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arXiv:cond-mat/9705223 · Physical review. B, Condensed matter

Onsager loop transition and first-order flux-line lattice melting in high- Tc superconductors

Anh Kiet Nguyen, Asle Sudbø

Published Feb 1, 1998• 58 citations
arXivHTMLPDF

Abstract

Monte Carlo simulations in conjunction with finite-size scaling analysis are used to investigate the $(H,T)$-phase diagram in uniaxial anisotropic high-${T}_{c}$ superconductors, both in zero magnetic field $(B=0)$ and in intermediate magnetic fields $(0\ensuremath{\ll}B\ensuremath{\ll}{B}_{c2})$ for various mass anisotropies. The model we consider is the uniformly frustrated anisotropic Villain model, which is dual to the lattice London model with an infinite London penetration length. The quantities we consider are various helicity moduli, the structure function, the specific heat, and the distribution of closed non-field-induced vortex loops as a function of the loop size. In zero magnetic field, and for all anisotropies considered, we find one single second-order phase transition, mediated by an Onsager vortex-loop unbinding transition, or blowout. This is the superconductor--normal-metal transition. A comparison with numerical simulations and a critical scaling analysis of the zero-field loop transition yields the same exponent of the loop-distribution function at the critical point. In the intermediate magnetic-field regime, we find two anomalies in the specific heat. The first anomaly at a temperature ${T}_{m}$ is associated with the melting transition of the flux-line lattice. The Lindemann ratio at the melting is given by ${c}_{L}\ensuremath{\approx}0.24.$ The second anomaly at a temperature ${T}_{z}$ is one where phase coherence in the BCS order parameter across the sample along the field direction is destroyed. We argue that ${T}_{m}{=T}_{z}$ in the thermodynamic and continuum limit. Hence, there is no regime where the flux-line lattice melts into a disentangled flux-line liquid. The loss of phase coherence parallel to the magnetic field in the sample is argued to be due to the proliferation of closed non-field-induced vortex loops on the scale of the magnetic length in the problem, resulting in flux-line cutting and recombination. In the flux-line liquid phase, therefore, flux lines appear no longer to be well-defined entities. Above the melting temperature, the system always exhibits an incoherent vortex-liquid phase characterized by lack of phase coherence in the BCS order parameter parallel to the magnetic field. For increasing anisotropy, we resolve a \ensuremath{\delta}-function peak in the specific heat. A finite-size scaling analysis of the \ensuremath{\delta}-function peak specific-heat anomaly at the melting transition is used to extract the discontinuity of the entropy at the melting transition. This entropy discontinuity is found to increase rapidly with mass anisotropy, at least for not too layered compounds.

DOI
10.1103/physrevb.57.3123

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Monte Carlo simulations in conjunction with finite-size scaling analysis are used to investigate the (H,T)(H,T)(H,T)-phase diagram in uniaxial anisotropic high-Tc{T}_{c}Tc​ superconductors, both in zero magnetic field (B=0)(B=0)(B=0) and in intermediate magnetic fields (0\ensuremath≪B\ensuremath≪Bc2)(0\ensuremath{\ll}B\ensuremath{\ll}{B}_{c2})(0\ensuremath≪B\ensuremath≪Bc2​) for various mass anisotropies. The model we consider is the uniformly frustrated anisotropic Villain model, which is dual to the lattice London model with an infinite London penetration length. The quantities we consider are various helicity moduli, the structure function, the specific heat, and the distribution of closed non-field-induced vortex loops as a function of the loop size. In zero magnetic field, and for all anisotropies considered, we find one single second-order phase transition, mediated by an Onsager vortex-loop unbinding transition, or blowout. This is the superconductor--normal-metal transition. A comparison with numerical simulations and a critical scaling analysis of the zero-field loop transition yields the same exponent of the loop-distribution function at the critical point. In the intermediate magnetic-field regime, we find two anomalies in the specific heat. The first anomaly at a temperature Tm{T}_{m}Tm​ is associated with the melting transition of the flux-line lattice. The Lindemann ratio at the melting is given by cL\ensuremath≈0.24.{c}_{L}\ensuremath{\approx}0.24.cL​\ensuremath≈0.24. The second anomaly at a temperature Tz{T}_{z}Tz​ is one where phase coherence in the BCS order parameter across the sample along the field direction is destroyed. We argue that Tm=Tz{T}_{m}{=T}_{z}Tm​=Tz​ in the thermodynamic and continuum limit. Hence, there is no regime where the flux-line lattice melts into a disentangled flux-line liquid. The loss of phase coherence parallel to the magnetic field in the sample is argued to be due to the proliferation of closed non-field-induced vortex loops on the scale of the magnetic length in the problem, resulting in flux-line cutting and recombination. In the flux-line liquid phase, therefore, flux lines appear no longer to be well-defined entities. Above the melting temperature, the system always exhibits an incoherent vortex-liquid phase characterized by lack of phase coherence in the BCS order parameter parallel to the magnetic field. For increasing anisotropy, we resolve a \ensuremath{\delta}-function peak in the specific heat. A finite-size scaling analysis of the \ensuremath{\delta}-function peak specific-heat anomaly at the melting transition is used to extract the discontinuity of the entropy at the melting transition. This entropy discontinuity is found to increase rapidly with mass anisotropy, at least for not too layered compounds.
We study the effect of critical fluctuations on the (B,T)(B,T)(B,T) phase diagram in extreme type-II superconductors in zero and finite magnetic field. In zero magnetic field the critical fluctuations are transverse phase fluctuations of the complex scalar Ginzburg-Landau order parameter, which when excited thermally will induce topological line defects in the form of closed vortex loops into the system. The distribution function D(p)D(p)D(p) of vortex loops of perimeter p changes from an exponential function $D(p)\ensuremath{\sim}{p}^{\ensuremath{-}\ensuremath{\alpha}}\mathrm{exp}[\ensuremath{-}\ensuremath{\varepsilon}{(T)p/k}_{B}T]$ to a power law distribution $D(p)\ensuremath{\sim}{p}^{\ensuremath{-}\ensuremath{\alpha}}$ at the zero-field critical temperature T=Tc.{T=T}_{c}.T=Tc​. We find that the long-wavelength vortex-line tension vanishes as $\ensuremath{\varepsilon}(T)\ensuremath{\sim}|T\ensuremath{-}{T}_{c}{|}^{\ensuremath{\gamma}};\ensuremath{\gamma}\ensuremath{\approx}1.45,$ as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c}.$ At T=Tc,{T=T}_{c},T=Tc​, an extreme type-II superconductor suffers an unbinding of large vortex loops of order the system size. When this happens, the connectivity of the thermally excited vortex tangle of the system changes abruptly. The loss of phase stiffness in the Ginzburg-Landau order parameter, the anomaly in specific heat, the loss of vortex-line tension, and the change in the connectivity of the vortex tangle are all found at the same temperature, the critical temperature of the superconductor. At zero magnetic field, unbinding of vortex loops of order the system size can be phrased in terms of a global U(1)\mathrm{U}(1)U(1)-symmetry breaking involving a local complex disorder field which is dual to the order parameter of the usual Ginzburg-Landau theory. There is one parameter in the theory that controls the width of the critical region, and for the parameters we have used, we show that a vortex-loop unbinding gives a correct picture of the zero-field transition even in the presence of amplitude fluctuations. A key result is the extraction of the anomalous scaling dimension of the dual field directly from the statistics of the vortex-loop excitations of the Ginzburg-Landau theory in the phase-only approximation. A scaling analysis of the vortex lattice melting line is carried out, yielding two different scaling regimes, namely, a high-field scaling regime and a distinct low-field three-dimensional XY critical scaling regime. We also find indications of an abrupt change in the connectivity of the vortex tangle in the vortex liquid along a line TL(B),{T}_{L}(B),TL​(B), which at low enough fields appears to coincide with the vortex line lattice melting transition line within the resolution of our numerical calculations. We study the temperature at which this phenomenon takes place as a function of system size and shape. Our results show that this temperature decreases and appears to saturate with increasing system size, and is insensitive to aspect ratios of the systems on which the simulations are performed, for large enough systems.
Phase transitions in a number of models related to hightemperature superconductors are investigated, using scalingmethods and Monte Carlo simulations. This thesis considers twomain topics. The first topic is phase transitions, phase diagrams, andvortex motion in high temperature superconductors at finitetemperature, subject to magnetic fields and disorder. We studya vortex glass model at finite temperature, with stronguncorrelated vortex pinning and a magnetic field. We find thatthe vortex glass exists at finite temperature and calculate thecritical exponents of the transition. We also investigate hightemperature superconductors with columnar disorder in zero andapplied magnetic fields. Some of these studies are alsorelevant for the superfluid to Mott insulator transition ofbosons in two dimensions. We find that the unscreened Boseglass transition belongs to a new universality class. Wecalculate the critical exponents of the superconductingtransition with columnar defects in zero applied magneticfield. The transverse Meissner transition is studied, and wefind an exotic universality class with a correlation volumethat is infinitely anisotropic in all directions. The second topic is confinement-deconfinement transitions incompact Abelian Higgs models. We develop a new order parameter,related to a large Wilson loop for fractionalized charges, anduse it to study the concept of topological order. Thesetransitions may be relevant for strongly correlated electronsin two dimensions.
We investigate the effect of random columnar disorder on the superconducting phase transition of a type-II superconductor in zero applied magnetic field using numerical simulations of three dimensional XYXYXY and vortex loop models. We consider both an unscreened model, in which the bare magnetic penetration length is approximated as infinite, and a strongly screened model, in which the magnetic penetration length is of order the vortex core radius. We consider both equilibrium and dynamic critical exponents. We show that, as in the disorder free case, the equilibrium transitions of the unscreened and strongly screened models lie in the same universality class, however scaling is now anisotropic. We find for the correlation length exponent $\ensuremath{\nu}=1.2\ifmmode\pm\else\textpm\fi{}0.1$, and for the anisotropy exponent $\ensuremath{\zeta}=1.3\ifmmode\pm\else\textpm\fi{}0.1$. We find different dynamic critical exponents for the unscreened and strongly screened models.
Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences.
Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences.
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