Benjamin Sacépé Benjamin Sacépé Institut Néel, CNRS & Université Joseph Fourier, Grenoble Localization of preformed Localization of preformed Cooper-pairs Cooper-pairs in disordered superconductors in disordered superconductors Lorentz Center, Leiden 2011
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Benjamin Sacépé Institut Néel, CNRS & Université Joseph Fourier, Grenoble Localization of preformed Cooper-pairs in disordered superconductors Lorentz.
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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
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)