Reentrant phase diagram for granular superconductors

Šimánek, E.

doi:10.1103/physrevb.32.500

Cited by 44 publications

(41 citation statements)

References 13 publications

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“…We also find that orientational order is short-ranged at low temperatures. The validity of our conclusion is supported by the fact that for the twodimensional model mean-field theory [9,10] is in agreement with quantum Monte Carlo [11,12] simulations on the overall shape of the phase diagram.…”

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confidence: 77%

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Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

2005

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We develop a multi order parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where ortho-para distinction is valid. We apply our formalism to solid H2 and D2. We find an anomalous reentrant orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As temperature is increased the correlation increases along the phase boundary. We also find that even extremely small odd-J concentrations (1%) can trigger short-range orientational ordering.PACS numbers: 61.43.-j,64.70.-p,67.65.+z Quantum effects dominate the low temperature (T < 200K) phase diagram of solid molecular hydrogen in a wide range of pressures from ambient up to ∼ 100 GPa [1,2]. In this regime the coupling between molecules is smaller than the molecular rotational constant, so quantum effects are generally described by means of weakly coupled quantum-rotor models [3]. Homonuclear molecules (H 2 and D 2 ) can assume only even or odd values of the rotational quantum number J, depending on the parity of the nuclear spin. Important differences exist in the phase diagrams of even-J (para-H 2 and ortho-D 2 ), odd-J (ortho-H 2 and para-D 2 ) and all-J (HD) species. (For a summary of experimental results on the orientational ordering in H 2 , D 2 , and HD see Fig. 1b of reference 4.) At low pressure or high temperature, even-J species are found in a rotationally disordered free-rotor state (phase I). Increasing pressure causes an increase of the intermolecular coupling, and eventually leads to an orientationally ordered state (phase II). Odd-J systems on the other hand are orientationally ordered at low temperature and ambient pressure and remain ordered as pressure is increased. The stronger tendency of ortho-H 2 to order can be traced to the fact that its J = 1 lowest rotational state allows for a spherically asymmetric ground state, unlike the J = 0 ground state of even-J species. The pressure-temperature phase diagram of HD exhibits a peculiar reentrant shape [5]. Reentrance refers to phase diagrams where in some range of pressure the system reenters the disordered phase at ultra-low temperatures (see HD in Fig. 1). The zero-temperature orientationally disordered phase is characterized by an energy gap against J = 1 excitations. When this gap is sufficiently small and the temperature is finite, the thermally generated J = 1 excitations suffice to induce ordering, which is then reentrant, as also shown by mean-field the- * Present address

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confidence: 77%

“…When this gap is sufficiently small and the temperature is finite, the thermally generated J = 1 excitations suffice to induce ordering, which is then reentrant, as also shown by mean-field the- ory [6,7,8]. Reentrance is also found in models of twodimensional rotors [9], such as the quantum anisotropic planar rotor (QAPR) model [10,11,12].…”

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confidence: 90%

Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

2005

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“…One of the most notorious of these is the possibility of having a low temperature instability of the superconducting state. A possible reentrant transition was originally found within a mean field theory treatment of the self-capacitive XY model [16,[20][21][22]]. An explicit twodimensional study of the self-capacitative XY model, within a WKB renormalization group (WKB-RG) analysis also found evidence of a low temperature reentrant instability, triggered by a quantum fluctuation induced proliferation of vortices [13].…”

Section: Introductionmentioning

confidence: 95%

“…A large number of studies, both experimental [2][3][4][5][6][7] and theoretical [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have been devoted to them. Initially, part of the interest in JJA came from their close relation to one of the most extensively studied theoretical spin models, i.e.…”

Section: Introductionmentioning

confidence: 99%

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

Rojas

José

1996

Phys. Rev. B

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We present results from an extensive analytic and numerical study of a twodimensional model of a square array of ultrasmall Josephson junctions. We include the ultrasmall self and mutual capacitances of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson, E J , as well as the charging, E C , energies between superconducting islands. The corresponding quantum partition function is expressed in different calculationally convenient ways within its path-integral representation. The phase diagram is analytically studied using a WKB renormalization group (WKB-RG) plus a self-consistent harmonic approximation (SCHA) analysis, together with non-perturbative quantum Monte Carlo simulations. Most of the results presented here pertain to the superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very good agreement between the WKB-RG and QMC results when compared to the experimental data. To fit the data, we only used the experimentally determined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low temperature instability i.e. a Quantum Induced Transition (QUIT). We carefully analyze the possible existence of the QUIT via the QMC simulations and carry out a finite size analysis of T QU IT as a function of the magnitude of imaginary time axis L τ . We find that for some relatively large values of α = E C E J (1 ≤ α ≤ 2.25), the L τ → ∞ limit does appear to give a non-zero T QU IT , while for α ≥ 2.5, T QU IT = 0. We use the SCHA to analytically understand the L τ dependence of the QMC results with good agreement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low temperature QUIT, up to lowest order in α −1 .

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“…While the classical APR model accounts for the orientational ordering, a more quantitative description of the system necessitates the inclusion of quantum effects [11]. Also, models of coupled quantum planar rotors are useful in describing other systems, such as granular superconductors [12,13,14,15,16,17] and more recently the bosonic Hubbard model [18,19].…”

Section: Introductionmentioning

confidence: 99%

2D and 3D Quantum Rotors in a Crystal Field: Critical Points, Metastability, and Reentrance

Freiman

Hetényi

Tretyak

2010

Metastable Systems Under Pressure

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An overview of results of models of coupled quantum rotors is presented. We focus on rotors with dipolar and quadrupolar potentials in two and three dimensions, potentials which correspond to approximate descriptions of real molecules adsorbed on surfaces and in the solid phase. Particular emphasis is placed on the anomalous reentrant phase transition which occurs in both two and three-dimensional systems. The anomalous behaviour of the entropy, which accompanies the reentrant phase transition, is also analyzed and is shown to be present regardless if a phase transition is present or not. Finally, the effects of the crystal field on the phase diagrams are also investigated. In two-dimensions the crystal field causes the disappearance of the phase transition, and ordering takes place via a continuous increase in the value of the order parameter. This is also true in three dimensions for the dipolar potential. For the quadrupolar potential in three dimensions turning on the crystal field leads to the appearance of critical points where the phase transition ceases, and ordering occurs via

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Reentrant phase diagram for granular superconductors

Cited by 44 publications

References 13 publications

Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

2D and 3D Quantum Rotors in a Crystal Field: Critical Points, Metastability, and Reentrance

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