benjamin sacépé institut néel, cnrs & université joseph fourier, grenoble localization of...
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Benjamin SacépéBenjamin SacépéInstitut Néel, CNRS & Université Joseph Fourier, Grenoble
Localization of preformed Cooper-pairs Localization of preformed Cooper-pairs
in disordered superconductorsin disordered superconductors
Lorentz Center, Leiden 2011
Benjamin SacépéBenjamin SacépéInstitut Néel, CNRS & Université Joseph Fourier, Grenoble
Localization of preformed Cooper-pairs Localization of preformed Cooper-pairs
in disordered superconductorsin disordered superconductors
Thomas Dubouchet, Claude Chapelier, Marc SanquerThomas Dubouchet, Claude Chapelier, Marc SanquerCEA Grenoble
Maoz Ovadia, Dan ShaharMaoz Ovadia, Dan ShaharWeizmann Institute of Science, Rehovot
M. Feigel’manM. Feigel’manL.D. Landau Institut for Theoretical Phyiscs, Moscow
L. IoffeL. IoffeRutgers University, Piscataway
Lorentz Center, Leiden 2011
Superconductor-Insulator Transition (SIT)Superconductor-Insulator Transition (SIT)
Main ingredients :
1. Disorder localization
2. Attractive pairing superconducting phase
3. Coulomb interaction competes with pairing
4. Reduced dimensionality affects 1,2 and 3
d =
d =
Quench condensed Bismuth
D.B. Haviland, Y. Lui, A.M. Goldman, PRL (‘89)
Amorphous indium oxideAmorphous indium oxide
G. Sambandamurthy, et al. PRL 94, 017003, (2005)
Magnetic field-tuned SITMagnetic field-tuned SIT
For similar results in TiN films see : T. Baturina, et al. PRL (2007)
V. F. Gantmakher et al., JETP 82, 951 (1996)
0.20K
SuperconductorSuperconductor
Magnetic field-tuned SITMagnetic field-tuned SIT
0.20K
InsulatorInsulator
Positive magnetoresistance at low field :
Superconducting correlations in insulators !?
SuperconductorSuperconductor
Magnetic field-tuned SITMagnetic field-tuned SIT
0.20K
InsulatorInsulator
Positive magnetoresistance at low field :
Superconducting correlations in insulators !?
« Insulating correlations » in superconductors ???
SuperconductorSuperconductor
Magnetic field-tuned SITMagnetic field-tuned SIT
E
µL
µR
NR(E)NL(E)
TipTip SampleSample
2ΔeV
E
µL
µR
NR(E)NL(E)
TipTip SampleSample
2ΔeV
mK-STM setup : tunneling spectroscopymK-STM setup : tunneling spectroscopy
Cryostat : inverted dilution
50mK< T< 6K
C. Chapelier’s setup, CEA Grenoble
Combined transport and spectroscopy measurements
Thickness : 15 nm (blue) and 30 nm (red)
3D regime
Samples : e-gun evaporation onto Si/SiO2 substrate of high purity In2O3 under O2 pressure
1 mm
InO#1
InO#2
AmorphousAmorphous Indium Oxyde (a-InO Indium Oxyde (a-InOxx))
Thickness : 15 nm (blue) and 30 nm (red)
3D regime
1 mm
InO#1
InO#2
AmorphousAmorphous Indium Oxyde (a-InO Indium Oxyde (a-InOxx))
V. F. Gantmakher et al., JETP 82, 951 (1996)
Samples : e-gun evaporation onto Si/SiO2 substrate of high purity In2O3 under O2 pressure
Fit : s-wave BCS density-of-states
Typical spectrum measured at 50 mKTypical spectrum measured at 50 mKInO#1
Tunneling spectroscopy of amorphous indium oxydeTunneling spectroscopy of amorphous indium oxyde
Inhomogeneities of Inhomogeneities of ΔΔ(r)(r)
Map of the spectral gapMap of the spectral gap
8%
Gaussian distribution
For similar results in TiN and NbN films see :
B. Sacépé, et al. PRL 101, 157006 (2008)
M. Mondal, et al. PRL 106, 047001 (2011)
Spectra measured at different locations Spectra measured at different locations (T=50mK)(T=50mK)
G,
Nor
mal
ized
G,
Nor
mal
ized
Inhomogeneities of Inhomogeneities of ΔΔ(r)(r)
Gaussian distribution
8%
For similar results in TiN and NbN films see :
B. Sacépé, et al. PRL 101, 157006 (2008)
M. Mondal, et al. PRL 106, 047001 (2011)
BCS ratio BCS ratio ΔΔ/T/Tcc =1.76 =1.76 ? ?
Fluctuations of Fluctuations of ΔΔ(r) and superconducting transition(r) and superconducting transition
Fluctuations of Fluctuations of ΔΔ(r) and superconducting transition(r) and superconducting transition
Definition of Tc : zero-resistance state (macroscopic phase coherence)
2 ( )6 11 !?
c
r
T
G, N
orm
aliz
edG
, Nor
mal
ized
Fluctuations of peak heights !Fluctuations of peak heights !
Fluctuations of the BCS peaksFluctuations of the BCS peaks
( ) ( )
( )
G G eVR
G eV
Fluctuations of the BCS peaksFluctuations of the BCS peaks
( ) ( )
( )
G G eVR
G eV
Fluctuations of the BCS peaksFluctuations of the BCS peaks
Fluctuations of the BCS peaksFluctuations of the BCS peaks
0!?R
Extreme case : « Insulating » gap Extreme case : « Insulating » gap
Spectra measured at different locations Spectra measured at different locations (T=50mK)(T=50mK)
0!?R
G,
Nor
mal
ized
G,
Nor
mal
ized
High disordersample
Let’s approach the SITLet’s approach the SIT
( ) ( )
( )
G G eVR
G eV
Sample InO#2 : disorder Sample InO#2 : disorder 2 2
InO#1
InO#2
resistivity × 2
8%
InO#1Tc ~ 1.7 K
InO#2Tc ~ 1.3 K
16%
Proliferation of gaps without peaksProliferation of gaps without peaks
Let’s approach the SITLet’s approach the SIT
Increase of disorderIncrease of disorder
InO#1
InO#2
λ
Superconductivity and disorderSuperconductivity and disorder
With increasing disorder : Superconductivity becomes « granular-like » Spectral gap remains finite even at large disorder Spectral gap is NOT anymore the SC order parameter
λ
Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave SuperconductorRole of Spatial Amplitude Fluctuations in Highly Disordered s-Wave SuperconductorA. Ghosal, M. Randeria, N. Trivedi, PRL 81, 3940, (1998) and PRB 6565, 014501 (2001)
λ
Insulating gap induced by pairing interactionInsulating gap induced by pairing interaction
λ
Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave SuperconductorRole of Spatial Amplitude Fluctuations in Highly Disordered s-Wave SuperconductorA. Ghosal, M. Randeria, N. Trivedi, PRL 81, 3940, (1998) and PRB 6565, 014501 (2001)
Superconductivity and disorderSuperconductivity and disorder
M. Ma, and P. A. Lee, PRB 32, 5658, (1985)M. Feigel’man, et al., PRL 98, 027001, (2007)M. Feigel’man, et al, Ann. Phys. 325, 1390 (2010)M. Feigel’man, et al, PRB (2010)
3~gap loc
loc
E
Insulating gap due to pairingInsulating gap due to pairing
P. W. Anderson, J. Phys. (Paris) Colloq. 37, C4-339 (1976)
M. Ma, and P. A. Lee, PRB 32, 5658, (1985)
K. A. Matveev and A. Larkin, PRL. 78, 3749, (1997)
A. Ghosal, et al. PRL 81, 3940, (1998) and PRB 6565, 014501 (2001)
M. Feigel’man, et al. PRL 98, 027001, (2007)
M. Feigel’man, et al. Ann. Phys. 325, 1390 (2010)
M. Feigel’man, et al. PRB 82, 184534 (2010)
In the lowest order:
2~ D
locgapE
3~gap loc
loc
E
† † †j j j jk j j k k
j jk
H c c M c c c c
Reduced BCS Hamiltonian built on eigenstates of the Anderson problem
2 2jk j kM dr with
In the high-disorder regime when
43
1( )jk jk j jk
loc
M dr r
loc
λ
Insulating gap induced by pairing interactionInsulating gap induced by pairing interaction
λ
Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave SuperconductorRole of Spatial Amplitude Fluctuations in Highly Disordered s-Wave SuperconductorA. Ghosal, M. Randeria, N. Trivedi, PRL 81, 3940, (1998) and PRB 6565, 014501 (2001)
Superconductivity and disorderSuperconductivity and disorder
M. Ma, and P. A. Lee, PRB 32, 5658, (1985)M. Feigel’man, et al., PRL 98, 027001, (2007)M. Feigel’man, et al, Ann. Phys. 325, 1390 (2010)M. Feigel’man, et al, PRB (2010)
3~gap loc
loc
E
Superconductivity and disorderSuperconductivity and disorder
Recent QMC simulationsRecent QMC simulationsK. Bouadim, Y. Loh, M. Randeria, N. Trivedi, arXiv:1011.3275
Dis
orde
rD
isor
der
SC
Insulator
Pairing gap in the insulatorPairing gap in the insulator
resis
tivity
× 2
Proliferation of incoherent –localized— Cooper-pairs Proliferation of incoherent –localized— Cooper-pairs
when approaching the SIT when approaching the SIT
Pairing gap in the insulatorPairing gap in the insulator
resis
tivity
× 2
Proliferation of incoherent –localized— Cooper-pairs Proliferation of incoherent –localized— Cooper-pairs
when approaching the SIT when approaching the SIT
Simulations on the Bethe latticeSimulations on the Bethe latticeLev Ioffe, Misha Feigel’man
M. Feigel’man, et al., PRL (2007)M. Feigel’man, et al, Ann. Phys. (2010)M. Feigel’man, et al, PRB (2010)
Tc
Pseudogap above TPseudogap above Tcc : preformed pairs : preformed pairs
T-dependence of the local DOST-dependence of the local DOS
Pseudogap in TiN and NbN films :
B. Sacépé, et al. Nature Commun. 1:140 (2010)
M. Mondal, et al. PRL 106, 047001 (2011)
Pseudogap in quasi-2D conventional superconductorsPseudogap in quasi-2D conventional superconductors
A. Varlamov and V. Dorin, Sov. Phys. JETP 57, 1089, (1983)
B. Sacépé, et al. Nature Commun. 1:140 (2010)
Superconducting fluctuations in quasi-2D TiN films ( thickness < 5nm )
Local versus macroscopic phase coherenceLocal versus macroscopic phase coherence
Tpeak : Temperature below which peaks start to grow
BCS peaks give a local signature of the superconducting phase coherence BCS peaks give a local signature of the superconducting phase coherence
BCS peaks appears at Tc BCS peaks appears at Tc
independently of gap inhomogeneitiesindependently of gap inhomogeneities
« Insulating » gap at T<<T« Insulating » gap at T<<Tcc
Local pairing without phase coherence at T << Tc
Formation of a pseudogap without BCS peaks at T>TFormation of a pseudogap without BCS peaks at T>Tcc
Local pairing without phase coherence at T > Tc
Spectral signature of localized Cooper pairs
Preformed Cooper-pairs
Condensation versus localization of preformed Cooper pairsCondensation versus localization of preformed Cooper pairs
ConclusionsConclusions
Localization of preformed Cooper pairs in disordered superconductors
Nature Physics 7, 239 (2011)
• Preformed Cooper-Pairs above TcPseudogap in the DOS between Tc and ~ 3-4 Tc
• “Partial” condensation of pairs below Tc
Rectangular spectra at 50mK = localized Cooper pairs
• SIT occurs through the localization of Cooper pairsGap in the DOS remains & coherence peaks disappear
Disorder-enhanced Coulomb interactionDisorder-enhanced Coulomb interaction
B. Altshuler, et al., Phys. Rev. Lett. 44, 1288, (1980)
Coulomb interaction : Zero-Bias AnomalyCoulomb interaction : Zero-Bias Anomaly
Soft coulomb gapSoft coulomb gap
Superconducting fluctuationsSuperconducting fluctuations
We need a global theoryWe need a global theory !
ln lni c
T
G T
TiN 1
Quantum corrections to the DOSQuantum corrections to the DOS
TR
A
Q
ln0
Superconducting fluctuationsSuperconducting fluctuations (2D Aslamasov-Larkin correction (2D Aslamasov-Larkin correction
…)…)
Disorder-enhanced Coulomb interactionDisorder-enhanced Coulomb interaction(2D weak-localization/Aronov-Altshuler (2D weak-localization/Aronov-Altshuler
corrections)corrections)
Quantum corrections to the conductivityQuantum corrections to the conductivity
Dynamical Coulomb blockadeDynamical Coulomb blockade
P. Joyez and D. Estève, PRB 56, 1848, (1997)
Magnetic field-tuned SITMagnetic field-tuned SIT
Huge magnetoresistance peak : superconductivity-related ?
Amorphous indium oxydeAmorphous indium oxyded = 15 nmd = 15 nm
Spectral gap map Coherence peak map
Spectral fluctuationsSpectral fluctuations
Disorder-induced inhomogeneities in TiNDisorder-induced inhomogeneities in TiN
B. Sacépé, et al. PRL 101, 157006 (2008)
Titanium nitrideT. Baturina (Novosibirsk)V. Vinokur (Argonne National Lab.)
Gaped insulator Gaped insulator made of localized made of localized Cooper pairs ?Cooper pairs ?
Disorder-tuned SIT in ultra-thin films of TiN Disorder-tuned SIT in ultra-thin films of TiN
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