Phys. Rev. Lett. 100, 187001 (2008) Yuzbashyan Rutgers Altshuler Columbia Urbina Regensburg Richter Regensbur g Sangita Bose, Tata, Max Planck Stuttgart Kern Ugeda, Brihuega arXiv:0911.1559 Nature Materials 2768, May 2010 Finite size effects in superconducting grains: from theory to experiments Antonio M. García-García
Finite size effects in superconducting grains: from theory to experiments. Antonio M. Garc í a- Garc í a. Phys. Rev. Lett. 100, 187001 (2008). Sangita Bose, Tata, Max Planck Stuttgart. arXiv:0911.1559. Yuzbashyan Rutgers. Altshuler Columbia. Nature Materials 2768, May 2010. - PowerPoint PPT Presentation
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Phys. Rev. Lett. 100, 187001 (2008)
Yuzbashyan Rutgers
Altshuler Columbia
Urbina Regensburg
Richter Regensburg
Sangita Bose, Tata, Max Planck Stuttgart
Kern Ugeda, Brihuega
arXiv:0911.1559
Nature Materials
2768, May 2010
Finite size effects in superconducting grains: from theory to experiments
Antonio M. García-García
L
1. Analytical description of a clean, finite-size non high Tc superconductor?
2. Are these results applicable to realistic grains?
Main goals
3. Is it possible to increase the critical temperature?
Can I combine this?
BCS superconductivity
Is it already done?
Finite size effects
V Δ~ De-1/
V finite Δ=?
Brute force?
i = eigenvalues 1-body problem
No practical for grains with no symmetry
Semiclassical techniques
1/kF L <<1 Analytical?
Quantum observables in terms of classical quantities Berry,
Gutzwiller, Balian, Bloch
Non oscillatory terms
Oscillatory terms in L,
Expansion 1/kFL << 1
Gutzwiller’s trace formula
Weyl’s expansion
Are these effects important?
Mean level spacing
Δ0 Superconducting gap
F Fermi Energy
L typical length
l coherence length
ξ SC coherence length
Conditions
BCS / Δ0 <<
1
Semiclassical1/kFL << 1
Quantum coherence l >> L ξ
>> L
For Al the optimal region is L ~ 10nm
Go ahead! This has not been done before
In what range of parameters?
Corrections to BCS smaller or larger?
Let’s think about this
Is it done already?
Is it realistic?
A little history
Parmenter, Blatt, Thompson (60’s) : BCS in a rectangular grain
Heiselberg (2002): BCS in harmonic potentials, cold atom appl.
Shanenko, Croitoru (2006): BCS in a wire
Devreese (2006): Richardson equations in a box
Kresin, Boyaci, Ovchinnikov (2007) Spherical grain, high Tc
Olofsson (2008): Estimation of fluctuations in BCS, no correlations
Superconductivity in particular geometries
Nature of superconductivity (?) in ultrasmall systems
Breaking of superconductivity for / Δ0 > 1? Anderson (1959)
Experiments Tinkham et al. (1995). Guo et al., Science 306, 1915, “Supercond. Modulated by quantum Size Effects.”
Even for / Δ0 ~ 1 there is “supercondutivity
T = 0 and / Δ0 > 1 (1995-)
Richardson, von Delft, Braun, Larkin, Sierra, Dukelsky, Yuzbashyan