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arXiv:cond-mat/0109260 · Physical review. B, Condensed matter

Order of the metal-to-superconductor transition

S. Mo, J. Hove, Asle Sudbø

Published Jan 31, 2002• 85 citations
arXivHTMLPDF

Abstract

We present results from large-scale Monte Carlo simulations on the full Ginzburg-Landau (GL) model, including fluctuations in the amplitude and the phase of the matter field, as well as fluctuations of the noncompact gauge field of the theory. From this we obtain a precise critical value of the GL parameter ${\ensuremath{\kappa}}_{\mathrm{tri}}$ separating a first-order metal-to-superconductor transition from a second-order one, ${\ensuremath{\kappa}}_{\mathrm{tri}}=(0.76\ifmmode\pm\else\textpm\fi{}0.04)/\sqrt{2}.$ This agrees surprisingly well with earlier analytical results based on a disorder theory of the superconductor to metal transition, where the value ${\ensuremath{\kappa}}_{\mathrm{tri}}=0.798/\sqrt{2}$ was obtained. To achieve this, we have done careful infinite volume and continuum limit extrapolations. In addition we offer an interpretation of ${\ensuremath{\kappa}}_{\mathrm{tri}},$ namely, that it is also the value separating type-I and type-II behavior.

DOI
10.1103/physrevb.65.104501

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We present a finite temperature Monte Carlo study of the $\mathrm{XY}$ model in the vortex representation and study its dynamical critical behavior in two limits. The first neglects magnetic-field fluctuations, corresponding to the absence of screening, which should be a good approximation in high-${T}_{c}$ superconductors $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ except extremely close to the critical point. Here, from finite-size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be $z\ensuremath{\approx}1.5$. The second limit includes magnetic-field fluctuations in the strong screening limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}0)$ corresponding to the true asymptotic inverted $\mathrm{XY}$ critical regime, where we find the unexpectedly large value $z\ensuremath{\approx}2.7.$ We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin-wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.

arXiv:cond-mat/9711236•Physical review. B, Condensed matter•Aug 1, 1998•41 citations
We present results from large-scale Monte Carlo simulations on the full Ginzburg-Landau (GL) model, including fluctuations in the amplitude and the phase of the matter field, as well as fluctuations of the noncompact gauge field of the theory. From this we obtain a precise critical value of the GL parameter \ensuremathκtri{\ensuremath{\kappa}}_{\mathrm{tri}}\ensuremathκtri​ separating a first-order metal-to-superconductor transition from a second-order one, \ensuremathκtri=(0.76\ifmmode±\else\textpm\fi0.04)/2.{\ensuremath{\kappa}}_{\mathrm{tri}}=(0.76\ifmmode\pm\else\textpm\fi{}0.04)/\sqrt{2}.\ensuremathκtri​=(0.76\ifmmode±\else\textpm\fi0.04)/2​. This agrees surprisingly well with earlier analytical results based on a disorder theory of the superconductor to metal transition, where the value \ensuremathκtri=0.798/2{\ensuremath{\kappa}}_{\mathrm{tri}}=0.798/\sqrt{2}\ensuremathκtri​=0.798/2​ was obtained. To achieve this, we have done careful infinite volume and continuum limit extrapolations. In addition we offer an interpretation of \ensuremathκtri,{\ensuremath{\kappa}}_{\mathrm{tri}},\ensuremathκtri​, namely, that it is also the value separating type-I and type-II behavior.
The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics, the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004)] is used. Assuming relaxational dynamics for both quantities, the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the melectric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the timescales of the order parameter and the gauge field are different.
The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004)] is used. Assuming relaxational dynamics for both quantities the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the measurable electric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the time scales of the order parameter and the gauge field are different.
In this paper we study the Ginzburg-Landau (GL) equation for Fermi liquid superconductors with strong Landau interactions F0F_0F0​ and F1F_1F1​. We show that Landau interactions renormalize two parameters entering the GL equation leading to renormalization of superfluid density and separation of length and energy scales for amplitude and phase fluctuations. The separation of energy/length scales for amplitude and phase fluctuations in term leads to unconventional (2D) KT transition and vortex liquid phase. Application of the GL equation to describe underdoped high-TcT_cTc​ cuprates is being discussed.
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.
For High-Tc superconductors the fluctuation regime is much wider than conventional superconductors due to the short coherence length and high transition temperature. AC measurements can probe the conductivity at a wide range of frequencies, and therefore provide a test of the scaling properties predicted from theory. The measured critical exponents and width of the fluctuation peak are sample dependent, which suggests that the sample inhomogeneities may play an important role in the critical region. In this thesis we study the effects of disorder on the fluctuation conductivity in the critical regime of zero-field normal-superconducting transition by the time-dependent Ginzburg-Landau theory. We set up a discretized model of the superconductor and calculate the two-dimensional and three-dimensional scaling function without disorder above Tc. The result of the discretized model deviates slightly from previous theoretical studies of the continuous model, which can be explained by a finite short wavelength cutoff in Ginzburg-Landau theory. Our results agree well with other theoretical investigations on cutoff effects from an analytical approach. Disorder in a superconductor is modeled by a distribution of Tc's at the lattice sites. We add random disorder to a two-dimensional lattice and calculate the scaling functions averaged over 1000 disorder configurations. When disorder is weak, the scaling functions are increased when T is close Tc . At strong disorder anomalous behavior may occur at the region close to Tc.
We present a finite temperature Monte Carlo study of the XY\mathrm{XY}XY model in the vortex representation and study its dynamical critical behavior in two limits. The first neglects magnetic-field fluctuations, corresponding to the absence of screening, which should be a good approximation in high-Tc{T}_{c}Tc​ superconductors $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ except extremely close to the critical point. Here, from finite-size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be $z\ensuremath{\approx}1.5$. The second limit includes magnetic-field fluctuations in the strong screening limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}0)$ corresponding to the true asymptotic inverted XY\mathrm{XY}XY critical regime, where we find the unexpectedly large value $z\ensuremath{\approx}2.7.$ We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin-wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.