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How to enhance Tc in nano-structured materialsAntonio M. García-García
Cavendish Laboratory, Cambridge University, Lisbon University
http://www.tcm.phy.cam.ac.uk/~amg73/
WaySanta Barbara
Pedro Ribeiro Dresden
BermudezCambridge
Sangita Bose Bombay
Klaus Kern Stuttgart
MayohCambridge
Altshuler Columbia
Richter RegensburgYuzbashyan
RutgersUrbina
Regensburg
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Mavericks
MgB2 39K 2001 Akimitsu Cuprates ~100K 1986 Mueller & Bednorz
FeSC ~50K 2006 Hotsono
Quantum critical points ©
Superconductivity
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Librarians
Control
Pb ~7K Al ~1K Sn ~3.7K Nb ~9.3K
Thinner
Cleaner
Smaller
BCS + …. Abeles, Tinkham, Devoret, Goldman, Xue, Kern, Di Fazio, Schoen, Halperin, Leggett,Blatt….
Granular
Thin filmsJosephson Junctions
Nanowires
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5.33 Å
0.00 Å
0 nm
7 nm
Far from equilibrium
Grainy
Packed
Smaller
Higher Tc?
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Abeles, Cohen, Cullen, Phys. Rev. Lett., 17, 632 (1966)
A.M. Goldman, Dynes, Tinkham…
Thin Films?
Crow, Parks, Douglass, Jensen, Giaver, Zeller....
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BCS superconductivity Finite size effects
V Δ~ De-1/
V finite Δ=?
Shell EffectsParmenter, Phys. Rev. 166,
392 (1967)L ~ 5nm
Level Degeneracy
20Tc!
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Shape Resonances
Blatt, Thompson, Phys. Lett. 5, 6 (1963)
Thin Films
Fluctuations?
Charge neutrality?
Substrate?
10Tc!
Bermudez, AGG, Phys. Rev. B 89, 064508 (2014) 89, 024510 (2014)
Yu, et al.,Rev. B 14, 996 (1976)
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A.M. Goldman et al. PRL 62 2180 (1989)PRB 47 5931 (1993)
Smoother
Thinner
Disordered
Transition
𝑅𝑁>𝑅𝑞
BKT
(anti)Vortex unbinding
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Xue et al., Science 306, 1915 (2004) Shih et al., Science 324, 1314 (2009)
2000 Atomic scale control
Pb
Size effects but not higher Tc
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STM
Epitaxial growth
No impurities
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Is enhancement of superconductivity possible?
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Cuprates high Tc Heterostructures
Bozovic et al., Nature 455, 782 (2008)
Higher Tc!!
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Xue et al., Nature Communications 3, 931 (2013)
Iron Based Heterostructures
Feng, et. al, arXiv:1402.1357
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Grains
Enhancement, yesOrigin?
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>>
Heiselberg (2002): harmonic potentials, cold atom
Kresin, Ovchinnikov, Boyaci (2007) : Spherical, too high Tc
Peeters, et al, (2005-): BCS, BdG in a wire, cylinder..
Olofsson (2008): Estimation of fluctuations in BCS
Devreese (2006): Richardson equations in a box
Grains
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3d integrable
Al grainkF = 17.5 nm-1
0 = 0.24mV
PRL 100, 187001 (2008) PRB 83, 014510 (2011)
3d chaotic
Δ≫𝛿1
𝑘𝐹 𝐿≪1
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R ~ 4-30nm
Single, Isolated Sn and Pb grains
A gap is still observed
Tunneling conductance
Almost hemispherical
Kern Bose
STM
5.33 Å
0.00 Å
0 nm
7 nm
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+
Bose, AGG, Nature Materials 2010
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Pb
More fun? Why not
Ribeiro, Dresden
Beyond mean field
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B closes gapOdd-even effects
~
Superconductivity?
Isolated grain?
Yes, superconductivity
1959
Ralph, Black,Tinkham,
Superconductivity in
Single Metal Particles PRL 74, 3241-3244
(1995).
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von Delft, Braun, Larkin, Sierra, Dukelsky, Yuzbashyan, Matveev, Smith, Ambegaokar
BCS fine until / Δ0 ~ 1/2
T = 0/ Δ0 ~ 1
BCS: transition Richardson: only
crossover
J. von Delft et al., Phys. Rep., 345, 61 (2001)
Richardson’s BCS exact solution
T≠0Path IntegralStatic Path Approach
Scalapino, et al.,70’s
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Richardson’s equations
Static Path Approach
PRB 84,104525 (2011)Editor‘s Suggestion
Quantum Fluctuations
Thermal Fluctuations
and
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Quantum + Thermal?
Ribeiro and AGG, Phys. Rev. Lett. 108, 097004 (2012)
T, / Δ0 << 1 Divergences at intermediate T Rossignoli and Canosa
Ann. of Phys. 275, 1, (1999)
Harmful Zero Modes
Polar coordinates
Quantum fluctuations ~ Charging effects
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Mason, et al, Nature Physics 8 59 (2012)
Josephson array?
True phase coherence in single nanograins? 𝚫𝑵𝚫𝝓 ≥ℏ
No
Maybe
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Deutscher 73’
Al evaporated on a glass substrate
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Engineering granular materials
Mayoh, AGG, arXiv:1311.0295
Tc=1.3Tcbulk
Tc=1.5Tcbulk
Tc=3.0Tcbulk!!!
Optimal but realistic
Size Variance Packing
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7nm
𝑇≫𝑇 𝑐𝑏𝑢𝑙𝑘
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𝑇 ≥𝑇 𝑐𝑏𝑢𝑙𝑘
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What?
3D Clean
JJ array
Nano spheres
𝑅≥ 4𝑛𝑚R:
How?Open grain JJ Array
Capacitance
Quasi particle tunnelling
BCSSemiclassical
Mean fieldPercolation
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Single grain
Tunneling Smooth DOS
Weaker size effectsOpen grain
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3D Array
HOMOGENEOUS
INHOMOGENEOUSDp ~ 2.55
Tc ?T#SCG
Schoen, Zaikin,Fazio..
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Wait!
Percolation?
Mean field?
Tc T#SCG
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𝜎=0.1,0.6 ,1 ,1.4𝑛𝑚𝑅=5𝑛𝑚𝜆=0.25
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𝜎=1𝑛𝑚𝑅=5𝑛𝑚
𝜆=0.2 ,0.25 ,0.3 ,0.35
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𝜎=1𝑛𝑚𝑅=5𝑛𝑚
𝑃𝑎𝑐𝑘𝑖𝑛𝑔=𝐶𝑢𝑏𝑖𝑐 ,𝐵𝐶𝐶 ,𝐹𝐶𝐶
𝜆=0.25
Enhancement is possible!Experiments?
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Other ways to enhance Tc
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LaAlO3 /SrTiO3
Heterostructures
Triscone, Nature 456 624 (2008)
Control &Tunability
Spin-OrbitDisorder
Magnetism
PRB 85, 020457 (2012)PRL 104, 126803 (2010)
LocalizationExotic Quantum
MatterLesueur, arXiv:1112.2633
E Field effect
Topology
Relevance
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Mocking Cuprates
Electric Field Effect
2D LTO/STO
+
Pseudogap
Mannhart et al., Nature 502, 528 (2013)
Higher Tc by coupling to a metallic layer?
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Graphene
Granular Sn+
Sn
Stabilization of SC fluctuations?
Allain, Bouchiat, et al., Nat. Mat. 11, 590 (2012)
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Transient Superconductivity
ARPES
Femtosecond Pulses
Pump & Probe
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How to enhance?
Engineering of nano-structured materials
Suppresion of phase fluctuations by controlled coupling.
Steady non-thermal superconductivity
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1966+Experimental
control
+Predictive power
1995
Now
?Engineering of high Tc materials
5.33 Å
0.00 Å
0 nm
7 nm
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Danke!