Superconductivity at the Nanoscale

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Superconductivity at the Nanoscale
D. Stroud and N. Trivedi

• Why are nano superconductors useful/important?
• How is superconductivity at the nanoscale
  modeled?
• Behavior or nanoscale superconducting wires and
  devices

Contact e-mail trivedi_at_mps.ohio-state.edu
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Small Josephson junctions as qubits
What are nano superconductors good for?

• 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.

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A superconductor is a material which can carry
current with no resistance!!
Tc
Zero resistance is seen below a
material dependent critical temperature Tc
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Maximum Tc 130K Achieved in the copper oxide
high Tc materials -- useful because Tcgt boiling
pt. of liquid nitrogen
Tc
Nobel Prizes for studies of SC in 1913, 1972,
1973, 1987, 2003 SCs useful as low-dissipation
current carriers valuable in producing
ultra-high magnetic fields, and for microwave
applications.
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Types of nanoscale SCs to be studied
Zero-dimensional SC
Two coupled zero-dimensional SCs
J
One-dimensional SC (thin wire)
Two-dimensional SC (nm layer thickness)
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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 tunneling
SINGLE ELECTRON TRANSISTOR
SC requires mean level spacing lt SC gap Effect
of odd/even numbers of electrons seen!
Ralph, Black and Tinkham, PRL 74, 3241 (1995)
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Quantum Phase Fluctuations in nano SCs
charging energy to put an electron on nano SC
Capacitance of a grain Cd
10-20 nm dia
causes quantum fluctuations of the phase
Josephson coupling between two nano
superconductors
J
Josephson weak link (nonlinear circuit element)
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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?
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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.

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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)
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Scanning tunneling spectroscopy
Ghosal, Randeria, Trivedi PRB 63, 20505 (2000)
THEORY
EXPT J.C. Davis Nature 403, 746 (2000)