Scaling Analysis of Magnetic-Field-Tuned Phase Transitions in One-Dimensional Josephson Junction Arrays

Kuo, Wu‐Hsien; Chen, Chin-Der

doi:10.1103/physrevlett.87.186804

Cited by 36 publications

(45 citation statements)

References 19 publications

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“…This provides a posteriori justification of the approximation used to obtain G S (T,B). The value of the critical exponent z≈ 2 predicted by the pair-breaking critical theory is distinct from the z≈ 1 value typically associated with the Bose insulator state 2,10 that was observed experimentally in MoGe films 17 and 1D Josephson junction arrays 27 . The pair-breaking frequency α in 1D superconductors with strong spin-orbit scattering can be related to magnetic field as α = kB 2 , where the coefficient k contains both spin and orbital contributions and depends on the orientation of the field (see Supplementary Information for more details).…”

Section: Letterscontrasting

confidence: 54%

Pair-breaking quantum phase transition in superconducting nanowires

et al. 2018

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Quantum phase transitions (QPT) between distinct ground states of matter are widespread phenomena [1][2][3][4][5] , yet there are only a few experimentally accessible systems 6,7 where the microscopic mechanism of the transition can be tested and understood. These cases are unique and form the experimentally established foundation for our understanding of quantum critical phenomena. Here we report that a magnetic-fielddriven QPT in superconducting nanowires-a prototypical one-dimensional system (d= 1)-can be fully explained by the critical theory 8,9 of pair-breaking transitions characterized by a correlation length exponent v≈1 and dynamic critical exponent z≈ 2. We find that in the quantum critical regime, the electrical conductivity is in agreement with a theoretically predicted scaling function and, moreover, that the theory quantitatively describes the dependence of conductivity on the critical temperature, field magnitude and orientation, nanowire crosssectional area, and microscopic parameters of the nanowire material. At the critical field, the conductivity follows a T Quantum phase transitions occur in many systems, including magnetic materials 1 , superconductors [13][14][15] , cold atomic gases 3 and also atomic nuclei 4 and stars 5. Similar to the thermal fluctuations in classical temperature-driven phase transitions, strong quantum fluctuations near the critical point of a QPT lead to the emergence of universal long-range behaviour, which can be common in very diverse systems. However, for a complete description of a QPT one must also identify and quantitatively incorporate into a theory specific microscopic processes which drive a system across the critical point and induce the fluctuations. Examples where such complete theories can be experimentally tested are scarce and include the two-channel Kondo effect in quantum dots 7 and Luttinger liquid behaviour in materials composed of weakly coupled one-dimensional (1D) spin-chains 6 . Superconducting systems present special interest in the context of QPTs because the fluctuations near the critical point can lead to the formation of unconventional superconducting phases (most notably this is one of the scenarios for high-temperature superconductivity in the cuprates 16 ). They also present a challenge-despite many years of efforts and overall success of phenomenological finite-size scaling analyses 2,13,14,17 , the microscopic mechanism of QPTs in 2d superconductors is still debated. In contrast, the physics of a QPT becomes much more transparent in 1D superconductors.Here we show that essentially all long-range and microscopic characteristics of a QPT driven in superconducting nanowires by a magnetic field can be described by a pair-breaking critical theory.A 1D superconductor can be defined as a wire with diameter smaller than π 2 1/2 ξ(0), where ξ(0) is the zero-temperature Ginzburg-Landau coherence length 18 . This condition ensures that vortices do not form within the wire and that the superconducting order parameter is approximately constant at a...

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Section: Letterscontrasting

confidence: 54%

Pair-breaking quantum phase transition in superconducting nanowires

et al. 2018

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“…The proposed experimental setup could be used to investigate systematically the superconductor-insulator transition in a 1DJJA under better controlled experimental conditions as compared to other setups used in the past. [14][15][16][17] In addition, our results could also be applied to other 1D superconducting systems showing a similar behavior, such as ultrathin superconducting wires built by molecular templating 8,10,51 or by e-beam lithography 52 techniques. In those systems, it is experimentally challenging to vary in situ the parameters controlling the SIT, in contrast to 1DJJAs where the effective Josephson energy E J is tuned via external magnetic fields.…”

Section: Discussionmentioning

confidence: 72%

“…1,2 In particular, an intriguing superconductor-to-insulator phase transition (SIT) 3,4 has been observed experimentally in superconducting films, [5][6][7] wires, [8][9][10] and in ultrasmall-capacitance Josephsonjunction arrays (JJAs) in two [11][12][13] and one dimensions. [14][15][16][17] In the case of one-dimensional (1D) superconductors, one special kind of excitation, the so-called quantum phase slip (QPS) processes, have been the focus of an intense research due to both their putative role in the SIT in one dimension, 18 as well as for their potential uses in novel qubit architectures, 19 a fact that has motivated recent experimental research in 1DJJAs. 20,21 More generally, a phase slip is a discrete process in a 1D superconductor in which the amplitude of the order parameter temporarily vanishes at a particular point, allowing the phase θ to change abruptly in units of 2π .…”

Section: Introductionmentioning

confidence: 99%

Superconductor-to-insulator transition in linear arrays of Josephson junctions capacitively coupled to metallic films

Lobos¹,

Giamarchi²

2011

Phys. Rev. B

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We study the low-temperature properties of linear Josephson-junction arrays capacitively coupled to a proximate two-dimensional diffusive metal. Using bosonization techniques, we derive an effective model for the array and obtain its critical properties and phases at T = 0 using a renormalization-group analysis and a variational approach. While static screening effects given by the presence of the metal can be absorbed in a renormalization of the parameters of the array, backscattering originated in the dynamically screened Coulomb interaction produces a nontrivial stabilization of the insulating ground state and can drive a superconductor-to-insulator transition. We study the consequences for the transport properties in the low-temperature regime. In particular, we calculate the resistivity as a function of the temperature and the parameters of the array, and obtain clear signatures of a superconductor-to-insulator transition that could be observed in experiments.

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“…[2][3][4][5][6] In addition to the condition of R S >dR Q , there is a threshold value of the E J /E C below which the insulating properties † are observed. The threshold of E J /E C becomes larger as the R S increases, and in the limit R S →∞, i.e., in unshunted arrays, it is 2.2 − 4.2 for 1D arrays, [9][10][11] and 0.2 − 0.8 for 2D arrays. 1,8) The difference in the threshold is consistent with a prediction that 1D arrays have a larger magnitude of quantum fluctuation of the order parameter phases and hence have a stronger tendency to become insulating.…”

Section: Methodsmentioning

confidence: 99%

Experimental Studies on Cooper Pair Transport in Josephson Junction Arrays

et al. 2003

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We have investigated how the transport properties of small-Josephson-junction arrays vary depending on a quantum control parameter (the ratio of the Josephson coupling energy E J to the charging energyE C ), the magnitude of dissipation, and the dimensionality d of the system. We found that the arrays show Coulomb blockade behavior when R S is larger than about dR Q (R Q ≡h/4e 2 = 6.45 kΩ) and E J /E C is smaller than a threshold depending on the value of R S and the dimensionality. The result is discussed in terms of quantum phase transition induced by the charging effect and the dissipation.

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Scaling Analysis of Magnetic-Field-Tuned Phase Transitions in One-Dimensional Josephson Junction Arrays

Cited by 36 publications

References 19 publications

Pair-breaking quantum phase transition in superconducting nanowires

Pair-breaking quantum phase transition in superconducting nanowires

Superconductor-to-insulator transition in linear arrays of Josephson junctions capacitively coupled to metallic films

Experimental Studies on Cooper Pair Transport in Josephson Junction Arrays

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