-Büttiker theory
Zero temperature :
e2 N
G(E F ) =
Tab (E F )
å
h a ,b =1
Finite temperatures :
æ df ö
G(T) = ò dE G(E)ç - ÷
è dE ø
0
¥
Rolf Landauer (1927-1999)
Markus Büttiker
Read until next week
Chapter
XI.1–7 Ballistic electron transport in QPCs