Transcript NIRT Presentation

Superconductivity at the
Nanoscale
D. Stroud and N. Trivedi
1. Why are nano superconductors
useful/important?
2. How is superconductivity at the nanoscale
modeled?
3. Behavior or nanoscale superconducting
wires and devices
Contact e-mail: [email protected]
What are nano superconductors good for?
Small Josephson junctions as qubits
• Small superconducting systems (e.g. Josephson
junctions) -- among the most promising
candidates for qubits
• Only two energy levels (which behave like “1” or
“0” bits)
qubit or quantum bit: “coherent superposition”
of “1” and “0”
• Qubits will generate vastly more computing
power than “classical” computers.
A superconductor is a
material which can carry
current with no resistance!!
Tc
Zero resistance is seen below a material
dependent critical temperature Tc
Maximum Tc ~130K
Achieved in the copper
oxide high Tc materials
-- useful because Tc>
boiling pt. of liquid
nitrogen
Nobel Prizes for studies of SC
in 1913, 1972, 1973, 1987,
2003
SC’s useful as low-dissipation
current carriers; valuable in
producing ultra-high magnetic
fields, and for microwave
applications.
Tc
Types of nanoscale SC’s to be studied
Zero-dimensional SC
J
Two coupled zero-dimensional SC’s
One-dimensional SC (thin wire)
Two-dimensional SC
(nm layer thickness)
When superconductors are made very small or thin,
they often lose the remarkable property of superconductivity.
Why does this loss of superconductivity happen?
SINGLE ELECTRON TRANSISTOR
Single electron tunneling
SC requires: mean level spacing < SC gap
Effect of odd/even numbers of electrons seen!
Ralph, Black and Tinkham, PRL 74, 3241 (1995)
Quantum Phase Fluctuations in nano SCs
charging energy to put an electron on nano SC
EC  e / 2C
2
10-20 nm dia
Capacitance of a grain C~d
causes quantum fluctuations of the phase
Josephson coupling between two
nano superconductors
~J
Josephson “weak link” (nonlinear circuit element)
e
 d i 
H

  J  cos( i   j )

2C i  d 
i j
2
2
Nano SC wires of width ~5nm
Bezryadin, Lau and Tinkham,
Nature 404, 971 (2000)
SC is destroyed in nanowires by thermal
fluctuations, quantum phase slips, and dissipation.
Is there a universal resistance of the nano-wire
above which the wire cannot superconduct?
Nanoscale superconductivity in 2D
• The high-Tc SCs: stacks of CuO2 layers, with
various other ions in between them. All the
superconducting “action” occurs in the CuO2 layers.
• Superconducting layers are inhomogeneous on a
nanoscale: The superconducting energy gap varies
from point to point within the layer, on a nanometer
scale (seen in STM experiments).
• Theoretical multiscale approach:
• (i) Solve for superconducting properties using a the
standard non-linear Bogoliubov-de Gennes
differential equations, modified to include nanoscale
inhomogeneity and phase fluctuations.
• (ii) Treat inhomogeneity at a larger, but still close to
nanoscale, using a mapping onto an effectively
Josephson-coupled layer.
Generation of self organised nanoscale structure
in a disordered superconductor
Spatial dependence of
pairing amplitude with
increasing disorder in an
inhomogeneous SC obtained
by solving Bogoliubov
deGennes equations
Ghosal, Randeria, Trivedi
PRL 81, 3940 (1998);
PRB 65, 1450 (2002)
Scanning tunneling spectroscopy
THEORY
Ghosal, Randeria, Trivedi
PRB 63, 20505 (2000)
EXPT: J.C. Davis
Nature 403, 746 (2000)