Superconductor-insulator quantum phase transition

Gantmakher, V. F.; Dolgopolov, V. T.

doi:10.3367/ufnr.0180.201001a.0003

Cited by 65 publications

(100 citation statements)

References 182 publications

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“…In the insulating state Cooper pairs with a finite amplitude are still present, but their global phase coherence is lost. Comprehensive review on SIT as a quantum phase transition [6] resumes that many characteristics in both scenarios are very similar and probably only a probe directly sensitive to the local variations of the superconducting energy gap/order parameter can discern the realized mechanism.The scanning tunneling microscope (STM) is a unique probe with such a capability. The available STM experiments on thin films of TiN, InO x and NbN [7][8][9][10][11][12][13] bring evidences that upon increasing disorder decreases more slowly than T c , the variation of on a scale of the superconducting coherence length  increases, a pseudogap appears above T c in the tunneling spectra, the spectral coherence peaks are suppressed, and the vortex lattice is fading out.…”

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Fermionic scenario for the destruction of superconductivity in ultrathin MoC films evidenced by STM measurements

et al. 2016

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We use sub-Kelvin scanning tunneling spectroscopy to investigate the suppression of superconductivity in homogeneously disordered ultrathin MoC films. We observe that the superconducting state remains spatially homogeneous even on the films of 3 nm thickness. The vortex imaging suggests the global phase coherence in our films. Upon decreasing thickness, when the superconducting transition drops from 8.5 to 1.2 K, the superconducting energy gap  follows perfectly T c . All this is pointing to a two-stage fermionic scenario of the superconductor-insulator transition (SIT) via a metallic state as an alternative to the direct bosonic SIT scenario with a Cooper-pair insulating state evidenced by the last decade STM experiments. [7][8][9][10][11][12][13] bring evidences that upon increasing disorder decreases more slowly than T c , the variation of on a scale of the superconducting coherence length  increases, a pseudogap appears above T c in the tunneling spectra, the spectral coherence peaks are suppressed, and the vortex lattice is fading out. This phenomenology strongly supports the bosonic scenario and raises the question about the universality of the bosonic SIT [14]. On the other hand, potential evidence for the fermionic mechanism was provided even sooner by the tunneling experiments on planar junctions on amorphous Bi and PbBi/Ge films [15,16] indicating that the Cooper pair amplitude vanishes at SIT. But the unambiguousness of these results was challenged by the fact that the spatially averaged tunneling spectra were gapless. This gaplessness could be explained by a very inhomogeneous gap distribution due to phase fluctuations. Then, superconducting pair correlations might also exist in insulators close to SIT, contradicting the fermionic scenario. KeywordsHere, we present sub-Kelvin STM experiments on ultra thin superconducting MoC films with atomic spatial resolution. We demonstrate the spatial homogeneity of the superconducting state for film thicknesses down to 3 nm and the closing of the superconducting energy gap/order parameter as T c vanishes, in agreement with the fermionic scenario. Thus, we bring the first direct evidence on the local behavior of the superconducting order parameter in this class of the transition.The MoC films were prepared by the magnetron reactive sputtering from a Mo target in an argon-acetylene atmosphere onto a sapphire c-cut substrate. The details can be found elsewhere [17]. The preparation followed the procedure of Lee and Ketterson [18] who manufactured continuous MoC films down to 0.4 nm thickness showing

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confidence: 99%

Fermionic scenario for the destruction of superconductivity in ultrathin MoC films evidenced by STM measurements

et al. 2016

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“…The interplay of superconductivity and localization has proven to be a rich and intriguing problem, especially in two dimensions [1][2][3][4][5][6][7]. Both paradigms stand on the shoulders of giants-the BCS theory of superconductivity and the Anderson theory of localization.…”

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Dynamical Conductivity across the Disorder-Tuned Superconductor-Insulator Transition

et al. 2014

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We calculate the dynamical conductivity σðωÞ and the bosonic (pair) spectral function PðωÞ from quantum Monte Carlo simulations across clean and disorder-driven superconductor-insulator transitions (SITs). We identify characteristic energy scales in the superconducting and insulating phases that vanish at the transition due to enhanced quantum fluctuations, despite the persistence of a robust fermionic gap across the SIT. Disorder leads to enhanced absorption in σðωÞ at low frequencies compared to the SIT in a clean system. Disorder also expands the quantum critical region, due to a change in the universality class, with an underlying T ¼ 0 critical point with a universal low-frequency conductivity σ Ã ≃ 0.5ð4e 2 =hÞ.

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“…At large density, however, excitons suffer a Mott transition to an electron-hole plasma 8 while Cooper pairs evolve toward a BCS superconducting condensate. The physics of this BEC-BCS crossover has also been shown to have some relevance for Cooper pairs in high-T c cuprates 9,10 .…”

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“…(10,11), as well as the definition of I 1 and I 2 , we can find the sum of z i at lowest order in γ. From it, we get the following expression for the energy of N -pair state…”

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“Moth-eaten effect” driven by Pauli blocking, revealed for cooper pairs

Pogosov

Combescot

2010

Jetp Lett.

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We extend the well-known Cooper's problem beyond one pair and study how this dilute limit is connected to the many-pair BCS condensate. We find that, all over from the dilute to the dense regime of pairs, Pauli blocking induces the same "moth-eaten effect" as the one existing for composite boson excitons. This effect makes the average pair binding energy decrease linearly with pair number, bringing it, in the standard BCS configuration, to half the single-pair value. This proves that, at odds with popular understanding, the BCS gap is far larger than the broken pair energy. The increase comes from Pauli blocking between broken and unbroken pairs. Possible link between our result and the BEC-BCS crossover is also discussed.PACS numbers: 74.20.Fg, 03.75.Hh, 67.85.Jk The continuous change from the dilute to the dense regime of correlated fermion pairs still is an open problem. Although this problem initially arose in the context of the microscopic theory of superconductivity 1-4 , its interest was recently renewed by increasing activity in ultra-cold atomic gases. The so-called BEC-BCS cross-over between the dilute Bose-Einstein condensate of molecules built out of two fermion-like atoms and the dense surperfluid state of atom pairs, is a current major question 5,6 . In the dilute regime, similarities between two-atom molecules and excitons should allow their description through a composite boson many-body formalism similar to the one we developed for excitons 7 . At large density, however, excitons suffer a Mott transition to an electron-hole plasma 8 while Cooper pairs evolve toward a BCS superconducting condensate. The physics of this BEC-BCS crossover has also been shown to have some relevance for Cooper pairs in high-T c cuprates 9,10 .In this Letter, we present a conceptually trivial but yet unveiled continuity between the Cooper's one-pair model 11 and the BCS superconductivity 12 . We do it by extending the Cooper's problem beyond the single pair limit. We start with a "frozen" Fermi sea |F 0 of noninteracting electrons and we increase the number of electron pairs, one by one, within a layer above |F 0 where the BCS potential acts. By using this approach, we can reach the BCS regime 13 continuously starting from the single pair limit.Although, at the present time, such a pair increase seems hard to experimentally achieve, the present analysis can at least be seen as a gedanken experiment to reveal a possible connection between two famous problems in order to more deeply understand the role of the Pauli exclusion principle in Cooper-paired states. This procedure can also be seen as a simple but well-defined toy model to shed some complementary light on the BEC-BCS crossover problem since, by changing the number of pairs, we do change their overlap.The extension of the Cooper's model beyond one pair faces a major many-body problem: the exact handling of the Pauli exclusion principle between a given number of composite particles made of fermion pairs. This can be the reason for this extension not to have be...

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Superconductor-insulator quantum phase transition

Cited by 65 publications

References 182 publications

Fermionic scenario for the destruction of superconductivity in ultrathin MoC films evidenced by STM measurements

Fermionic scenario for the destruction of superconductivity in ultrathin MoC films evidenced by STM measurements

Dynamical Conductivity across the Disorder-Tuned Superconductor-Insulator Transition

“Moth-eaten effect” driven by Pauli blocking, revealed for cooper pairs

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