Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

Ling, Xinsheng; Lezec, Henri J.; Higgins, M. J.; Tsai, J. S.; Fujita, J.; Numata, Hideaki; Nakamura, Yuka; Ochiai, Yusuke; Tang, Chao; Chaikin, P. M.; Bhattacharya, S.

doi:10.1103/physrevlett.77.410

Cited by 7 publications

(18 citation statements)

References 3 publications

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“…In the LT phase the Z 2 chiral symmetry is broken and the spin degrees of freedom show the same quasi-long-range order as in the 2-d XY model. We conclusively show that the square-lattice FFXY model undergoes two very close but separate transitions: a KT and then, as temperature increases, an Ising transition with δ ≡ (T ch − T sp )/T ch = 0.0159 (2). The same transition pattern is observed in the φ 4 and IsXY models when the transitions are continuous.…”

Section: Introductionsupporting

confidence: 67%

“…where f (x) is approximated by a polynomial. Fits of the chiral variables R c and B c for L ≥ 200 give ν = 0.78 (2) and ν = 0.80(3) with a reasonable, though not good, χ 2 , i.e.…”

Section: Continuous Transitionsmentioning

confidence: 93%

“…where R (1) and R (2) are O(2) rotation matrices. It is possible to argue that in the IsXY model chiral and spin modes cannot be critical at the same value of J and C, see, e.g., Ref.…”

Section: Modelsmentioning

confidence: 99%

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Critical behavior of two-dimensional fully frustrated XY systems

Hasenbusch

Pelissetto

Vicari

2006

J. Phys.: Conf. Ser.

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We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices L × L, L 10 3 . We show that the lowtemperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent ν eff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.

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Section: Introductionsupporting

confidence: 67%

“…where f (x) is approximated by a polynomial. Fits of the chiral variables R c and B c for L ≥ 200 give ν = 0.78 (2) and ν = 0.80(3) with a reasonable, though not good, χ 2 , i.e.…”

Section: Continuous Transitionsmentioning

confidence: 93%

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Critical behavior of two-dimensional fully frustrated XY systems

Hasenbusch

Pelissetto

Vicari

2006

J. Phys.: Conf. Ser.

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“…We follow eqts. (3)(4)(5) for N = 2. The Φ k variables are: Φ k (y i ) = (Φ 1 = α, Φ 2 = β, Φ 3 = γ, Φ 4 = κ), and the matrix ω, which can be read from eqt.…”

Section: Construction Of the Potentialmentioning

confidence: 99%

“…We find the potentials realize tilted ratchets analogous to a combustion motor. The resistive behavior of a two dimensional Josephson array with a given frustration parameter (the ratio of the perpendicular magnetic field to the flux quantum per plaquette, f = Φ/Φ 0 , where Φ 0 = hc/2e), has been a matter of study [1][2][3][4][5]. When the external bias is zero, a mean field approach based quantum interference method can be used to obtain phase diagrams(see [6] and references therein), in which a localization without disorder [7,8] is exploited.…”

mentioning

confidence: 99%

Multidimensional washboard ratchet potentials for frustrated two-dimensional Josephson junctions arrays on square lattices

Rangel

Negruz

2016

J. Phys. A: Math. Theor.

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In this work, we derive an analytical procedure for obtaining a multidimensional washboard ratchet potential U f for two-dimensional Josephson junctions array (TDJJA) with an applied magnetic field. The magnetic field is given in units of the quantum flux per plaquette or frustration of the form f = M N . The derivation is done under the assumption that the checkerboard pattern ground state or unit cell of a two-dimensional Josephson junctions array (TDJJA) is preserved under current bias. The RCSJ with a white noise term models the dynamics for each junction phase in the array. The multidimensional potential is the unique expression of the collective effects that emerge from the array in contrast to the single junction. First step in the procedure is to write the equation for the phases for the unit cell by considering the constraints imposed for the gauge invariant phases due to frustration. Secondly and key idea of the procedure, is to perform a variable transformation from the original systems of stochastic equations to a system of variables where the condition for the equality of mixed second partial is forced via the Poincaré's theorem for differentials forms. This leads to a nonlinear matrix equation (equation ( 9) in the text), where the new coordinates variables x f are evaluated and where the potential exist. The transform matrix also permits the correct transformation of the original white noise terms of each junction to the intensities in the x f variables. The commensurate symmetries of the ground state pinned vortex lattice, leads to discrete symmetries to the part of the washboard potential that does not contain a tilt due to the external bias current(equation( 10) in the text). In this work we apply the procedure for the important cases f = 1 2 , 1 3 . For f = 1 2 , we show that previously efforts for finding the potential are restricted, leading to a reduced dimension of the potential. Our potential reduces to their expression, if one forces their assumption which represents an unstable situation. New physics emerge when currents are applied in the x and y directions, in particular, we confirm analytically previous numerical work for f = 1 2 , concerning the border of stationary states, a landmark of the potential. For f = 1 3 , we give a generalization of previous work, in which we include both the currents in the x and y directions as well the noise terms. We find the potentials realize tilted ratchets analogous to a combustion motor.

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Finite superconducting square wire-network based on two-dimensional crystalline Mo₂C

Liu¹,

Yang²,

Xu³

et al. 2022

Chinese Phys. B

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Superconducting wire-networks are paradigms to study Cooper pairing issues, vortex dynamics and arrangements. Recently, emergent low-dimensional crystalline superconductors are reported in the minimal-disorder limit, providing novel platforms to reveal vortices-related physics. Study on superconducting loops with high-crystallinity is thus currently demanded. Here, we report fabrication and transport measurement of finite square-network based on two-dimensional crystalline superconductor Mo2C. We observe oscillations in the resistance as a function of the magnetic flux through the loops. Resistance dips at both matching field and fractional fillings are revealed. Temperature and current evolutions are carried out in magnetoresistance to study vortex dynamics. The amplitude of oscillation is enhanced due to the interaction between thermally activated vortices and the currents induced in the loops. The driving current reduces effective activation energy for vortex, giving rise to stronger vortex interaction. Moreover, by thermally activated vortex creep model, we derive effective potential barrier for vortex dissipation, which shows well-defined correspondence with structures in magnetoresistance. Our work shows that low-dimensional crystalline superconducting network based on Mo2C possesses pronounced potential in studying the modulation of vortex arrangements and dynamics, paving the way for further investigations on crystalline superconducting network with various configurations.

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Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

Cited by 7 publications

References 3 publications

Critical behavior of two-dimensional fully frustrated XY systems

Critical behavior of two-dimensional fully frustrated XY systems

Multidimensional washboard ratchet potentials for frustrated two-dimensional Josephson junctions arrays on square lattices

Finite superconducting square wire-network based on two-dimensional crystalline Mo₂C

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Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

Cited by 7 publications

References 3 publications

Critical behavior of two-dimensional fully frustrated XY systems

Critical behavior of two-dimensional fully frustrated XY systems

Multidimensional washboard ratchet potentials for frustrated two-dimensional Josephson junctions arrays on square lattices

Finite superconducting square wire-network based on two-dimensional crystalline Mo2C

Contact Info

Product

Resources

About

Finite superconducting square wire-network based on two-dimensional crystalline Mo₂C