Single- and two-particle energy gaps across the disorder-driven superconductor–insulator transition

Bouadim, Karim; Loh, Yen Lee; Randeria, Mohit; Trivedi, Nandini

doi:10.1038/nphys2037

Cited by 212 publications

(242 citation statements)

References 62 publications

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“…Following this relationship, the experiments on the B-SIT and the experiments tuning the carrier density form a dual set of experiments. Interestingly, this analogy implies that the disorder-driven SIT at B = 0 must have a different mechanism for the insulating state; a distinction that cannot be made from experiments: Transport and scanning tunnelling experiments [24][25][26] as well as microscopic model calculations 27,28 suggest that Cooper pairs persist also in the disorder-driven insulating state.…”

Section: T0/2tmentioning

confidence: 99%

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

et al. 2013

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The superconductor-insulator transition (SIT) is an accessible quantum phase transition 1,2 that is observed in a number of systems and can be driven by various experimental means 3-9 . A central outstanding issue regards the physical nature of the insulating phase terminating superconductivity 10 . Theoretical advances led to the proposition that this insulator is a new state of matter, termed a superinsulator 11,12 , because its properties can be inferred from the superconductor by invoking duality symmetry 13 . Here we report on the observation of duality symmetry near the magnetic-field-driven SIT in amorphous indium oxide. However, we show that the symmetry is broken by the emergence of the strong insulating state at low temperature.For the magnetic-field-driven SIT (B-SIT) in disordered films, the concept of vortex-charge duality was investigated in ref. 14, using the dirty boson model. In the superconductor, Cooper pairs are condensed into a superfluid at low temperature (T ) values leading to a zero resistivity (ρ) state, with vortices as bosonic excitations introducing dissipation and causing finite ρ. According to the duality concept, in the insulating state, vortices are condensed in a collective mode with zero conductivity (σ ), and the Cooper pairs are the bosonic excitation contributing to a finite σ .The vortex-charge duality has also been applied to the analysis of Josephson junction arrays 15,16 , which are often used as a model system for the SIT in disordered films 11,12,17 . In these systems the insulating state is commonly ascribed to a Coulomb blockade of superconducting islands. Duality is also applied to many other systems, for example, boson duality in two-dimensional electron gases 18 . Recently, evidence for the vortex-charge duality near a SIT was found in LaAlO 3 /SrTiO 3 interfaces 13 .Here, we experimentally investigate the duality symmetry across the B-SIT. We apply a duality transformation relating states within the superconductor to states in the B-driven insulator. We observe vortex-charge duality symmetry that holds up to one order of magnitude in B, T and ρ. The new aspect of this work is that we find systematic deviations from duality symmetry that originate in the B-induced magnetoresistance (ρ(B)) peak 5 . These deviations are qualitatively different at low and high T , as will be shown in detail below.In Fig. 1 we present ρ(B) isotherms obtained from sample RAM005b, which is superconducting at B = 0 with T c = 1.3 K. For all T values where reliable Ohmic data could be collected ρ increases with B until it reaches a T -dependent peak at B peak between 8.5-9.7 T. We restrict ourselves to T > 0.15 K because in the insulating phase, at T < 0.15 K, severe bi-stability of the electron T develops 19 , resulting in strongly nonlinear I -V , that prevented reliable measurements of ρ.The isotherms exhibit a weakly T -dependent crossing point close to h/(2e) 2 , where h is Planck's constant and 2e is the charge

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Section: T0/2tmentioning

confidence: 99%

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

et al. 2013

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“…[18][19][20][21][22][23][24][25][26] These hamiltonians then are either treated within a standard Bogoljubov-de Gennes approximation 19,[21][22][23]25,26 or with more sophisticated approaches like Monte-Carlo methods. 18,20,24 Bosonic models are then obtained from a large-U expansion, as e.g. the pseudospin XY model in a transverse field 29 , where the hopping of Cooper pairs (corresponding to pseudospins aligned in the XY plane) competes with localization due to random fields (corresponding to pseudospins aligned in the perpendicular direction).…”

Section: Introductionmentioning

confidence: 99%

Amplitude, density, and current correlations of strongly disordered superconductors

2015

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We investigate the disorder dependence of the static density, amplitude and current correlations within the attractive Hubbard model supplemented with on-site disorder. It is found that strong disorder favors a decoupling of density and amplitude correlations due to the formation of superconducting islands. This emergent granularity also induces an enhancement of the density correlations on the SC islands whereas amplitude fluctuations are most pronounced in the 'insulating' regions. While density and amplitude correlations are short-ranged at strong disorder we show that current correlations have a long-range tail due to the formation of percolative current paths in agreement with the constant behavior expected from the analysis of one-dimensional models.

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“…[1-3, 6-10] Recently, due to the availability of local scanning probes, attention has turned to the tunneling behavior [11][12][13][14][15]. In the case of the disorder-tuned SIT [15], it has become clear that the SIT is ultimately due to a bosonic mechanism [16] rather than a fermionic one [17]. The last step towards a full characterization of the SIT is to develop an understanding of the behavior of the AC conductivity.…”

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confidence: 99%

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Loh¹,

Dhakal²,

Neis³

et al. 2014

J. Phys.: Condens. Matter

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Random inductor-capacitor (LC) networks can exhibit percolative superconductor-insulator transitions (SITs). We use a simple and efficient algorithm to compute the dynamical conductivity σ(ω, p) of one type of LC network on large (4000 × 4000) square lattices, where δ = p − pc is the tuning parameter for the SIT. We confirm that the conductivity obeys a scaling form, so that the characteristic frequency scales as Ω ∝ |δ| νz with νz ≈ 1.91, the superfluid stiffness scales as Υ ∝ |δ| t with t ≈ 1.3, and the electric susceptibility scales as χE ∝ |δ| −s with s = 2νz − t ≈ 2.52. In the insulating state, the low-frequency dissipative conductivity is exponentially small, whereas in the superconductor, it is linear in frequency. The sign of Im σ(ω) at small ω changes across the SIT. Most importantly, we find that right at the SIT Re σ(ω) ∝ ω t/νz−1 ∝ ω −0.32 , so that the conductivity diverges in the DC limit, in contrast with most other classical and quantum models of SITs. [4,5]. As a quantum phase transition occurring at zero temperature, this superconductor-insulator transition (SIT) has attracted much interest. Early work focused on the most easily measurable quantity, the DC conductivity.[1-3, 6-10] Recently, due to the availability of local scanning probes, attention has turned to the tunneling behavior [11][12][13][14][15]. In the case of the disorder-tuned SIT [15], it has become clear that the SIT is ultimately due to a bosonic mechanism [16] rather than a fermionic one [17]. The last step towards a full characterization of the SIT is to develop an understanding of the behavior of the AC conductivity. This is a powerful probe of fluctuations on both long and short length and time scales, and it is of great interest especially as recent technological developments begin to open up more windows of the electromagnetic spectrum for measurement [18][19][20][21].One of the most important questions concerns the AC conductivity in the "collisionless DC" limit [22,23] [52], σ * = lim ω→0 lim T →0 σ(ω, T ). This has been the subject of a large body of work, including analytical arguments involving charge-vortex duality arguments, quantum Monte Carlo calculations in various representations, and experiments [1,4,16,23,[25][26][27][28][29][30][31][32]. It is often claimed that at the SIT σ * is finite and takes a universal value of the order of σ Q = 4e 2 /h, but there are large discrepancies between the "universal" values from various studies, and it is not clear whether there really is a universal value.

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Single- and two-particle energy gaps across the disorder-driven superconductor–insulator transition

Cited by 212 publications

References 62 publications

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

Amplitude, density, and current correlations of strongly disordered superconductors

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

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