Resistive transition in frustrated Josephson-junction arrays on a honeycomb lattice

We isolated flux disorder effects on the transport at the critical point of the quantum magnetic field tuned Superconductor to Insulator transition (BSIT). The experiments employed films patterned into geometrically disordered hexagonal arrays. Spatial variations in the flux per unit cell, which grow in a perpendicular magnetic field, constitute flux disorder. The growth of flux disorder with magnetic field limited the number of BSITs exhibited by a single film due to flux matching effects. The critical metallic resistance at successive BSITs grew with flux disorder contrary to predictions of its universality. These results open the door for controlled studies of disorder effects on the universality class of an ubiquitous quantum phase transition.Transport phenomena near quantum critical points receive ongoing scrutiny. Much attention comes from efforts to understand strange metal behavior in high T c [1,2] and heavy fermion compounds [3,4]. Others who are developing string theory based techniques to calculate many body properties of condensed matter in the strong coupling limit have focussed on quantum critical transport as well [5][6][7]. An interesting case is the superfluid to insulator transition in charged two dimensional systems such as superconducting films. This Superconductor to Insulator transition (SIT) appears in numerous thin film systems [8,9] as a change from superconducting to insulating transport when a physical parameter such as thickness [10,11] magnetic field [12] or a gating field [13][14][15][16] is tuned. At the critical value of the tuning parameter, film resistances asymptote to a constant value in the zero frequency, low temperature limit. The limiting critical resistance assumes a value near the quantum of resistance for electron pairs R c ∼ h 4e 2 = R Q [8,9]. Despite the simplicity of this behavior, questions remain regarding its universality and the influence of disorder.Indeed, the critical resistance near a superconductor to insulator transition is at the heart of studies, both theoretical and experimental. Fisher [17] and collaborators [18] provided the original arguments supporting the universality of R c . They focussed on bosonic systems presuming that fermion degrees of freedom in the form of unpaired electrons play no role. They argued that R c is likely to be constant in ordered systems within a universality class [18] especially in magnetic field. Disorder appeared to lead to an increase in R c . Numerical simulations [19,20] that R c grows with the normal state resistance, which is a similar measure of disorder. In both cases R c assumes values that are about a factor of two higher than observed in the most ordered systems, micro-fabricated Josephson Junction Arrays (JJA) [26,27]. Such an elaborate picture reflects the variety of approaches and systems employed to study R c . It suggests that deriving a new method for controllably varying disorder and selecting a thin film system with a bosonic SIT is crucial to making further experimental progress.Opportunities to care...

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“…Quantum superconductor to insulator transitions [52] are evident in the magneto-resistance oscillations in Figs. 1c,g.…”

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confidence: 92%

“…Quantum superconductor to insulator transitions [52] perconducting sides of the SIT, respectively (cf. Ref.…”

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confidence: 99%

Disorder influences the quantum critical transport at a superconductor-to-insulator transition

et al. 2015

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“…Recently, however, there has been a growing interest in a related system, in the form of an ultra-thin superconducting film with a triangular lattice of nanoholes [18][19][20][21][22] . A simple model for this system consists of a Josephson-junction array on a honeycomb lattice, with the triangular lattice of nanoholes corresponding to the dual lattice, and it has already been used to investigated the thermal resistive transition in absence of charging effects 17 . Nevertheless, quantum phase fluctuations should be taken into account since the system undergoes a superconductor to insulator transition for decreasing film thickness.…”

Section: Introductionmentioning

confidence: 99%

“…For the honeycomb array, however, the dual lattice is triangular and the resulting vortex lattice is incommensurate, with a macroscopically degenerate ground state 24 . Thermal fluctuations leads to unusual phase-coherence and vortex-order transitions as a function of temperature, which has been investigated both analytically 25,26 and numerically 17,24,[27][28][29] but are still not well understood. However, the phase-coherence and vortex-order transitions at zero temperature for increasing quantum phase fluctuations have not been investigated in detail.…”

Section: Introductionmentioning

confidence: 99%

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

Granato

2016

Eur. Phys. J. B

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We study the superconductor to insulator transition at zero temperature in a Josephson-junction array model on a honeycomb lattice with f flux quantum per plaquette. The path integral representation of the model corresponds to a (2+1)-dimensional classical model, which is used to investigate the critical behavior by extensive Monte Carlo simulations on large system sizes. In contrast to the model on a square lattice, the transition is found to be first order for f = 1/3 and continuous for f = 1/2 but in a different universality class. The correlation-length critical exponent is estimated from finite-size scaling of vortex correlations. The estimated universal conductivity at the transition is approximately four times its value for f = 0. The results are compared with experimental observations on ultrathin superconducting films with a triangular lattice of nanoholes in a transverse magnetic field.

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“…In fact, it is closely related to the Bose-Hubbard model, where Cooper pairs interact on a lattice potential, in the limit of a large number of bosons per site 8,12 , to the quantum rotor model [12][13][14] and to ultracold atoms on optical lattices [15][16][17] . For a periodic nanohole film at low magnetic fields, the simplest model consists of a frustrated array of superconducting "grains", where the phase is well defined locally, coupled by Josephson junctions or weak links on a periodic lattice, with the lattice of nanoholes corresponding to the dual lattice, which acts as a vortex pinning center 18,19 . The number of flux quanta per unit cell of the nanohole lattice, which is proportional to the external magnetic field, corresponds to the frustration parameter f of the Josephson-junction array model.…”

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Magnetic flux disorder and superconductor-insulator transition in nanohole thin films

Granato

2016

Phys. Rev. B

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We study the superconductor-insulator transition in nanohole ultrathin films in a transverse magnetic field by numerical simulation of a Josephson-junction array model. Geometrical disorder due to the random location of nanoholes in the film corresponds to random flux in the array model. Monte Carlo simulation in the path-integral representation is used to determine the critical behavior and the universal resistivity at the transition as a function of disorder and average number of flux quanta per cell, fo. The resistivity increases with disorder for noninteger fo while it decreases for integer fo, and reaches a common constant value in a vortex-glass regime above a critical value of the flux disorder D There is growing interest in the superconductorinsulator (SI) transition in ultra-thin films with a lattice of nanoholes [1][2][3][4][5][6] . This system is an important testing ground for models of the universality class of the quantum phase transition since the patterned nanostructure provides a sensitive probe for distinguishing between phase and amplitude fluctuations of the superconducting order parameter. The magnetoresistance oscillatory behavior at low magnetic fields near the transition is analogous to the one observed in microfabricated Josephsonjunction arrays, which undergo a SI transition due to the small electrical capacitance of the superconducting grains 7-11 . This common feature results from phase coherence effects, which can be described by the same generic model of phase fluctuations of the superconducting order parameter, a Josephson-junction array model, with a wider applicability. In fact, it is closely related to the Bose-Hubbard model, where Cooper pairs interact on a lattice potential, in the limit of a large number of bosons per site 8,12 , to the quantum rotor model [12][13][14] and to ultracold atoms on optical lattices 15-17 . For a periodic nanohole film at low magnetic fields, the simplest model consists of a frustrated array of superconducting "grains", where the phase is well defined locally, coupled by Josephson junctions or weak links on a periodic lattice, with the lattice of nanoholes corresponding to the dual lattice, which acts as a vortex pinning center 18,19 . The number of flux quanta per unit cell of the nanohole lattice, which is proportional to the external magnetic field, corresponds to the frustration parameter f of the Josephson-junction array model. The zero-temperature quantum phase transition in the array model, driven by the competition between the charging energy and Josephson-coupling energy at different frustration parameters, corresponds to the SI transition in the nanohole film in the external magnetic field. The resistivity at the transition is expected to be finite and universal 12,13,20,21 , depending only on the universality class of the transition, which generally changes in the presence of a magnetic field and disorder.Very recently, intriguing experimental results have been obtained near the SI transition in thin films with a disordered triangular l...

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Resistive transition in frustrated Josephson-junction arrays on a honeycomb lattice

Cited by 11 publications

References 46 publications

Disorder influences the quantum critical transport at a superconductor-to-insulator transition

Disorder influences the quantum critical transport at a superconductor-to-insulator transition

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

Magnetic flux disorder and superconductor-insulator transition in nanohole thin films

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